African Journal of Business Management Vol. 5(2), pp. 505-514, 18 January, 2011 Available online at http://www.academicjournals.org/AJBM ISSN 1993-8233 ©2011 Academic Journals
Full Length Research Paper
Soft system modeling in transportation planning: Modeling trip flows based on the fuzzy inference system approach J.Jassbi1, P.Makvandi1*, M. Ataei2 and Pedro A. C. Sousa3 1
Department of Industrial Management, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran. 2 College of Business Administration, University of Missouri (UM-SL), St. Louis, USA. 3 Faculdade de Ciencias e Tecnoiogia, Universidade Nova de Lisboa, Portugal. Accepted 14 October, 2010
Transportation planning is one the most important problems of urban management systems. Meanwhile, modeling trip flows between metropolitan zones is vital to a successful transportation planning. Due to importance of the problem, different models have been developed in recent years but because of the complex nature of the problem that deals with human behavior and existence of different independent variables that affect number of trips, it is always hard to develop a model with acceptable forecasting error that is computationally efficient. In this paper a three phases fuzzy inference system (FIS) proposed to map social and demographic variables to total number of trips between origin-destination (OD), pairs. Fuzzy rule bases in the model are in fact the exploration of transportation experts’ subjective patterns. Key words: Transportation planning, trip forecasting, fuzzy inference system, fuzzy rule base.
INTRODUCTION Traffic flows and trip distribution resulted from human choices that are affected by social and individual variables of the commuters. Due to this fact that human decision making are more consistent with fuzzy logic in comparison with crisp mathematics, it seems that fuzzy logic could be a logical tool to map such areas. Modeling a trip distribution system with fuzzy inference systems would enjoy the exploration of subjective pattern of decision makers. Transportation planning is one the basic concern and problems of many developed and also developing countries all around the world. It is important because it deals with cost, time and security. On the other hand, it could be important for governments because it could be related to the satisfaction of citizens. Transportation planning activities are commonly based on the forecasting. Usually, the under studied zone is
*Corresponding author. E-mail:
[email protected]. Tel: +98 21 447 32 947. Fax: +98 21 447 32 947.
divided into exact regions and planners trying to forecast trip flow between regions as OD pairs (i.e. for 20 years after). Based on this information, a proper transportation infrastructure such as subway, highway, etc. is designed and executed to serve the transportation demands. A trip could be defined as follows: “To move between origin mode
on route
to destination
by
in an exact period of time.”
Meanwhile, one of the most important parts of forecasting procedure is to predict the trips flow between a given origin-destination pair. Different models have been developed to forecast trip flows in recent years. The key to a successful forecasting is to recognize the existing patterns correctly. Obviously, models with minor forecastting errors would be more suitable for transportation planning but, because of complex nature of the transportation planning problems that deals with human behavior, it is always hard to find the optimal solution. The traditional
506
Afr. J. Bus. Manage.
