Passive Location Resource Scheduling Based on an Improved ... - MDPI

sensors Article

Passive Location Resource Scheduling Based on an Improved Genetic Algorithm Jianjun Jiang *, Jing Zhang, Lijia Zhang, Xiaomin Ran and Yanqun Tang National Digital Switching System Engineering and Technological Research Center (NDSC), Zhengzhou 450000, China; [email protected] (J.Z.); [email protected] (L.Z.); [email protected] (X.R.); [email protected] (Y.T.) * Correspondence: [email protected]; Tel.: +86-150-3823-2583





Received: 5 May 2018; Accepted: 26 June 2018; Published: 29 June 2018

Abstract: With the development of science and technology, modern communication scenarios have put forward higher requirements for passive location technology. However, current location systems still use manual scheduling methods and cannot meet the current mission-intensive and widely-distributed scenarios, resulting in inefficient task completion. To address this issue, this paper proposes a method called multi-objective, multi-constraint and improved genetic algorithm-based scheduling (MMIGAS), contributing a centralized combinatorial optimization model with multiple objectives and multiple constraints and conceiving an improved genetic algorithm. First, we establish a basic mathematical framework based on the structure of a passive location system. Furthermore, to balance performance with respect to multiple measures and avoid low efficiency, we propose a multi-objective optimal function including location accuracy, completion rate and resource utilization. Moreover, to enhance its practicability, we formulate multiple constraints for frequency, resource capability and task cooperation. For model solving, we propose an improved genetic algorithm with better convergence speed and global optimization ability, by introducing constraint-proof initialization, a penalty function and a modified genetic operator. Simulations indicate the good astringency, steady time complexity and satisfactory location accuracy of MMIGAS. Moreover, compared with manual scheduling, MMIGAS can improve the efficiency while maintaining high location precision. Keywords: passive location; NP-hard; scheduling; genetic algorithm; angle-of-arrival

1. Introduction Passive location plays a significant role in modern communication scenarios for its satisfactory concealment based on the passive reception pattern. In addition, with the characteristics of long distance measurement and high robustness [1], passive location techniques are of significance in both civil and military areas. The major passive location technique is angle-of-arrival (AOA) [2], which obtains the target location by combining the measured angles of each station and whose performance is highly affected by scheduling plans [3,4]. Resource scheduling is implemented to establish an optimized task-to-resource dispatch with the purpose of maximizing the total performance (such as location accuracy and task completion rate) and avoiding the conflicts effectively. However, despite its importance, little attention is paid to the scheduling mechanism. In recent years, studies in passive location have mainly focused on location algorithms [5,6], accuracy analysis [7], filters and tracking [8,9]. There is little information available in the literature about passive location resource scheduling. The scheduling method mostly used today, which we call traditional manual scheduling, is unable to handle the increasing number of tasks and overloaded resources, thus leading to the following serious problems.

Sensors 2018, 18, 2093; doi:10.3390/s18072093

www.mdpi.com/journal/sensors

Sensors 2018, 18, 2093

• •

2 of 24

Low efficiency. Because manually allocated broadcast resources cannot achieve parallel processing very well, when task conflicts occur, some signals may be lost, reducing efficiency. Unstable location accuracy. Because location accuracy is highly relevant to the stations-to-tasks schedule plans, it is possible to encounter low location accuracy due to mistakes caused by human subjectivity.

To address these problems and achieve high efficiency and location accuracy, new intelligent automated scheduling methods urgently need to be studied. Xiu et al. [10] analyzed constellations in bearing-only location systems and proposed an optimal geometric relationship to improve location precision and minimize circular probable error, providing an important reference for station scheduling. Prasan et al. [11] proposed the pre-scheduling-based k-coverage group scheduling and self-organized k-coverage scheduling algorithms to address problems in existing sleep-scheduling algorithms. Hu et al. [12] established a centralized framework for sensor scheduling in wireless sensor networks and modeled the problem using integer linear programming. In [13], the proposed algorithms, which deal directly with minimizing the mean squared error, are based on the convex relaxation approach to address the binary optimization scheduling problems that are formulated in sensor network scenarios. Xu et al. [3] analyzed the Cramer-Rao lower bound of AOA and discussed the measurement of location accuracy based on the information matrix. Wei et al. [9] proposed a modified binary particle swarm optimization (BPSO) algorithm motivated by the information matrix in the wireless sensor network nodes scheduling problem for tracking. Sun et al. [14] were inspired by Xu et al. and Wei et al. and proposed a BPSO algorithm motivated by geometric dilution of precision deduced from the information matrix for station scheduling. However, Sun et al. did not solve the problem thoroughly because they neglected to consider complex constraints and efficiency. Furthermore, previous studies seldom discuss scheduling strategies for scenes with multiple concurrent tasks. Therefore, to solve passive location station scheduling more specifically, the scheduling method must satisfy these conditions. (1) The optimal objective must involve not only accuracy but also other important factors, especially efficiency. (2) Complex constraints are formulated. (3) The method can support multiple concurrent task scenarios. Inspired by the factors mentioned above, we propose a new method called multi-object, multi-constraint and improved genetic algorithm-based Scheduling (MMIGAS), enhancing the efficiency and practicability for passive location resource scheduling. Our first contribution is to construct a mathematical primary centralized optimization model of passive location resource scheduling according to a practical system framework. Second, we introduce position dilution of precision (PDOP) to measure the location accuracy and define other objective values, such as completion rate, resource utilization and task priority. These values are combined into a multi-objective function to ensure that our schedule can balance performance with respect to multiple aspects, specially efficiency. Third, based on several important assumptions, we formulate complex constraints in three categories: frequency, station capability and task cooperation requirement, thus improving practicability. Moreover, since the model is an NP-hard problem, we conceive an improved genetic algorithm (IGA) by introducing constraint-proof initialization (CI), penalty function (PF) and modified genetic operator (MGO), which can achieve a better convergence rate and global optimization ability. Simulations show that MMIGAS has a satisfactory astringency and stability of time complexity. Additionally, the method is appropriate for multiple concurrent targets. Compared with manual scheduling, MMIGAS can clearly improve the efficiency while maintaining high location accuracy. The remainder of this paper is organized as follows. Section 2 introduces the primary framework of the location system, clarifies some critical assumptions and establishes a basic mathematical optimization model. In Section 3, we demonstrate our design for multiple objectives and multiple constraints. In Section 4, we illustrate the three steps of the IGA: CI, PF and MGO. Section 5 presents the experimental results and analyses the performance of proposed method. Section 6 concludes the paper.

Sensors 2018, 18, 2093

3 of 24

Sensors 2018, 18, x

3 of 24

2. Problem Formulation Sensors 2018, 18, x

3 of 24

2. Problem Formulation

The passive location channel is heavily crowded due to the narrowband and dense signals. 2. Problem Formulation The passive location channel is heavily crowded due to the narrowband and dense signals. The The time-varying fading and silence zones also cause many problems, making the passive location time-varying fading and channel silence zones alsocrowded cause many makingand thedense passive location The passive location heavily due toproblems, the narrowband signals. The problem a difficult task and topic of isinterest [15–20]. To increase the location accuracy and flexibility, problem a difficult task andsilence topic ofzones interest [15–20]. increase the location accuracy and flexibility, time-varying fading and also cause To many problems, making the passive location a location system generally uses a cooperative location approach [21], which consists ofsteps the steps of aproblem location cooperative location [21], which consists of the of asystem difficultgenerally task and uses topicaof interest [15–20]. To approach increase the location accuracy and flexibility, task arrival, command downloading, data uploading and position output, as shown in Figure 1. task arrival, command downloading, data uploading and position[21], output, as shown inof Figure 1. of a location system generally uses a cooperative location approach which consists the steps task arrival, command downloading, data uploading and position output, as shown in Figure 1.

Tasks Arrival Tasks Arrival Command center Command center

Stations Stations

Command center Command center

Assigning stations for tasks Assigning stations for tasks

... ... Calculates the positionsthe Calculates positions

Figure 1. Procedure for passive location in a practical system.

Figure 1. Procedure for passive location in a practical system. Figure 1. Procedure for passive location in a practical system.

Moreover, the system has a centralized architecture consisting of the command center and Moreover, the system has a centralized architecture consisting of the command center and direction-finding stations, shown in Figure architecture 2. Therefore,consisting the essence scheduling a Moreover, the systemashas a centralized of of thestation command center is and direction-finding stations, as shown in Figure 2. Therefore, the essence of station scheduling centralized tasks-to-resources allocation, which guides us to establish a combination optimization direction-finding stations, as shown in Figure 2. Therefore, the essence of station scheduling is a is a model. centralized tasks-to-resources allocation, which guides us to establish a combination centralized tasks-to-resources allocation, which guides us to establish a combination optimization

optimization model. model.

1.Tasks arrival 1.Tasks arrival 4. Result of 4.location Result of location

2. Scheduling Project 2. Scheduling Command center Command center

Project

3. Data of direction-finding 3. Data of direction-finding

Station1 Station1 Station2 Station2 Station3 Station3 Station4 Station4 Station5 Station5

Figure 2. Architecture of a passive location system. Figure Architecture of of a passive Figure 2. 2.Architecture passivelocation locationsystem. system.