four-step model has been widely used in travel demand forecasting. The standard model includes: trip generation, trip distribution, modal split and route choice sequentially in a top-down sequential process (Ortuzar and Willumsen, 2001). The four-step model is based on the functions that try to approximate the trips between the metropolitan zones. The approximation migrates and is reinforced from each step to the next one and this could lead to final significant calculations deviation. Although each step of the transportation planning is important for transportation planners but, trip timing and mode choice decisions of the commuters are the most important. These two decisions along with route choice directly determine the temporal distribution of demand experienced on any given piece of transportation infrastructure in an urban area (Susilo and Kitamura, 2007). The reliability of forecasting results influences the following steps such as trip distribution, mode split, and route choice. Therefore, improved trip generation models are needed to improve forecasting precision (Golob, 2000). The trip distribution models have been classified in two broad categories as aggregate and disaggregate models. The disaggregate models try to explain individuals’ behaviors in selecting the origins and destinations of their spatial movements while the aggregate models analyze total number of flows between analysis zones. Since disaggregate models work at individual level, proponents of such models claim that the data requirement for calibration of these types of models may be significantly lower (Ruiter and Ben-Akiva, 1978). Even though there have been many alternative formulations for the aggregate trip distribution models (namely, growth factor, fratar, intervening opportunities, gravity or regression models), the gravity model is the most preferred one over the years despite all of its drawbacks (Murat and Celik, 2010). An analysis of the factors influencing traveler behavior and destination selection shows that the attractiveness of the traffic zone strongly affects the trip generation volume (Yao Liya et al, 2008). Different studies have been considered the impact of social variables and private information on trip generation (Smiller and Hoel, 2006). But none of the researches mapped generation variables of the origin and attraction variables of destination to final trip flows between origin-destination. Due to the stochastic nature of traffic flow and the strongly nonlinear characteristics of traffic dynamics, methods of soft computing have received much attention since early 90s and considered as alternatives for the traditional statistical models (Celikoglu and Cigizoglu, 2007). Among these methods the artificial neural network (ANN) have been commonly applied in a number of areas of transport (Dougherty, 1995), including the studies of traffic volume forecasting (Yun et. al. 1998), short-term traffic flow prediction (Chen and Muller, 2001, Messai et. al., 2002), macroscopic modeling of freeway traffic (Zhang et al.,
1997). Diverse kinds of NNs have been proposed in the literature.
Fuzzy logic in transportation Fuzzy logic provides an effective means of dealing with problems involving imprecise and vague phenomena. Fuzzy concepts enable assessors to use linguistic terms to assess indicators in natural language expressions and each linguistic term can be associated with a membership function. Furthermore, fuzzy logic has found significant applications in management sciences. However, the gradual evolution of the expression of uncertainty using probability theory was challenged, first in 1937 by max black, with his studies in vagueness, then with the introduction of fuzzy sets by Lotfi Zadeh in 1965. Zadeh’s work had a profound influence on the thinking about uncertainty because it challenged not only probability theory as the sole representation for uncertainty, but the very foundations upon which probability theory was based: classical binary (two valued) logic (Ross, 2004). Without denying the importance of binary logic as the basis for the development of many scientific disciplines and technology leading to the prosperity of man's society, we must note that it cannot deal effectively with passengers', dispatchers' or drivers' feelings of uncertainty, vagueness and ambiguity. Since the fuzzy set theory recognizes the vague boundary that exists in some sets, different fuzzy set theory techniques need to be used in order to properly model traffic and transportation problems characterized by ambiguity, subjectivity and uncertainty (Teodorovic, 1999). A fuzzy logic system is a nonlinear system that maps a crisp input vector into a crisp scalar output. When solving a large number of different traffic and transportation problems, this is what we actually do: map a crisp input vector into a crisp scalar output. Fuzzy logic could be used successfully to model situations in which people make decisions in complex environments that are very hard to develop a mathematical model. Such situations for example often occur in the field of traffic and transportation when studying the work of dispatchers or modeling choice problems. Present experience shows that there is room for the development of different approximate reasoning algorithms when solving complex problems of this type (Teodorovic, 1999). Fuzzy set theory has a successful background in solving transportation problems that is presented in the works of Chen et al. (1990), Lotan and Koutsopoulos (1993a,b), Xu and Chan, 1993), Teodorovic and Babic (1993), Chang and Shyu (1993), Chanas et al. (1993), Deb (1993), Nanda and Kikuchi (1993), Vukadinovic and Teodorovic (1994), Teodorovic et al. (1994), Teodorovic and Kalic (1995), Milosavljevic et al. (1996). In this paper we have tried to propose a framework to
Jassbi et al.
507
Figure 1. Conceptual model of trip forecasting input-output space mapping.
develop transportation experts’ subjective pattern based on generation and attraction variables of a given origindestination pair. Meanwhile, fuzzy inference system approach is used to map these variables to total number of trips between origin-destination pair.