2.1. Assumptions and Scenario Declaration Because the passive location scenario is extremely complicated due to complex channels [22], we make some critical assumptions to simplify this problem.

Sensors 2018, 18, 2093

•

•

•

•

• •

•

4 of 24

We ignore the silence zone. This assumption is made to reduce the space constraint and make the model more concise. According to related studies, potential silence zones can be fully avoided if appropriate locations for building stations are chosen [10]. Signals from all directions have the same gain in the receiving antennas. This assumption is made to ensure the strength of the signal directly reflects the distance between the station and the target, which simplifies the discussion about geographical relationships. This can be achieved by using an omnidirectional antenna. Targets are static or moving slowly enough that their locations do not noticeably change over a short time. This assumption avoids a heavy time delay or even invalidation of the scheduling due to drastic changes in geographical relationships. Prior knowledge about targets is available. This assumption ensures that the approximate potential area of the target is known, which is an essential condition of using the proposed scheduling method. In addition, the scenario discussed in this paper is specified by the following declarations. We only discuss the scheduling activity in one slot. We define one slot as the duration of a scheduling and location process. It is the minimum interval needed to implement one complete activity in the passive location system. Therefore, any length of time can be considered to be a sum of several slots. We only discuss narrow-band stations because wide-band stations can be considered the sum of several different narrow-band stations.

2.2. Notation Stations and signals are considered to be resources and tasks, respectively. And to demonstrate their allocation relationship, we structure a scheduling matrix as follows. 1.

2.

Task: We denote tasks as T = {t1 , t2 , . . . , ti , . . . t Nm }, where Nm is the total number of tasks. We use four attributions to describe a task: frequency, location, collaboration and priority,  ∀ti ∈ T, ti = Zˆ i , λˆ i , Bˆ i , Hˆ i , where i denotes the task sequence number. h i = fˆmin (i ), fˆmax (i ) gives the frequency range of the task signal, where fˆmin (i ) ∈ R, fˆmax (i ) ∈ R and fˆmin (i ) ≤ fˆmax (i ). • λˆ i = ( xˆi , yˆi ) denotes the two-dimensional coordinates of task i, where xˆi ∈ R, yˆi ∈ R. • Bˆ i gives the cooperative station number requirement for task location, where Bˆ i ∈ Z + . • Hˆ i ∈ {1, . . . , 6}. We define the priority of tasks as an integer ranging from 1 to 6. The task is more important if its Hˆ i is higher.  Resources: We denote Ns direction-finding stations as K = k1 , k2 , . . . , k j , . . . , k Ns . We use three attributions to describe one station (resource): frequency, location and capability,  ∀k j ∈ K, k j = Zj , λ j , Cj . Here, j denotes the station sequence number.

•

Zˆ i

•

Zj = [ f min ( j), f max ( j)] is the frequency range at which the station implements direction-finding, where f min ( j) ∈ R, f max ( j) ∈ R and f min ( j) ≤ f max ( j).
λ j = x j , y j denotes the two-dimensional coordinates of station j, x j ∈ R, y j ∈ R.

• • 3.

Cj is the maximum number of tasks the station can process synchronously, implying its working capacity, where Cj ∈ Z + .

Scheduling matrix: We design a binary solution matrix with Ns columns and Nm rows as   A = aij N × N , where aij indicates the relation between station j and task i. Here aij = 1 means m s that station j is assigned to process task i, while aij = 0 means j is not assigned to process i.

Sensors 2018, 18, 2093

5 of 24

2.3. Optimization Model Based on the analysis mentioned above, we formulate the passive location resource scheduling problem as a combination optimization problem. Denote F as the objective function, hi as the equality constraints and gi as the inequality constraints. Then, the mathematical model is:     

s.t.

max{ F {A}} hi {A} = 0, i = 1, 2, 3 . . . gi {A} ≥ 0, j = 1, 2, 3 . . .

(1)

3. Multi-Objective and Multi-Constraint Properties 3.1. Objective Function To balance different aspects of the performance and obtain a comprehensive solution, we design a multi-objective function using a linear weighting as follows: F =

∑ ϕq ωq

(2)

q

Here ϕq is the objective and ωq is the weight. The definition and calculation of objectives and weights is illustrated in the following part of this section. 3.1.1. Location Accuracy Because the fundamental requirement of passive location resource scheduling is to obtain a scheduling plan with a satisfactory location accuracy, the objective function must involve the location accuracy. We introduce PDOP as the measure of location accuracy. PDOP quantifies the geographical relationships between receivers and targets, which can directly impact the performance of the location activity. Smaller PDOP means better performance and on the contrary, larger PDOP means worse performance. Based on [14,23], PDOP is calculated as follows: (

M1

∑

j −1

pi =

det( Li ) =

∑

{u,v} ∈ M2

)1

2

1  rj 2

1 σφ ( j)

2

(3)

1

det( Li ) 2



σφ (u)

1 2 

σφ (v)

2

sin2 (φu − φv ) ru 2 rv 2

(4)

Here, pi is the PDOP value of task i, Li is the Fisher information matrix, r j is the distance from station j to the target, φj is the direction angle, σφ ( j) is the measurement error of φj , M1 denotes the number of stations that participate in the task and M2 denotes the set of every match of two stations in M1 . For example, when M1 = {1, 2, 3}, then M2 = {{1, 2}, {2, 3}, {1, 3}}. To make the objective factor positive with respect to location accuracy, we formulate ϕ p as the reciprocal of the sum of PDOP as: 1 ϕp = (5) ∑ pi i

Additionally, we set ω p = 1 and the objective function is: F = ϕ p + ∑ ϕ q ωq q

(6)

Sensors 2018, 18, 2093

6 of 24

3.1.2. Completion Rate To avoid the task missing problem and low efficiency, we define an objective factor named completion rate ϕ1 which is equal to the ratio of completed tasks n to the total number of tasks Nm . ϕ1 =

n Nm

(7)

Weight ωq is calculated as the product of scaling factor ηq and concern level cq . ω q = ηq c q

(8)

Here, ηq transforms objective factor ωq to the same order of magnitude of ϕ p , which avoid poor performance of F caused by the wrong size of ϕ p . It helps F to reflect various factors evenly. Objective factor ηi is calculated as follows: ηi = 10

log10 b

ϕp ϕi

c

(9)

Here b x c means the maximum integer value less than x and cq indicates a user’s concern about the objective factor, which is shown as Equation (10).   cq ∈ [0, 1] s.t. ∑ cq = 1 (10)  q

3.1.3. Resource Utilization To prevent resource waste, we introduce the resource utilization in Equation (11), which is the ratio of occupied resources m to the total number of resources Ns . m Ns

ϕ2 =

(11)

Analogously, weight ω2 is calculated by (8)–(10). 3.1.4. Task Priority Inspired by priority scheduling [24], we design objective factor ϕ3 based on task priority, which makes the model prefer the task with the highest priority, shown in Equation (12). ϕ3 =

∑ Hˆ i

(12)

i

Here, ϕ3 equals the sum of priorities of completed tasks. As above, weight ω3 is analogously calculated by (8)–(10). In conclusion, the formulation of multi-objective function F is as follows: 3

F = ϕp +

∑

q −1

3

ϕq ωq = ϕ p +

∑ ϕ q ηq c q

(13)

q −1

3.2. Constraints Due to the complexity of wireless communication channels [25], the resource scheduling problem, involving many constraints on time, space, frequency and other factors, need to be analyzed and formulated to ensure our mathematical model is reasonable. Based on our assumptions, we ignore the constraints in the time and space domains and simplify the complex conditions into three categories: frequency, station capability and task cooperation requirements.

Sensors 2018, 18, 2093

7 of 24

3.2.1. Frequency The direction-finding activity cannot be implemented when the frequency of the task is beyond the station’s range. We formulate such a constraint as follows:     aij fˆmin (i ) − f min ( j) ≥ 0   ∀ti ∈ T, ∀k j ∈ K,  aij f max ( j) − fˆmax (i ) ≥ 0

(14)

3.2.2. Station Capability For narrow-band stations, receivers are highly restricted, leading to the limitation of the number of tasks that can be implemented by one station synchronously. NS

∀ j ∈ [1, Ns ], ∑ aij ≤ Cj

(15)

i −1

3.2.3. Task Cooperation Requirement Because different tasks may have different cooperation requirements, a sufficient number of stations should be allocated to the task. Ns

∀i ∈ [1, Nt ], ∑ aij ≥ Bˆ i

(16)

j −1

4. IGA Due to the strong relevant effects among tasks and resources, the proposed model becomes an NP-hard problem [26], for which a genetic algorithm (GA) is suitable for searching for a solution because of its adaptive global optimization ability. Originally, a GA was conceived based on the simulation of heredity and evolution in the natural environment [27]. In the algorithm initialization, various initial feasible solutions are randomly generated as the original genetic group. During the iterations, genetic operators construct the offspring based on the parental genetic group, where the genes with highest environmental fitness can survive and multiply, thus conveying the dominated characteristics into the final generation. Eventually, the algorithm obtains an optimal solution. Compared with other algorithms, GA has low complexity and high practicability [28], thus being appropriate for the passive location resource scheduling problem. However, the normal GA has the disadvantages of a low convergence rate and local optimization dilemma. To make it more suitable for our application scenario, we make several improvements by implementing CI, PF and MGO, helping the algorithm to obtain a satisfying solution quickly. The objective function is utilized as the fitness function, while the decision matrix is used for gene construction. The process of the algorithm is shown in Figure 3 and details in Algorithm 1.