Novelties of the proposed approach The novelties of the proposed approach could be summarized as follows: 1. Moving from computation efficiency to decreasing forecasting error could be pronounced as a dilemma in decision making and forecasting problems and also could be translated as a trade off problem. The complex problems challenge decision makers to define the transfer function more precisely with more variables. Although this could help to define the system but, calculations of dynamic systems in simulation process would increase exponentially. Modeling traffic flows and trip forecasting is a complex problem that applying fuzzy concept in this field could be helpful because of its capabilities in modeling complex system in none computationally expensive manner. 2. Although there are different forecasting models existing in modeling traffic flows and trip forecasting between metropolitan regions, but most of them are hard models. This fact most be noted that traveling between two points in a city (that could be generalized to two regions in a metropolis) is a human behavior that could be adopted from human perception to overcome his/her needs. Thus, applying a fuzzy concept that maps human subjective patterns to mathematical models could be resulted in more meaningful results. Due to our best knowledge the combination of the fuzzy proposed model has never been reported in literature before.
PROBLEM DEFINITION The final goal of any transportation planning method is to forecast the number of trips between two given region of under studied zone. Based on the forecasted trips between two given regions, transportation infrastructures (such as bridges, highways, tunnels, subways, etc.) are designed to serve the demands in predefined level of service. This problem could be interpreted as a function approximation problem in which we aim to map input space to output space where: Input space is ‘Trip Generation variables and trip attraction variables’. These are the variables that have direct impacts on the generation and attraction of trips of any given region. These variables have normally the social and economical nature and are common variables that are used in transportation planning studies. Table 1 shows the variables that are used in Tehran transportation planning program. Output space is ‘the number of trips between two given regions’. The number of trips would be approximated by a transfer function that is formed based on the relations of trip generation capabilities of origin and trip attraction capacities of destination.
Conceptual model Figure 1 illustrates the conceptual framework of the trip forecasting problem. The main concern of the problem is to approximate the transfer function that is capable of mapping trip attraction and generation variables to number of trips between two given regions. As it addressed in introduction section, Different kinds of transfer functions had been used in this problem. Here, a hybrid fuzzy inference system is used to map input space to output space.
508
Afr. J. Bus. Manage.
Table 1. Variables with impacts on trip generation and attraction based on the goal of the trip.
Trip goals
Work trips
Educational Trips
Shopping trips
Social trips
Trips that are not started from or ended to home
Generation Occupation in the residence area Population Residential space Number of residential buildings Population density Household number Average of automobile per household Average price of the one square meter of the land Population Population of the students Car Ownership Residential space Traffic zone space Average of automobile per household
Attraction Occupation in the working area Business/administrative/agricultural/industrial Land space Business/administrative/agricultural/industrial building space Number of Business/administrative/ agricultural/industrial units
Schools’ spaces Number of schools/ number of students/ number of schools classes. Number of universities/ number of universities students
Population Occupation in the residence area Household numbers Residential space Car Ownership Residential Space Land/building price
Business land use space Number of business units
Population Number of residential buildings Car Ownership
Number of retail stores Number and capacity of cinemas/ mosques/ exhibition centers/ parks/ hospitals
Distance to entertainment complexes
Social land use space Population
All generation variables
All attraction variables
Fuzzy logic and fuzzy inference systems Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. In contrast with "crisp logic", where binary sets have binary logic, fuzzy logic variables may have a truth value that ranges between 0 and 1 and is not constrained to the two truth values of classic propositional logic (Novák et al., 1999). Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made, or patterns discerned. The process of fuzzy inference involves: i. Defining If-Then rules ii. Defining membership functions iii. Appling logical operations
Business land space Occupation in the working area
There are two types of fuzzy inference systems that usually can be implemented: Mamdani-type and Sugenotype. These two types of inference systems vary somewhat in the way outputs are determined. Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multidisciplinary nature, fuzzy inference systems are associated with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory, fuzzy logic controllers, and simply (and ambiguously) fuzzy systems. The input space variables could be summarized as Tables 2 and 3. Mamdani's fuzzy inference method is the most commonly seen fuzzy methodology. Mamdani's method was among the first control systems built using fuzzy set
Jassbi et al.
509
Table 2. Generation variables (input space variables).