Sensors 2018, 18, x

8 of 24

However, the normal GA has the disadvantages of a low convergence rate and local optimization dilemma. To make it more suitable for our application scenario, we make several improvements by implementing CI, PF and MGO, helping the algorithm to obtain a satisfying solution quickly. The Sensorsobjective 2018, 18, 2093 function is utilized as the fitness function, while the decision matrix is used for gene8 of 24 construction. The process of the algorithm is shown in Figure 3 and details in Algorithm 1. Start

Constraint-proof initialization

YES

Terminate?

YES

Constrain satisfying?

NO

NO

Calculate the fitness with the penalty function

solution

Select next generation

Next generation

Crossover between chromosomes and individuals And mutation

Figure 3. Procedure for the Improved Genetic Algorithm (IGA).

Figure 3. Procedure for the Improved Genetic Algorithm (IGA). Algorithm 1. IGA. Algorithm 1. IGA. setting and constraint-proof initialization. 1. Parameters 1. 2. 3. 4. 5. 6.

2. Terminate? Yes→Step 6, No→Step3. Parameters setting and constraint-proof initialization. 3. Calculate the fitness with the PF and select next generation. Terminate? Yes→Step 6, No→Step3. 4. Usethe MGO to with get next generation. Calculate fitness the PF and select next generation. Use5.MGO to get next generation.Yes→step 2, No→Step 4. Constrain satisfaction? Constrain 6. Get satisfaction? the solution.Yes→step 2, No→Step 4. Get the solution. 4.1. CI

4.1. CI

Traditional GA is very sensitive to the initial values [29]. When the initial values do not meet the

constraints, the unable totocalculate the fitness thus the evolution direction is unclear, Traditional GAalgorithm is very is sensitive the initial valuesand [29]. When the initial values do not meet which substantially reduces the convergence rate and even leads to the non-convergence. Therefore, the constraints, the algorithm is unable to calculate the fitness and thus the evolution direction is in order to provide a specific evolution direction at the beginning and improve the astringency, we unclear, which substantially reduces the convergence rate and even leads to the non-convergence. implement the CI by building a taboo-table which marks out the element unable to satisfy the Therefore, in order to provide a specific evolution direction at the beginning and improve the astringency, frequency constrain and coding the scheduling matrix stepwise. The process is shown in Figure 4. we implement the CI by building a matrix taboo-table which marks outofthe element unableBuild to satisfy Step ①. Generate the original according to the number tasks and stations. up a the frequency constrain and coding the scheduling matrix stepwise. The process is shown in Figure taboo-table by using Equations (14)–(16). And take away the taboo-table from the original matrix 4. to 1theGenerate Step the original matrix according to the number of tasks and stations. Build up a obtain : frequency-satisfying matrix. taboo-table by②. using Equations (14)–(16). And as take away which the taboo-table from original table matrix to Step Select one column of the matrix a vector, indicates the taskthe scheduling of the onefrequency-satisfying station. Value it randomly within the capability of the resource and then use it as a task obtain matrix. allocation vector.one column of the matrix as a vector, which indicates the task scheduling table 2 Select

: Step Step ③. RepeatitStep ② for every column in the frequency-satisfying to obtain taska task of one station. Value randomly within the capability of the resourcematrix and then usethe it as allocation vectors of all stations. allocation vector. Step ④. Combine the task allocation vectors as a decision matrix. 3 Repeat Step 2 for every column in the frequency-satisfying matrix to obtain the task Step : allocation vectors of all stations. 4 Combine the task allocation vectors as a decision matrix. Step :

SensorsSensors 2018, 2018, 18, 2093 18, x

9 of 249 of 24

Figure 4. 4.Procedure initialization (CI). Figure Procedurefor for constraint-proof constraint-proof initialization (CI).

4.2. PF 4.2. PF To enhance the the algorithm performance, originalgenetic geneticgroup group must satisfy all constraints in To enhance algorithm performance, the the original must satisfy all constraints in our model. CI guarantees the original genetic group the constraints on frequency our model. CI guarantees the original genetic group will will meetmeet the constraints on frequency andand resource resource capability. the task cooperation constraint, we introduce PF method based on Section capability. For the taskFor cooperation constraint, we introduce the PFthe method based on Section 2.2 and 2.2 and Equation (1). Equation (1). Ns

  Denote the penalty Set1, Ω . Define number of  ∈1,  Denote Ω as  the as penalty factor. factor. Set Ω > Z + .ZDefine Xi =X i ∑ aijaijas as thethe number of stations

Ns

j−1j 1

stationsfor scheduled for task . The PF isasdenoted as P : scheduled task i. The PF is idenoted P: Nm

P N m  (i B −i  X )

P = Therefore, the fitness function becomes:

Therefore, the fitness function becomes:

B X

i 1 Ω ∑

i

i

(17)

(17)

i −1

Fitness  F  P

(18)

According to (17) and (18), if one solution Fitnessdoes = not F −meet P the task cooperation requirement, its (18) P will increase exponentially, rapidly reducing its fitness and causing it to be eliminated during the iteration. Therefore, solutions that survive must satisfy task cooperationrequirement, constraint. its P According to (17) and (18), eventually if one solution does not meet thethe task cooperation will increase exponentially, rapidly reducing its fitness and causing it to be eliminated during the 4.3. MGO iteration. Therefore, solutions eventually that survive must satisfy the task cooperation constraint. The preceding section introduces the generation of the initial solution and the penalty function.

4.3. MGO Then, we will introduce the modified genetic operation of the solution which contains roulette wheel, elitism selection, crossover and mutation.

The preceding section introduces the generation of the initial solution and the penalty function. Then,4.3.1. we will introduce genetic operation of the solution which contains roulette wheel, Roulette Wheel the and modified Elitism Selection elitism selection, crossover and mutation. We introduce a combined roulette-wheel and elitism selection strategy, which can keep the randomness of offspring and prevent the loss of the best individual in the group. First, the individuals 4.3.1. Roulette Wheel and Elitism Selection with the highest fitness are directly saved to the next generation. Second, parents are selected

We introduce a combined and elitism selection strategy, which can keep the p g roulette-wheel according to probability , of individual l , which is calculated as follows: randomness of offspring and prevent the loss of the best individual in the group. First, the individuals

Sensors 2018, 18, x

10 of 24

Sensors 2018, 18, 2093

pg  l  

Fitness  l 

10 of 24

Np

 Fitness  j  with the highest fitness are directly saved to the next generation. Second, parents are selected according j 1

Sensors 2018, 18, x

to probability p g , of individual l, which is calculated as follows:

(19)

10 of 24

where N p is the population of genetic group in this algorithm and Fitness  l  is the fitness of p g (plg) l= 

individual l .

p

 j ( j) Fitness ∑Fitness

(19)

(19)

1 1 jj−

4.3.2. Crossover where N

Fitness Fitness  l(l )

N Np

is the population of genetic group in this algorithm and Fitness  l  is the fitness of

p Np is the population of genetic group in this algorithm and Fitness(l ) is the fitness of individual l. 1. where Crossover between chromosomes

individual l .

There is a probability pcc that chromosome crossover will happen for each individual. In the 4.3.2. Crossover 4.3.2. Crossover

case,1. two chromosomes will be randomly selected and exchange their gene in the same location. Crossover between chromosomes 1. Crossover between chromosomes Parameters pcc is set according to human experience, normally ranging from 0.3 to 0.7. Figure 5 There is a probability pcc pthatthat chromosome willhappen happenforfor each individual. chromosomecrossover crossover will each individual. In theIn the cc case, case, two two chromosomes will be randomly selected and exchange their gene in the same location. chromosomes will be randomly selected and exchange their gene in the same location. Parameters pcc is pset according to human experience, normally ranging from 0.30.3 to to 0.7.0.7. Figure 5 shows Parameters is set according to human experience, normally ranging from Figure 5 cc the crossover shows theprocess. crossover process.

There is a probability shows the crossover process.

Figure 5. Individual crossover. Figure5.5. Individual Individual crossover. Figure crossover.

2.

Crossover between individuals 2. Crossover between individuals

2.

Crossover between individuals

In theway, same we way,need we need to considerthe the concurrent concurrent processing of multiple tasks. So, there So, is a there is a In the same to consider processing of multiple tasks. In thep same needcrossover tocrossover consider the concurrent processing ofismultiple tasks. So,one there is one probability for we individual among the entire group, which the is operation that pway, ci probability for individual among the entire group, which the operation that ci

a probability for individual group, which is the operation that one individualpexchanges part of itscrossover genes withamong another.the Theentire location at which the gene exchange happens

ci individual exchanges part of its genes with another. The location at which the gene exchange happens is selected randomly. is set by experience as well,atnormally ranging 0.3 to happens 0.7. individual exchanges partProbability of its genespciwith another. The location which the gene from exchange is selected randomly. Probability is set by experience as well, normally ranging from 0.3 to 0.7. p ci is selected randomly. Probability p is set by experience as well, normally ranging from 0.3 to 0.7. Figure 6 shows the process of two concurrent tasks. ci

Figure 6 shows thethe process tasks. Figure 6 shows processofoftwo twoconcurrent concurrent tasks.

Figure 6. Chromosome crossover.

3.

Mutation

In every individual, there is a probability pm of mutation, which is when one or more genes Figure crossover. Figure 6. 6. Chromosome Chromosome crossover. inside this individual change themselves randomly. Parameter pm usually ranges from 0.01 to 0.1.

3.

An example of mutation is shown in Figure 7. Mutation

In every individual, there is a probability pm of mutation, which is when one or more genes inside this individual change themselves randomly. Parameter pm usually ranges from 0.01 to 0.1. An example of mutation is shown in Figure 7.

Sensors 2018, 18, 2093

3.

11 of 24

Mutation

In every individual, there is a probability pm of mutation, which is when one or more genes inside this individual change themselves randomly. Parameter pm usually ranges from 0.01 to 0.1. An example of 18, mutation is shown in Figure 7. Sensors 2018, x 11 of 24

Figure7.7.Mutation. Mutation. Figure

5. Experiment Results Discussion 5. Experiment Results andand Discussion 5.1. Simulation Setting 5.1. Simulation Setting We simulate a passive location scenario based on AOA. The exact location, frequency and

We simulate a passive location scenario based on AOA. The exact location, frequency and capability of stations are all known. Moreover, the approximate area, communication frequency, capability of and stations are allrequirement known. Moreover, approximate area, frequency, priority cooperation of tasks arethe known as well. Note that communication we only discuss the onepriority and cooperation requirement of tasks are known as well. Note that we only discuss slot and narrow-band condition. Scenario and algorithm parameters are shown in Table 1–3. First, the one-slot narrow-band Scenario and algorithm parameters shown in Tables 1–3. we and mainly consider thecondition. location accuracy and completion rate, so in thisare experiment objective c  1 c  c  0 First, function we mainly consider the location accuracy and completion rate, so in this experiment objective 1 2 3 weights are set as and . In addition, chromosome crossover probability, function weights are set as c = 1 and c = c = 0. In addition, chromosome crossover probability, individual crossover probability and 2mutation probability are set according to Section 4.3. The 3 1 individual crossover probability and mutation probability are set according to Section 4.3. The N direction 0,1 direction angle error associated with the positioning accuracy is generated according to angle error associated with the positioning accuracy is generated according to N 0, 1 Gaussian ( ) Gaussian distribution and the penalty factor is   5 . Moreover, the population number of distribution and the penalty factor is Ω = 5. Moreover, the population number of chromosomes is 10 chromosomes is 10 and the max iteration of genetic algorithm is 2000. and the max iteration of genetic algorithm is 2000. Table 1. Parameter settings for the algorithm.

Table 1. Parameter settings for the algorithm.

Chromosome Individual Mutation Penalty Crossover Crossover Population Iteration Probability Factor Chromosome Individual Penalty Probability Probability Mutation Crossover Crossover Population Iteration Probability Factor Probability Probability 5 0.8 0.8 0.1 10 1000 0.8

0.8

0.1

10

1000

Ω = 5

Objective Probability Function Objective Distribution Probability Weights Function Distribution Gaussian c  1 1 Weights N  0,1 c2  c3  0 c1 = 1 Gaussian c2 = c3 = 0 N (0, 1)

Table 2. Parameter settings for the station scenario.

Table 2. Parameter settings for the station scenario. Location Area Beginning Frequency (HZ) Band (HZ) Capacity Probability Distribution (km × km) Area Beginning Probability 50 ×Location 50 1000~5000 1~2 Uniform Distribution Band2000~3000 (HZ) Capacity (km × km) 50 × 50 Location Area (km × km) 50 × 50

Frequency (HZ)

Distribution

1000~5000 1~2scenario.Uniform Distribution Table 3. Parameter2000~3000 settings for the task Beginning Frequency Band Cooperation Table(HZ) 3. Parameter settings scenario. (HZ) for the task Requirement 1000~5000 2000~3000 2~3

Probability Distribution Uniform Distribution

Location Area Beginning Cooperation Probability Band (HZ) (km × km) Frequency (HZ) Requirement Distribution The stations and task signals were randomly distributed in a 50 km × 50 km area. The frequency 50 × 50 1000~5000 2000~3000 2~3 Uniform Distribution range of stations and tasks were decided by their beginning frequencies and bands. The capabilities are randomly varied between 1 and 2, while the cooperation requirements are randomly varied between 2 and 3. And locations stations and task signalsinare randomly generated to The stations and taskthe signals wereofrandomly distributed a 50 km × 50 km area.according The frequency uniform distribution.

range of stations and tasks were decided by their beginning frequencies and bands. The capabilities are randomly varied between 1 and 2, while the cooperation requirements are randomly varied 5.2. Experiment Results between 2 and 3. And the locations of stations and task signals are randomly generated according to We built up a scenario with 15 stations and six tasks. The solution given by the proposed uniform distribution. algorithm is shown in Figure 8 and Table 4. The result indicates that the method can work out an appropriate solution and handle the NP-hard problem effectively.

Sensors 2018, 18, 2093

12 of 24

5.2. Experiment Results We built up a scenario with 15 stations and six tasks. The solution given by the proposed algorithm is shown in Figure 8 and Table 4. The result indicates that the method can work out an appropriate solution and handle the NP-hard problem effectively. Sensors 2018, 18, x

12 of 24

Sensors 2018, 18, x

12 of 24

(a)

(b)

Figure 8. Passive location resource scheduling diagram with 15 stations and six tasks: (a) distribution Passive location resource diagram with stations and six tasks: (a) of resources and tasks; (b) thescheduling scheduling plan: dotted green line15 represents task assignment.

Figure 8. distribution of resources and tasks; (b) the scheduling plan: dotted green line represents task assignment. Table 4. Scheduling results of 15 stations and six tasks.

(a) (b)tasks. Task 1 2 results3 of 15 stations 4 5 six 6 Table 4. Scheduling and Station

1, 3, 14

2, 3, 9

5 ,6, 10

8, 12, 13

2 , 4, 11

6 , 7, 9

Figure 8. Passive location resource scheduling diagram with 15 stations and six tasks: (a) distribution Notes: the numbers of plan: task and station are shown in Figure 8.assignment. of resources and tasks; (b) dotted Task 1 the scheduling 2 3 green line4 represents task 5 6

Station we ran 1, 3,a14Monte-Carlo 2, 3, 9 experiment 5, 6, 10 by8,repeating 12, 13 2, 4, simulation 11 6, 7, 9300 times to Furthermore, this Table 4. Scheduling results of 15 stations and six tasks. examine the astringency. To better show effect the algorithm, the in 300Figure experiments were divided Notes: the numbers ofthe task andofstation are shown 8. Task 2 3 including 4 60 experiment 5 6 into five groups (No. 1~No. 5),1where each group results and each curve Stationvalue 1, 3,of14 3, 9 5In,6,each 10 experiment, 8, 12, 13 2 the , 4, location 11 6 , 7,of9the targets and the representing the average each2,group. Furthermore, we ran a Monte-Carlo experiment by repeating this simulation 300 times to examine Notes: the numbersgenerated. of task and The station are shown incurves Figure 8. location of the stations are randomly convergence are shown in Figure 9, the astringency. To better show the effect of the algorithm, the 300 experiments divided into five illustrating that the convergence values are very close to one another. This method canwere enlarge the Furthermore, we the ranalgorithm a Monte-Carlo experiment by repeating thisallsimulation 300 times to search space and help jump out of local minima. Moreover, the curves reached their groups (No. 1~No. 5), where each group including 60 experiment results and each curve representing examine the astringency. better show theshowing effect of the the 300 experiments were that divided convergence in less thanTo100 iterations, the algorithm, rapid convergence which means the the average value ofgroups each group. In each experiment, the location of the targets and the location of into five (No. 1~No. 5), where each group including 60 experiment results and each curve algorithm can finish calculation in a short time. Such a characteristic is very important for the passive representing the average value of each group. In each experiment, the location of the targets and the the stations are randomly location problem. generated. The convergence curves are shown in Figure 9, illustrating that location of the stations are randomly generated. The convergence curves are shown in Figure 9, the convergence values are very close to one another. This method can enlarge the search space and illustrating that the convergence values are very close to one another. This method can enlarge the help the algorithm jump minima. allMoreover, the curves reached theirtheir convergence in search space and out help of the local algorithm jump outMoreover, of local minima. all the curves reached convergence in less than 100 iterations, showing the rapid convergence which means that the less than 100 iterations, showing the rapid convergence which means that the algorithm can finish algorithm can finish calculation in a short time. Such a characteristic is very important for the passive calculation in a short time. Such a characteristic is very important for the passive location problem. location problem.

Figure 9. Convergence curves in the Monte-Carlo experiment.

Figure 9. Convergence curves in the Monte-Carlo experiment.

Figure 9. Convergence curves in the Monte-Carlo experiment.