Input space variables
Adapted from Tehran comprehensive (http://trafficstudy.tehran.ir)
Generation variables Occupation in the residence area Population Residential space Population density Number of households Car ownership rate Average price of one square meter of land Students population Traffic zone space Number of residential buildings Distance to entertainment complexes transportation
and
traffic
studies
Co.
(TCTTS).
Table 3. Attraction variables (input space variables).
Input space variables
Attraction variables Occupation in the working area Business/ Administrative/Agricultural/Industrial Land Space Administrative building space Number of Administrative/Business/Industrial Buildings Schools’ space Number of Students/Schools/Classes Number of Universities/Students Number of Retailers Number and Capacity of Cinemas/Mosques/ Exhibitions/ Parks/Hospitals Sport and Social Centers Spaces
Adapted from Tehran comprehensive transportation and traffic studies Co. (TCTTS). (http://trafficstudy.tehran.ir).
theory. It was proposed in 1975 by Ibrahim Mamdani (Mamdani 1975) as an attempt to control a steam engine and boiler combination by synthesizing a set of linguistic control rules obtained from experienced human operators. As the most part of fuzzy logic are common knowledge now, readers are referenced to bibliography (Jang 1997, Mamdani 1975, Sugeno 1985). PROBLEM FORMULATION In order to forecast the trips based on fuzzy inference approach, a fuzzy rule base must be developed. The relations between variables would form the fuzzy rule base. These relations have been adapted from: i. Transportation experts’ opinions about the impacts of the input space variables on the number of trips ii. Literature review: Past studies including soft and hard approaches
that revealed the impacts of the generation and attraction variables on trip distributions. iii. Transportation planning procedures in metropolises (Tehran Comprehensive Traffic Study Company). To map input space to output space, different fuzzy scenarios could be considered. Figure 2 illustrates the framework of conceptual fuzzy model that is used to forecast the number of trips in this work. As it illustrated in Figure 2, three independent fuzzy inference systems are used. The first FIS is aimed to map generation variables to number of generated trips . The second FIS is designed to map attraction variables to number of attracted trips . At the end, the third FIS is designed to combine the output of the first and second FIS.
RESULTS As it is shown in Figure 2, this scenario consists of three phases in which each phase has its own FIS.
510
Afr. J. Bus. Manage.
Figure 2. Conceptual fuzzy model: Mapping trip generation and attraction variables to total number of trips between two given regions.
Phase I
“If
Mapping trip generation variables as input space to total number of generated trips by the given region ( ), as the output space using a proper FIS as the function approximator.
In fact, the whole fuzzy system is an exploration of expert’s subjective pattern that maps input space to output space. Input space consists of 11 demographic variables ( ) with direct impacts on trip generation that are presented in Table 2. The designed FIS for this phase is a Mamdani type fuzzy inference system as illustrated in Figure 3.
Phase II Mapping trip attraction variables as input space to total number of attracted trips by the given region ( ), as the output space using a proper FIS as the function approximator.
Phase III and for two given regions and Aggregation of calculating the final total number of trips between two regions ( ). Every phase has its own FIS that maps input space to output space. As it shown in the problem definition section, the final solution of the problem would pass through three phases. The modeling procedure is: Phase I The initial fuzzy rules and membership functions types and shapes are adjusted based on experts’ opinions. In order to catch experts’ subjective pattern about the impacts of generation variables on number of generated trips, a proper fuzzy questionnaire is designed to ask about the relations. The results are aggregated and 70 initial rules are generated. Enjoying rules reduction techniques, number of rules has been reduced to 48. The structure of rules is for example as follows:
is low and
then
is medium”
Phase II The structure of modeling in this phase is similar to Phase I. Input space consists of 10 demographic variables ( ) with direct impacts on trip attraction of the exact region that are presented in Table 3. The designed FIS for this phase is a Mamdani type fuzzy inference system as shown in Figure 4. Similar to phase I rule generation procedure, fuzzy rule base in this phase is shaped based on transportation expert’s opinions. After aggregation of expert’s opinions and eliminating rules overlaps, 39 rules are selected. Now, we have two different FIS that map demographic variables to trip attraction and generation conditions of two given regions, respectively. In order to forecast the trip flows between an OD pair, the output of the previous phases have to be combined in a new FIS. Phase III Based on Phases I and II, the trip generation condition of the origin and trip attraction condition of the destination are known. Thus, we need to design another FIS to map trip attraction condition, as input space to trip generation condition, as output space. Figure 5 shows this procedure.
Jassbi et al.
511
Figure 3. Phase I fuzzy inference system.
Figure 4. Phase II Fuzzy Inference System.
this procedure. This fuzzy inference system accepts outputs of Phases I and II as its inputs. Here, Tproduct is the output of Phase I fuzzy inference system and Tattract is
the output of Phase II fuzzy inference system. Rule base of this fuzzy inference system consists of 11 rules that are adapted from transportation experts. The output of
512
Afr. J. Bus. Manage.
Figure 5. Phase III fuzzy inference system.
Figure 6. Surface of phase III FIS rules.
the model is the number of trips between two given regions that is represented by Tnum. Figure 6 visualized the surface of number of trips, as the output versus trip attraction condition and trip generation condition, as the input. The three phases model, maps demographical variables to number of trips. In order to forecast the number of trips between two given regions, demographic variables must be fed to the model and result would be the number of trips. Figure 7 shows the block diagram of continuous simulated framework of the model.
Conclusion Trip, as defined, “to move between origin to destination by mode on route in an exact period of time”, is completely a human choice that is made based on conditions. Here we defined the condition as the combination of variables with impacts on reasons of the trips. The reasons are social variables that made commuters to move from exact location to another one in a metropolitan area. These variables are, operative in trip generation and trip attraction of regions. As it mentioned
Jassbi et al.
513
Figure 7. Proposed fuzzy Simulink™ model.
in introduction section of the paper, the key to successful forecasting of the future is to recognize the existing patterns correctly. In fact we need functions to help us discover existing patterns of trips between regions. Because of fuzzy nature of human decision making process, it seems that phenomena that are related to human choice could be explained using fuzzy logic more accurately. In this paper a logical framework is proposed based on fuzzy inference systems to approximate trip distribution function.
REFERENCES Celikoglu B, Hilmi Cigizoglu K, Hekmet (2007). Public transportation trip flow modeling with generalized regression neural networks. Adv. Eng. Softw., 38: 71–79. Chanas S, Delgado M, Verdegay JL, Vila MA (1993). Interval and fuzzy extensions of classical transportation problems. Transp. Plann. Technol. 17: 203-218. Chang YH, Shyu TH (1993). Traffic signal installation by the expert system using fuzzy set theory for inexact reasoning. Transp. Plan. Technol., 17: 191-202. Chen H, Muller SG (2001). Use of sequential learning for short-term traffic flow forecasting. Transp. Res. Part C Emerg. Technol., 9(5): 319–336. Chen L, May A, Auslander D (1990). Freeway ramp control using fuzzy set theory for inexact reasoning. Transp. Res., 24A: 15-25. Deb SK (1993). Fuzzy set approach in mass transit mode choice. In: Ayyub, B.M. (Ed.), Proceedings of ISUMA '93, Second International Symposium on Uncertainty Modeling and Analysis. IEEE Computer Press, College Park, Maryland, pp.262-268. Dougherty MS (1995). A review of neural networks applied to transport. Transp Res Part C Emerg Technol., 3(4): 247–260.