Sensors 2018, 18, 2093

13 of 24

Sensors 2018, 18, x 5.3. Results and Discussion

13 of 24

5.3. Results and Discussion The experimental results show that the proposed algorithm can solve the multi-objective and multi-constraint scheduling problems. To further verifyalgorithm the performance IGA and analyze The experimental results show that the proposed can solveof thethe multi-objective and the experimental results, we analyze the performance and indicators, including the and performance multi-constraint scheduling problems. To further verify the performance of the IGA analyze theof the IGA and some experiment as time complexity and locationthe accuracy. experimental results, weindicators, analyze thesuch performance and indicators, including performance of the IGA and some experiment indicators, such as time complexity and location accuracy.

5.3.1. Performance of the IGA 5.3.1. Performance of the IGA

CI has an advantage with respect to astringency because it can provide a specific evolution has beginning an advantage respect to astringency because it can provide specific evolution direction CI at the of with the iterations. Random initialization means thearandom generation of direction at the beginning of the iterations. Random initialization means the random generation of initial solutions which directly participate in the next operation of the genetic algorithm without initial solutions which directly participate in the next operation of the genetic algorithm without checking constraints. In this experiment, in order to compare the difference between CI initialization checking constraints. In this experiment, in order to compare the difference between CI initialization and random initialization, the parameters are set the same as Table 1 except for the initialization step. and random initialization, the parameters are set the same as Table 1 except for the initialization step. And the results areare shown Andexperiment the experiment results shownininFigure Figure10. 10.

Figure 10. Fitness curves for CI and random initializations

Figure 10. Fitness curves for CI and random initializations As shown in Figure 10, the random initialization method fails to find the direction of astringency

As shown in Figure 10, the random initialization method fails to find the direction of astringency because it is difficult for random initialization to find an initial value satisfying the constraints and it because it is difficult for random initialization to find an initial value satisfying the constraints and it is also difficult to achieve a continuous reduction of the optimization goals. The CI can accumulate is also difficult to achieve a continuous reduction of the optimization Thecan CI quickly can accumulate enough solutions to satisfy the constraints in the initialization so that thegoals. algorithm find enough to satisfy thedirection constraints in the initialization so thatthus themaintaining algorithm can quickly find the the solutions appropriate updating in the feasible solution space, a considerable appropriate in the feasible solution space, a considerable descent descent updating speed for direction the optimization target. The results provethus thatmaintaining CI can effectively improve the convergence rate of the algorithm. speed for the optimization target. The results prove that CI can effectively improve the convergence order to better prove the advantage of IGA algorithm, we conduct a contrast experiment rate of theInalgorithm. between particle swarm optimization andalgorithm, ant colony optimization A simulation In orderIGA, to better prove the advantage(PSO) of IGA we conduct(ACO). a contrast experiment with 6 tasks and 25 stations was set up and the parameter settings of PSO and ACO are shown in between IGA, particle swarm optimization (PSO) and ant colony optimization (ACO). A simulation Table 5. In the scenario, the station frequency of all sites could match the communication frequency with 6 tasks and 25 stations was set up and the parameter settings of PSO and ACO are shown in of the task, the maximum working capacity of the site was one and the cooperative number was two. TableThe 5. In the algorithms scenario, the station frequency ofiterations all sites could matchthe the communication of three were recorded over 1000 to optimize change of targets. Asfrequency shown the task, the maximum of the sitethan wasACO one and andPSO the and cooperative number was two. in Figure 11, IGA has working a strongercapacity global search ability it can resist the problem The three algorithms were recorded over 1000 iterations to optimize the change of targets. As shown of falling into locally optimal points to a certain extent. in Figure 11, IGA has a stronger global search ability than ACO and PSO and it can resist the problem of falling into locally optimal points to a certain extent.

2018, 18, x SensorsSensors 2018, 18, 2093

14 of 24 14 of 24

Table 5. Parameter settings for PSO and ACO.

Algorithm PSO

Algorithm

ACO

Table 5. Parameter settings for PSO and ACO. Maximum Iterations Population Search Parameters Other Parameters Vmax  10 1  2 ,  2  2 1000 10 Maximum Iterations Population Search Parameters Other Parameters , , cons  10   2   3   0.3 1000 10

PSO 1000 10 γ1 = 2, γ2 = 2 Vmax = 10 Notes: optimal factor particle  2 represent the global ACOIn PSO,  1 and1000 10 α =factor 2, β and = 3local optimal η = 0.3, consof = 10 velocity update in iteration and Vmax denotes the maximum velocity of a particle. In ACO,  and Notes: In PSO, γ1 and γ2 represent the global optimal factor and local optimal factor of particle velocity update in respectively represent pheromone and elicitation factor, pheromone  denotes  and iteration Vmax denotes the maximum velocityfactor of a particle. In ACO, α and β respectively represent pheromone factorvolatilization and elicitation factor, η denotes pheromone volatilization factor and cons denotes the of factor and cons denotes the total amount of pheromone released by an total ant atamount one pheromone released by an ant at one iteration. iteration.

Figure 11. Comparison of different algorithms.

Figure 11. Comparison of different algorithms. 5.3.2. Time Complexity

5.3.2. Time Complexity

Our requirements for time complexity are relatively high, because location tasks require very

Our requirements for time complexity are relatively high, because location tasks require very strict real-time performance, which means low time delay for processing tasks. strict real-time performance, which means low time delay for processing tasks. 1.

1.

Effect of population.

Effect of population.

To investigate the influence of population on time complexity, we built a scenario with 15

stations and sixthe tasks and vary the population fromcomplexity, 2 to 40. We the timewith spent To investigate influence of population on time weexamined built a scenario 15 for stations calculation and the fitness of the final solution. From the results of the experiment shown in Figure and six tasks and vary the population from 2 to 40. We examined the time spent for calculation and 12, we of canthe draw thesolution. followingFrom conclusions. (a) The calculation shown increasein approximately linearly the fitness final the results oftime the of experiment Figure 12, we can draw according to the population. (b) The fitness can be obviously enhanced by a bigger population at the to the following conclusions. (a) The time of calculation increase approximately linearly according beginning but when the population is larger than 10, the fitness is no longer sensitive. From this, we the population. (b) The fitness can be obviously enhanced by a bigger population at the beginning can make a final deduction: the population should not increase or decrease without limit and it but when the population is larger than 10, the fitness is no longer sensitive. From this, we can make should be appropriately chosen to balance low time complexity with good global search capability a final deduction: population should not increase or decrease without limit and it should be according to realthe application scenarios. appropriately chosen to balance low time complexity with good global search capability according to 2. Effect of coding length real application scenarios.

2.

To study the effect of coding length, also regarded as the number of stations, on time complexity,

Effect of coding we conducted anlength. experiment to observe the time spent on calculation in different scenarios with

different lengths. However, thealso results were not significant the delay caused by To study coding the effect of coding length, regarded as the numberbecause of stations, on time complexity, retrogression can enormously impact the final output and obscure the impact of the coding length. we conducted an experiment to observe the time spent on calculation in different scenarios with Hence, to avoid the retrogression and emphasize the influence of coding length, we fixed the values different coding lengths. However, the results were not significant because the delay caused by of the population, maximum number of iteration, frequency, task cooperation requirement and retrogression can enormously impact the final output and obscure the impact of the coding length. station capabilities. In addition, we varied the coding length from 10 to 19. The relationship between Hence, to avoid the retrogression and emphasize the influence of coding length, we fixed the values of the population, maximum number of iteration, frequency, task cooperation requirement and station capabilities. In addition, we varied the coding length from 10 to 19. The relationship between time

Sensors 2018, 18, 2093

15 of 24

Sensors 2018, 18, x

15 of 24

Sensors 2018, 18, x

15 of 24

complexity and codingand length becomes observable, as shown inasFigure 13 in (two experiments time complexity coding lengthmore becomes more observable, shown Figure 13 (two with five and six tasks were conducted). time complexity and and coding length becomes more observable, as shown in Figure 13 (two experiments with five six tasks were conducted). experiments with five and six tasks were conducted).

(b) (a) (b) (a) Figure 12. Relationships among time complexity, fitness and population: (a) Time complexityFigure 12. Relationships among time complexity, fitness and population: (a) Time complexityFigure 12. Relationships among time complexity, fitness and population: (a) Time complexitypopulation curve; (b) Fitness-population curve. population curve; (b) Fitness-population curve. population curve; (b) Fitness-population curve.

Figure 13. Relationship between time complexity and coding length. Figure 13. Relationship between time complexity and coding length.

Figure 13. Relationship between time complexity and coding length. Clearly, the time of calculation has an approximately linear relationship with the coding length. Clearly, the time of coding calculation hasmay an approximately linear relationship with the coding such length. Moreover, because the length change because of station network adjustments as Moreover, because the coding length change because of network adjustments such as Clearly, time of calculation has may an approximately relationship with the coding length. added orthe removed nodes, this experiment demonstrates thatlinear thestation algorithm can maintain a stable time added or removed this experiment the can not maintain a stable time complexity eventhe innodes, rapidly transforming scenarios suchthat as war and thisnetwork will lead to a saltation. Moreover, because coding length maydemonstrates change because of algorithm station adjustments such as complexity even inalgorithm rapidly scenarios suchstability as war and this will can not maintain lead to a saltation. Inor conclusion, the has good time complexity practice. added removed nodes, this transforming experiment demonstrates that thein algorithm a stable time In conclusion, the algorithm has good time complexity stability in practice. complexity even in rapidly transforming scenarios such as war and this will not lead to a saltation. 5.3.3. Location Accuracy In conclusion, the algorithm has good time complexity stability in practice. 5.3.3. Location Accuracy This section discusses the variation tendency of location accuracy during the iterations, which is section discusses thetasks. variation location accuracy during the is veryThis important in location Wetendency calculateofthe PDOP by Equations (3)iterations, and (4) which and the very important in location tasks. We calculate the PDOP by Equations (3) and (4) and the measurement error  is calculated as follows: measurement error  is calculated as follows:

Sensors 2018, 18, 2093

16 of 24

5.3.3. Location Accuracy This section discusses the variation tendency of location accuracy during the iterations, which is very important in location tasks. We calculate the PDOP by Equations (3) and (4) and the measurement error ∆ is calculated as follows: Sensors 2018, 18, x

16 of 24

∆ =

Nt

q

∑ i−  1 Nt

i 1

( xˆi − xi )2 + (yˆi − yi )2

x  x   y  y  2

i

i

i

(20)

2

i

(20)

Here, xˆi and yˆi are the measured coordinates of the targets while xi and yi are the real Here, x and y i are the measured coordinates of the targets while xi and yi are the real values, respectively. values, respectively. The behaviors of ∆ and PDOP during the iterations are shown in Figure 14. Generally, as the The behaviors of  and PDOP during the iterations are shown in Figure 14. Generally, as the fitness increases during the iterations, the PDOP value and real measurement error of the solution fitness increases during the iterations, the PDOP value and real measurement error of the solution decrease, indicating that the location accuracy increases. As shown in Figure 14, as the number of decrease, indicating that the location accuracy increases. As shown in Figure 14, as the number of iterations increases, the the algorithm can improve accuracyunder under condition of satisfying iterations increases, algorithm can improvethe the location location accuracy thethe condition of satisfying multiple constraints and completing multiple tasks. multiple constraints and completing multiple tasks. i

Figure 14. Accuracy over iterations (with six tasks and 15 stations).

Figure 14. Accuracy over iterations (with six tasks and 15 stations). 5.4. Comparison with the Manual Method

5.4. Comparison with the Manual Method

We compare the proposed method and traditional manual scheduling. Here, to simulate the

We compare theallproposed method andrandomly traditional manual Here, to task simulate manual method, stations select the same allocated taskscheduling. for one slot; that is, the itself the manual method,allocated all stations select the perform same randomly allocated task formetrics one slot; that is,their the task is randomly but all stations the same one. We used two to examine andbut taskallcompletion rate, to the indicate location accuracy and efficiency, itself performance, is randomly PDOP allocated stations perform samethe one. We used two metrics to examine The results, shown Figure 15 andFigure 16, illustrate two preliminary their respectively. performance, PDOP and task in completion rate, to indicate the location accuracyconclusions. and efficiency, First, MMIGAS has the same location accuracy as the manual scheduling in a scenario with sufficientFirst, respectively. The results, shown in Figures 15 and 16, illustrate two preliminary conclusions. resources. When the station number is small, the PDOP of manual scheduling is lower than that of MMIGAS has the same location accuracy as the manual scheduling in a scenario with sufficient MMIGAS because the manual scheduling only finishes one task every slot. However, the gap resources. When the station number is small, the PDOP of manual scheduling is lower than that of between them gets smaller and finally goes to zero as the number of stations increases. The proposed MMIGAS because the manual scheduling only finishes one task every slot. However, the gap between method and manual scheduling reach the same accuracy when the number of stations is equal to or them more gets smaller finally goes to has zeroaashigher the number of stations increases. proposed method than 60.and Second, MMIGAS completion rate than manual The scheduling, which and manual reachThis theresult samealso accuracy when number rate of stations is equal to or more indicatesscheduling better efficiency. shows that thethe competition grows when the number than 60. Second, MMIGAS has a higher completion rate than when manual which of stations increases. Eventually, we draw our final conclusion: the scheduling, number of stations is indicates high enough, MMIGAS can effectively enhance the efficiency with just a little or even no loss of location better efficiency. This result also shows that competition rate grows when the number of stations accuracy.

Sensors 2018, 18, 2093

17 of 24

increases. Eventually, we draw our final conclusion: when the number of stations is high enough, MMIGAS enhance the efficiency with just a little or even no loss of location 17 accuracy. Sensorscan 2018,effectively 18, x of 24 Sensors 2018, 18, x

17 of 24

Figure 15. Completion rate in different scenario. Figure 15. Completion rate in different scenario.

Figure 15. Completion rate in different scenario.

Figure 16. Position dilution of precision (PDOP) in different scenario. Figure 16. Position dilution of precision (PDOP) in different scenario. Figure 16. Position dilution of precision (PDOP) in different scenario. For further discussion, we define two values: Q1 and Q2 , which are respectively calculated Q1 Q2

For discussion, we define two values: and , which are respectively calculated using (21)further and (22). For further discussion, we define two values: Q1 and Q2 , which are respectively calculated using using (21) and (22). (21) and (22). p1  p2

Q1  (21) p1 pp2 Q1  max (21) p − p 2 1 Q1 = max  p  (21) max( p) and manual scheduling respectively. The Here, p1 and p2 are the PDOP values of MMIGAS p1 and pQ2 are the PDOP values of MMIGAS and manual scheduling respectively. The Here, Here, p meaning and p ofare1 is the of MMIGAS and manual scheduling respectively. physical thePDOP relative values loss of accuracy. 1

2

Q

physical meaning meaning of loss of accuracy. The physical of Q1 1isisthe therelative relative loss of accuracy. Q  R R 2

1

2

Q2  R1  R2

Q2 = R1 − R2

(22) (22)

(22)

Sensors 2018, 18, 2093

18 of 24

Sensors 2018, 18, x

18 of 24

Here R1 and R are the completion rates of MMIGAS and manual scheduling respectively. Here R1 and2 R2 are the completion rates of MMIGAS and manual scheduling respectively. The physical meaning of Q2 is the improvement in completion rate. The physical meaning of Q2 is the improvement in completion rate. For five tasks, the curve of Q1 and Q2 are shown in Figure 17. Clearly, as the number of stations For five tasks, the curve of Q1 and Q2 are shown in Figure 17. Clearly, as the number of increase, Q1 decreases nearly to zero and Q2 increases nearly to one, showing that the loss of location Q1 decreases nearly to zero and Q2 increases nearly to one, showing that the loss stations increase, accuracy is cut down while the efficiency is significantly improved. Hence, the following can be of location accuracy is cut down while the efficiency is significantly improved. Hence, the following concluded: when the number of stations is high enough, this method can substantially enhance can be concluded: when the number of stations is high enough, this method can substantially enhance efficiency at a little cost of location accuracy. efficiency at a little cost of location accuracy.

2 in different scenario (with 5 tasks). Figure17. 17.QQ1 and and QQin Figure different scenario (with 5 tasks). 2 1

5.5. Multi-Objective Function Weights 5.5. Multi-Objective Function Weights According to Equation (13), c , c and c respectively represent the weights of completion

2 3 According to Equation (13), c1 , c1 2 and c3 respectively represent the weights of completion rate, rate, resource utilization and task priority. In Section 5.1, we mainly considered the location accuracy resource utilization and task priority. In Section 5.1, we mainly considered the location accuracy and and task completion rate, which mainly aims at accomplishing as many tasks as possible while task completion rate, which mainly aims at accomplishing as many tasks as possible while ensuring ensuring accuracy, so the weights are set as c1  1 , c2  c3  0 . Then, we will set different values for accuracy, so the weights are set as c1 = 1, c2 = c3 = 0. Then, we will set different values for c1 , c , c2 and c3 to verify the effectiveness of the proposed algorithm for multi-objective situations. c2 and1 c3 to verify the effectiveness of the proposed algorithm for multi-objective situations.

5.5.1. Analysis of Multi-Objective Weights

5.5.1. Analysis of Multi-Objective Weights

First, we set the parameters as: c1  c2  0.1 , c3  0.8 . This setting is primarily about task

First, we set the parameters as: c1 = c2 = 0.1, c3 = 0.8. This setting is primarily about task priority and the simulation scenario is to prioritize important tasks when the stations are insufficient. priority and the simulation scenario is to prioritize important tasks when the stations are insufficient. We built up a scenario with eight stations and six tasks. The parameters settings for the algorithm are We built up in a scenario with eightscenario stationsparameters and six tasks. The parameters settings shown Table 6, the station are set as shown in Table 2 and for the the taskalgorithm scenario are shown in Table are 6, the station parameters are set as shown in Table 2 and the task 18. scenario parameters set as shownscenario in Table 3. The experiment results are shown in Table 7 and Figure parameters are set as shown in Table 3. The experiment results are shown in Table 7 and Figure 18. Table 6. Parameter settings for the algorithm.

Table 6. Parameter settings for the algorithm. Chromosome Individual Objective Mutation Penalty Probability Crossover Crossover PopulationIteration Function Probability Factor Chromosome Individual ObjectiveDistribution Mutation Penalty Weights Probability Probability Probability Crossover Crossover Population Iteration Function Probability Factor c  c  0.1 Distribution Gaussian Probability Probability Weights 1 2 5 0.8 0.8 0.1 10 1000 0.8

0.8

0.1

10

1000

Ω = 5

c3c = 0.8c = 0.1 N Gaussian 0,1 2 1 c3 = 0.8 N (0, 1)

Sensors 2018, 18, 2093

19 of 24

Sensors 2018, 18, x

19 of 24

Sensors 2018, 18, x

19 of 24

Table 7. Scheduling results of eight stations and six tasks. Table 7. Scheduling results of eight stations and six tasks. and six TaskTable 7.1 Scheduling 2 results of 3 eight stations 4 5 tasks. 6

Task

Priority Priority 6 Task Station 1, 5, 6

Station Priority Station

1 165

7, 8

2 3 25 4 34 4, 8

4 433

2, 6

5 52

6

2 61 2, 6

1, 65, 6 7,5 8 4,4 8 2,3 6 2,2 6 —— 1 1, 5, 6 7, 8 4, 8 2, 6 2, 6 ——

1 ——

Figure 18. Experiment results of eight stations and six tasks.

Figure 18. Experiment results of eight stations and six tasks. Figure 18. Experiment results of eight stations and six tasks.

As can be known from Table 7 and Figure 18, when the number of sites is insufficient, No.6 task As can be known fromlowest Table priority 7 and Figure 18, task when the number of sites isbest insufficient, No.6 task is is abandoned to the No.1 hasthe thenumber most stations and locationNo.6 accuracy As can bedue known from Table 7 andand Figure 18, when of sites is insufficient, task abandoned due to the lowest priority and No.1 task has the most stations and best location accuracy due to the highest is abandoned due topriority. the lowest priority and No.1 task has the most stations and best location accuracy due to the highest priority. To analyze the performance of the IGA and verify the experiment conclusions, we adopt the due to the highest priority. To analyze the performance ofofthe IGA and verify the experiment conclusions, we adopt performance andthe indicators in Section 5.3. And theverify analysis ofexperiment experimentconclusions, results is shown in Figure To analyze performance the IGA and the we adopt the the 19. In Figure 19a, IGA algorithm can 5.3. still ensure to is the optimal value. performance indicators Section thethe analysis ofcurve experiment results shown inisFigure performance andand indicators inin Section 5.3.And And thefitness analysis ofconverges experiment results shown in From 19b, findalgorithm out can that still thecan PDOP is oscillatory due to theconverges of 19. In Figure 19a, we IGAcan algorithm ensure the fitness converges toinfluence the optimal value. Figure 19. In Figure 19a, IGA stillcurve ensure thecurve fitness curve topriority. the optimal And Figure 19c shows that the completion rate did not reach 100% due to insufficient sites and of From Figure 19b, we can find out that the PDOP curve is oscillatory due to the influence of priority. value. From Figure 19b, we can find out that the PDOP curve is oscillatory due to the influence considering the shows priority, thethe completion alsoreach oscillated theto early stage. sites It canand be And Figure 19c that completionrate ratecurve did not 100% in due insufficient priority. And Figure 19c shows that the completion rate did not reach 100% due to insufficient sites and concluded from Figure 19d that because stations are not sufficient, the resource utilization is always considering the priority, the completion rate curve also oscillated in the early stage. It can be considering the priority, the completion rate curve also oscillated in the early stage. It can be concluded at 100%. from Figure 19d that because stations are not sufficient, the resource utilization is always concluded from at Figure 19d that because stations are not sufficient, the resource utilization is always at 100%. Through the experiment analysis, it can be concluded that when the stations are insufficient, 100%. Through the experiment analysis, be concluded that when stations are insufficient, MMIGAS can the give the optimal solutionitittocan different requirements. Through experiment analysis, can be concluded that when thethe stations are insufficient, MMIGAS can give the optimal solution to different requirements. MMIGAS can give the optimal solution to different requirements.

(b) (b)

(a) (a)

Figure 19. Cont.

Sensors 2018, 18, 2093

20 of 24

Sensors 2018, 18, x

20 of 24

(c)

(d)

Figure 19. the experiment results in the scenario with 8 stations and 6 tasks ( c  c  0.1 , c  0.8 ): (a)

Figure 19. The experiment results in the scenario with 8 stations and 6 tasks 1(c1 2= c2 =3 0.1, c3 = 0.8): fitness curve; (b) PDOP curve; (c) completion rate curve; (d) resource utilization curve. (a) fitness curve; (b) PDOP curve; (c) completion rate curve; (d) resource utilization curve. 5.5.2. Reliability in Different Scenarios

5.5.2. Reliability in Different Scenarios

Then, we will combine location accuracy, completion rate, resource utilization and task priority

Then, we will combine location accuracy, completion rate, resource utilization and task priority to test the proposed algorithm in different scenarios. Therefore, the task priority is set as Table 7, the to test the proposed algorithm in different scenarios. Therefore, the task priority is set as Table 7, 1  c2c  c= parametersare areset set as asc c1 = and 1the parameters settings for the algorithm are shown in 3 c the parameters = 2 1 33 3 and the parameters settings for the algorithm are shown in Table 8. The station and task scenario parameters areset also set in2Tables 2 and 3. The experiment Table 8. The station and task scenario parameters are also in Tables and 3. The experiment results results accordance the above experimental are as follows. in in accordance withwith the above experimental settingssettings are as follows. Figure 20,can it can foundout outthat that as as the the number increases, the the location accuracy FromFrom Figure 20, it bebe found numberofofstations stations increases, location accuracy gradually increases. But the station redundancy will occur later. The results show that excessive gradually increases. But the station redundancy will occur later. The results show that excessive stations bring a noticeable increasein inlocation location accuracy thethe station number is enough. stations will will not not bring a noticeable increase accuracywhen when station number is enough. In Figure 21, as the number of stations increases, the task completion rate gradually increases In Figure 21, as the number of stations increases, the task completion rate gradually increases until until 100%. Similarly, as the number of tasks increases, so does the number of stations needed to 100%. Similarly, as the number of tasks increases, so does the number of stations needed to complete complete all tasks. all tasks. Figure 22 shows that the utilization rate is 100% in the early stage due to the lack of sites. Figure 22 shows the utilization rate is in the early stage due appears to the lack sites. However, However, with thethat increase in the number of 100% stations, station redundancy andofthe resource with utilization the increase the number of stations, station redundancy appears and the resource utilization hasin gradually declined in all scenarios. has gradually declined in all scenarios. Table 8. Parameter settings for the algorithm.

Chromosome IndividualTable 8. Parameter settings for the algorithm. Objective Mutation Penalty Probability Crossover Crossover PopulationIteration Function Probability Factor Distribution Chromosome Individual Mutation Penalty Objective Probability ProbabilityCrossover Probability Weights Crossover Population Iteration Probability Factor Function Weights Distribution Gaussian Probability Probability 1   5 c1  c2  c3  0.8 0.8 0.1 10 1000 N Gaussian 0,1 3 1 0.8 0.8 0.1 10 1000 Ω = 5 c1 = c2 = c3 =

3

N (0, 1)

Sensors 2018, 18, 2093

21 of 24

Sensors 2018, 18, x Sensors 2018, 18, x

21 of 24 21 of 24

Figure 20.PDOP PDOP curve in different scenarios. Figure in different differentscenarios. scenarios. Figure20. 20. PDOP curve curve in

Figure 21. Completion rate curve in different scenarios.

Figure Completion rate rate curve scenarios. Figure 21.21.Completion curveinindifferent different scenarios.

Sensors 2018, 18, 2093

22 of 24

Sensors 2018, 18, x

22 of 24

Figure Resourceutilization utilization curve curve in Figure 22.22. Resource indifferent differentscenarios. scenarios.

the above experiment results, wedraw can draw the following two conclusions. the FromFrom the above experiment results, we can the following two conclusions. First, First, the algorithm algorithm proposed in this paper can well solve the multi-objective and multi-constraint resource proposed in this paper can well solve the multi-objective and multi-constraint resource scheduling scheduling problem of passive location. Secondly,algorithm the proposed algorithm has high reliability in problem of passive location. Secondly, the proposed has high reliability in different scenarios. different scenarios.

6. Conclusions

6. Conclusions

In this paper, we studied the scheduling problem for passive location resources and proposed In this paper, we studied the scheduling problem for passive location resources and proposed a a new solution method named MMIGAS. A multi-objective function was conceived to balance new solution method named MMIGAS. A multi-objective function was conceived to balance various various aspects the performance such asaccuracy, locationefficiency accuracy, efficiency and resource aspects of theofperformance such as location and resource utilization. And utilization. multiAnd multi-constraint (i.e., frequency, cooperation requirement and capability) was formulated for the constraint (i.e., frequency, cooperation requirement and capability) was formulated for the practicability of the approach. CI, PF and MGO were implemented to improve the GA, by enhancing practicability of the approach. CI, PF and MGO were implemented to improve GA, by enhancing the the convergence andoptimal global optimal ability. We evaluated the performance of MMIGAS by convergence rate andrate global ability. We evaluated the performance of MMIGAS by computer computer In various scenarios, method reach its convergence bound within 100 simulations. Insimulations. various scenarios, this methodthis can reach can its convergence bound within 100 iterations, iterations, showing astringency. a remarkable Moreover, astringency.its Moreover, its steady time complexity was illustrated showing a remarkable steady time complexity was illustrated because the because the calculation time was shown to have an approximately linear relationship with population calculation time was shown to have an approximately linear relationship with population and coding and coding length. Furthermore, we compared traditional manual scheduling and MMIGAS. The length. Furthermore, we compared traditional manual scheduling and MMIGAS. The results showed results showed that the efficiency is clearly improved by MMIGAS and the location accuracy is still that the efficiency is clearly improved by MMIGAS and the location accuracy is still maintained at maintained at a high level in a scenario of more than 50 resources at the same time. At last, we also a high level in aa multi-objective scenario of more than 50 resources at the same time.that Atthe last, we alsoisconducted a conducted parameter adjustment experiment to verify algorithm suitable multi-objective adjustment experiment verify that the algorithm is suitable for different for differentparameter target requirements and reliable into different scenarios. In conclusion, the proposed targetalgorithm requirements and reliable in different scenarios.ofInstation conclusion, the proposed can solve can solve the problem of scheduling resources in passivealgorithm location while maintaining high efficiency and stable locationin accuracy. the problem of scheduling of station resources passive location while maintaining high efficiency and stable location accuracy. Author Contributions: J.J.: Literature retrieval, research design, data analysis, manuscript writing; J.Z.: Research

guidance, data collection, guidance; L.Z.: Research analysis, research plan, J.Z.: Author Contributions: J.J.: experimental Literature retrieval, research design, databackground analysis, research, manuscript writing; manuscript writing; X.R.: Project analysis, financial support and direction guidance; Y.T.: Fund support, Research guidance, data collection, experimental guidance; L.Z.: Research analysis, background research, research experimental writing; support. X.R.: Project analysis, financial support and direction guidance; Y.T.: Fund support, plan, manuscript experimental support.

Funding: This work was supported in part by the National Natural Science Foundation of China under grant No. 61601516. Conflicts of Interest: The authors do not have financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work. The authors declare no conflicts of interest.

Sensors 2018, 18, 2093

23 of 24

References 1.

2.

3.

4. 5. 6. 7.

8.

9.

10. 11. 12.

13. 14.

15. 16. 17.

18. 19. 20. 21.

Li, Y.; Ma, Z.; Yang, A. Study on Theory of Signal and System in Modern Communication Technology. In Proceedings of the 2nd International Conference on Green Communications and Networks 2012 (GCN 2012); Springer: Berlin/Heidelberg, Germany, 2013; Volume 3, pp. 561–567, ISBN 978-3-642-35469-4. Lv, X.; Liu, K.; Hu, P. Geometry Influence on GDOP in TOA and AOA Positioning Systems. In Proceedings of the 2010 Second International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China, 24–25 April 2010; pp. 58–61. Xu, J.; Ma, M.; Law, C.L. AOA Cooperative Position Localization. In Proceedings of the IEEE GLOBECOM 2008—2008 IEEE Global Telecommunications Conference, New Orleans, LA, USA, 30 November–4 December 2008; pp. 233–237. Deng, P.; Liu, L.; Fan, P. A collaborative location model for cellular mobile position location. J. Electron. 2004, 21, 449–453. [CrossRef] Tang, T.; Wu, Y. A Fast Direction Finding Algorithm Based on Subspace. Telecommun. Eng. 2008, 234, 51–55. [CrossRef] Zhang, C.H.; Cheng, J.Q.; Chen, L.F. Simulation of Shortwave Channel Model and Research on Improved Algorithm. Command Control Simul. 2009, 31, 76–78. [CrossRef] Ngoc Nguyen, T.L.; Shin, Y. A new approach for positioning based on AOA measurements. In Proceedings of the 2013 International Conference on Computing, Management and Telecommunications (ComManTel), Ho Chi Minh City, Vietnam, 21–24 January 2013; pp. 208–211. Christensen, M.W.; Suzuki, K.; Zambri, B.; Stephens, G.L. Ship track observations of a reduced shortwave aerosol indirect effect in mixed-phase clouds: Ice-Cloud Indirect Effect in Ship-tracks. Geophys. Res. Lett. 2014, 41, 6970–6977. [CrossRef] Wei, S.; Zhang, J.; Sun, T. Nodes selection mechanism based on modified binary particle swarm optimization algorithm. In Proceedings of the First International Conference on Information Sciences, Machinery, Materials and Energy, Wuhan, China, 27–28 June 2015; pp. 2023–2027. Xiu, J.-J.; He, Y.; Wang, G.-H.; Xiu, J.-H.; Tang, X.-M. Constellation of multi-sensors in bearing-only location system. IEE Proc. Radar Sonar Navig. 2005, 152, 215–218. [CrossRef] Sahoo, P.K.; Thakkar, H.K.; Hwang, I.S. Pre-Scheduled and Self Organized Sleep-Scheduling Algorithms for Efficient K-Coverage in Wireless Sensor Networks. Sensors 2017, 17, 2945. [CrossRef] [PubMed] Hu, W.; O’Rourke, D.; Kusy, B.; Wark, T. A virtual sensor scheduling framework for heterogeneous wireless sensor networks. In Proceedings of the 38th Annual IEEE Conference on Local Computer Networks, Sydney, NSW, Australia, 21–24 October 2013; pp. 655–658. Rusu, C.; Thompson, J.; Robertson, N.M. Sensor Scheduling with Time, Energy, and Communication Constraints. IEEE Trans. Signal Process. 2017, 66, 528–539. [CrossRef] Sun, T.; Zhang, J.; Ran, X.; Li, Y. The Direction-finding Stations Scheduling Algorithm Based on BPSO. In Proceedings of the 2015 4th National Conference on Electrical, Electronics and Computer Engineering, Xi’an, China, 12–13 December 2015; pp. 1118–1123. Wang, X.; Chen, H. Research on improving the Accuracy of Shortwave Signal Positioning. Digit. Commun. World 2014, 111, 52–56. [CrossRef] Wang, Z.; Xia, N.; Yang, W.; Jian, C.; Station, S.M. Research and Design of High Precision Short Wave Positioning System Based on TDOA. Comput. Meas. Control 2015, 23, 3144–3147. [CrossRef] Cess, R.D.; Nemesure, S.; Dutton, E.G.; Deluisi, J.J.; Potter, G.L.; Morcrette, J.J. The Impact of Clouds on the Shortwave Radiation Budget of the Surface-Atmosphere System: Interfacing Measurements and Models. J. Clim. 1993, 6, 21–37. [CrossRef] Wyatt, L.R. Shortwave Direction and Spreading Measured with HF Radar. J. Atmos. Ocean. Technol. 2011, 29, 286–299. [CrossRef] Evans, R.; Krishnamurthy, V.; Nair, G.; Sciacca, L. Networked sensor management and data rate control for tracking maneuvering targets. IEEE Trans. Signal Process. 2005, 53, 1979–1991. [CrossRef] Johnson, R.L.; Black, Q.R.; Sonsteby, A.G. HF multipath passive single site radio location. IEEE Trans. Aerosp. Electron. Syst. 1994, 30, 462–470. [CrossRef] Fabrizio, G. Geolocation of HF skywave radar signals using multipath in an unknown ionosphere. In Proceedings of the 2014 IEEE Radar Conference, Cincinnati, OH, USA, 19–23 May 2014; pp. 422–425.

Sensors 2018, 18, 2093

22. 23. 24. 25. 26. 27. 28. 29.

24 of 24

Johnson, R.L.; Black, R.Q.; Sonsteby, A.G. Passive Means for Single Site Radio Location. U.S. Patent US5444451, 22 August 1995. Xue, S.; Yang, Y. Understanding GDOP minimization in GNSS positioning: Infinite solutions, finite solutions and no solution. Adv. Space Res. 2017, 59, 775–785. [CrossRef] Yang, X.; Vaidya, N.H. Priority Scheduling in Wireless Ad Hoc Networks. Wirel. Netw. 2006, 12, 273–286. [CrossRef] Schwob, P.R. Broadcast Receiver Capable of Selecting Stations Based upon Geographical Location and Program Format. U.S. Patent US4969209, 6 November 1990. Hillermeier, C. Nonlinear Multi-objective Optimization. J. Oper. Res. Soc. 1999, 51, 246. [CrossRef] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 2002, 6, 182–197. [CrossRef] Goldberg, D.E. Genetic Algorithms in Search, Optimization and Machine Learning, 1st ed.; Addison-Wesley Longman Publishing Co., Inc.: Boston, MA, USA, 1989; ISBN 978-0-201-15767-3. Potts, J.C.; Giddens, T.D.; Yadav, S.B. The development and evaluation of an improved genetic algorithm based on migration and artificial selection. IEEE Trans. Syst. Man Cybern. 1994, 24, 73–86. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).