Golob FT (2000). A simultaneous model of household activity participation and trip chain generation. In: Transportation Research Record, J. Transport. Res. Board., No. 34, TRB. Washington, USA. 355-376. Jang JSR (1997). Sun, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall. Lin CT, Chiu H, Chu PY (2006). Agility index in supply chain. Int. J. Prod. Econ. 100: 285-299. Lotan T, Koutsopoulos H, (1993). Route choice in the presence of information using concepts from fuzzy control and approximate reasoning. Transp. Plan. Technol., 17: 113-126. Lotan T, Koutsopoulos H (1993). Models for route choice behaviour in the presence of information using concepts from fuzzy set theory and approximate reasoning. Transport., 20: 129-155. Makvandi P, Alavi, SH, Hajiha A (2006). An Exploration of Experts' Subjective Patterns in Behavioral Based Job Qualification Using Choquet Integral, Proceedings of the 6th WSEAS Int. Conf. on Systems Theory, Scientific Computation, Elounda, Greece, August 21-23. 14-18. Mamdani EH, Assilian S (1975). An experiment in linguistic synthesis with a fuzzy logic controller." Int. J. Man-Machine Stud., 7(1): 1-13. Messai N, Thomas P, Lefebvre D, El Moudni A (2002). Optimal neural networks architectures for the flow-density relationships of traffic models. Math. Comput Simul., 60(3–5) 401–409. Milosavljevic N, Teodorovic D, Papic V, Pavkovic G (1996). A fuzzy approach to the vehicle assignment problem. Transp. Plan. Technol., 20:33-47. Murat H, Celik S (2010). Sample size needed for calibrating trip distribution and behavior of the gravity model. J. Transp. Geogr., 18: 83–190. Nanda R, Kikuchi S (1993). Estimation of trip O-D matrix when input and output are fuzzy. In: Ayyub, B.M. (Ed.), Proceedings of ISUMA '93, Second International Symposium on Uncertainty Modeling and Analysis. IEEE Computer Press, College Park, Maryland. pp.104111. Novák V, Perfilieva I, Močkoř J (1999) Mathematical principles of fuzzy logic Dodrecht: Kluwer Academic. ISBN 0-7923-8595-0.
514
Afr. J. Bus. Manage.
Ortuzar JD, Willumsen LG (2001). The Traffic Assignment Problem: Models and Methods. VSP, Wiley, New York. Utrecht, The Netherlands. Ross TJ (2004). Fuzzy Logic with Engineering Applications. Second Edition. John Wiley and Sons Ltd. The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England. Ruiter ER, Ben-Akiva ME (1978). Disaggregate travel demand models for the San Francisco area: system structure, component models and application procedures. Transp. Res. Record, 673: 121–128. Smiller J, Hoel LA (2006). Assessing the utility of private information in transportation planning studies: A case study of trip generation analysis. J. Socio-Econ. Plan. Sci., 40(3): 94-118. Sugeno M (1985). Industrial applications of fuzzy control. Elsevier Science Pub. Co. Susilo YO, Kitamura R (2007). Structural changes in commuters’ daily travel: the case of auto and transit commuters in the Osaka metropolitan area of Japan, 1980–2000. Transp. Res. Part A: Policy Pract. 42: 95–115. Teodorovic D (1999). Fuzzy logic systems for transportation engineering: the state of the art, Transport. Res. Part A 33: 337-364 Teodorovic D, Babic O (1993). Fuzzy inference approach to the flow management problem in air traffic control. Transp. Plan. Technol., 17: 165-178.
Teodorovic D, Kalic, M (1995). A fuzzy route choice model for air transportation networks. Transp. Plan. Technol., 19: 109-119. Vukadinovic K, Teodorovic D (1994). A fuzzy approach to the vessel dispatching problem. Eur. J. Oper. Res. 76: 155-164. Xu W, Chan Y (1993). Estimating an origin-destination matrix with fuzzy weights. Part 1: Methodology. Transport. Plan. Technol., 17: 127144. Yao L, Guan H, Yan H (2008). Trip Generation Model Based on Destination Attractiveness, Tsinghua Sci. Technol., 13(5): 632-635. Yun SY, Namkoong S, Rho JH, Shin SW, Choi JU (1998). A performance evaluation of neural network models in traffic volume forecasting. Math. Comput Model. 27(9–11): 293–310. Zhang H, Ritchie SG, Lo ZP (1997). Macroscopic modeling of freeway traffic using an artificial neural network. Transp. Res. Rec., 1588:110–119.
