Discrete-Event Simulation Optimization: A Review of ...

Proceedings SCSC '13 Proceedings of the 2013 Summer Computer Simulation Conference, Article No. 47 Society for Modeling & Simulation International Vista, CA ©2013 ISBN: 978-1-62748-276-9

Discrete-Event Simulation Optimization: A Review of Past Approaches and Propositions for Future Direction Linda Ann Riley, Ph.D. Roger Williams University School of Engineering, Computing and Construction Management [email protected]

Keywords: discrete-event simulation, optimization, algorithmic optimization techniques Abstract Over the past twenty years, a significant body of work has been undertaken on the topic of methods and approaches to optimizing discreteevent simulation models. Then, as is now, one of the greatest challenges in optimizing discreteevent simulations is the inability to precisely identify “the” optimal solution to a given system model. This is especially the case as the feasible solution space expands. Also over the past twenty years, computational speed has increased, computing and modeling costs have decreased and theoretical developments in the field of simulation optimization have emerged. Yet a divide appears to be widening. Recent literature indicates a lack of new, innovative approaches to optimizing large scale discrete-event simulation models as well as an absence in addressing the growing chasm between the simulation modeling, optimization and outcome improvement processes. Many of the studies and advances undertaken in the early to mid-90’s are those still cited today when discussing simulation optimization. This paper discusses and provides an overview of theoretical and methodological directions in discrete-event simulation optimization. In addition, it suggests areas of study for advancing the field. It is proposed that advances should move the field of study and application in the direction of blurring the boundaries between simulation modeling, optimization and change implementation communities instead of widening the gaps.

1. INTRODUCTION Academicians and practitioners have a number of tools to design, measure, study, analyze and improve large, complex systems. One such tool that has been utilized with especially good results is simulation. Discrete-event simulation specifically, allows for the realistic modeling of stochastic events and the many process variations found in most complex, systems. One of the primary outcomes of discrete-event modeling is improvement in a system’s measures of performance Discrete-event simulation is a widely used tool across many disciplines. Although each discipline has system specific applications, the goal of this technique usually involves system analysis and/or performance improvement. By simulating the dynamic nature of a system, one can better understand and control random process variations. Furthermore, a good simulation that realistically captures the system under study serves as a model for experimentation. Since almost all large-scale systems are both dynamic and stochastic in nature, discrete-event simulation is an excellent technique to study and analyze these systems. Algorithmic optimization approaches have evolved over time as discrete-event simulation has become more commonplace. Optimization techniques involve numerous dynamic evaluations of a simulation’s multi-dimensional solutionspace in the search for an optimal solution. Work in the area of discrete-event simulation optimization has concentrated for the most part on the design and evaluation of various algorithmic and heuristic approaches in searching a simulation’s solution space. At a higher level of abstraction, there has been less of a focus on defining optimi-

zation frameworks. Although far outweighed by the work in algorithmic development, work in the area of optimization frameworks has been undertaken by [Joshi et al. 1996] [Abkay 1996], IEEE, as well as the Department of Defense.

2. REVIEW OF DISCRETE-EVENT SIMULATION OPTIMIZATION APPROACHES Because computational time and cost are critical determinants of value and turn-around of the simulation optimization process, a great deal of ongoing work over the years has focused on applying the most appropriate algorithmic approach considering the problem under study. Widelyused search procedures for optimizing a simulation’s feasible solution space include: deterministic search methods; probabilistic search methods and hybrid techniques. Historically, a great deal of the literature in discrete-event simulation optimization is based on the probabilistic search techniques of: simulated annealing [Liu 1999] [Zolfaghari and Liang 1998] [Bailey et al. 1997] [Haddock and Mittenthal 1992] and evolutionary algorithms [Azadivar et al. 1999] [Hopper and Turton 1999] [Pierreval and Tautou 1997]. A second area of algorithmic optimization development has been in hybrid techniques. This approach combines multiple algorithms into a single optimization strategy [Shi et al. 1999] [Feyzbakhsh and Matsui 1999] [Gong et al. 1997]. More recently, optimization strategies developed using evolutionary or nature-inspired algorithms are referred to as metaheuristics [Glover 1986] [Fu et al. 2005] [Glover and Kochenberger 2003]. Metaheuristics provide a framework that overcomes the need to customize an optimization algorithm for different simulation problems. A number of authors have discussed and explored the theoretical underpinnings of metaheuristics as well as various applications [Olafsson 2006] [Yang 2010] [Vasant 2012]. The primary reasons why metaheuristic algorithms are particularly appropriate for discreteevent simulation optimization are that these methods: 1) handle both continuous and discrete input parameters in contrast to search methods

requiring that input factors be expressed explicitly; 2) deal well with conditions of local optima compared to response surface methods; 3) reduce computational complexity in contrast to other search techniques, thus reducing solution identification speed, and; 4) perform quite well under test conditions comparing a generated optimum with complete enumeration of the solution space. Other less applied algorithmic approaches for optimizing discrete-event simulation models include particle swarm optimization [Clerc 2006] [Olsson 2011], honey bee algorithms [Nakrani and Tovey 2006] and fire fly algorithms [Yang 2009]. Table 1, Overview of Commonly Used Discrete-Event Simulation Optimization Approaches and Algorithms presents the traditionally used simulation optimization algorithms with brief comments on the advantages, disadvantages and processes involved in undertaking each. The table also includes references to a sampling of the seminal work in the area. 3. CHALLENGES WITH ADVANCING THE KNOWLEDGE BASE OF DISCRETE-EVENT SIMULATION OPTIMIZATION One of the primary drawbacks of the system modeling process is the lack of integration between the simulation model, the optimization process and actions to enact system change as a result of the optimization process. Ultimately the goal of modeling many large-scale systems is to increase the efficiency with which the system operates as measured by the maximization or minimization of selected parameters of the objective function. Looking to the future, more emphasis should be placed on blurring the boundaries between the simulation model, optimization and change processes. To accomplish this goal, two propositions are advanced in this paper. 1. Move from viewing discrete-event simulation optimization as a static tool to one that is dynamically integrated into operating practices. For the most part, the present use of simulation optimization in large-scale system simulation scenarios is geared to problems that seek an op-

Table 1. Overview of Commonly Used Discrete-Event Simulation Optimization Approaches and Algorithms Method

General Advantages

General Disadvantages

Process

Intuitive Methods

 When used by an individual familiar with the system (expert), the method can yield good results.  This method is a good one to demonstrate the concept of simulation optimization in a teaching environment.

 Computational time.  Simulation time.  No guarantee or confidence that the ending solution is the optimal solution.  Continuous variables are problematic.  Difficulty in selecting both starting and stopping points for the search.

 The user selects input parameters and undertakes an iterative process that involves: 1) varying the parameter levels; 2) completing a statistically valid number of simulation replications and runs, and; 3) altering the input parameters and reevaluating the results. The objective of this method is to find increasingly better solutions.

Complete Enumeration

 Will produce the optimal solution with small models defined by a finite solution space.

 Complete factorial experiment of the model is undertaken. Analysis of all treatment combinations.

Tabu Search (see [Lopez-Garcia et al. 1999] [Glover 1977]

 Deals well with solution spaces characterized by local optima.

 Computational time and cost.  Works only with discrete variables.  Wasted effort due to testing every feasible solution in the feasible solution space.  Not well-developed as a simulation optimization methodology.  Few studies comparing accuracy and precision of results.  Works only for discrete optimization models.

Pattern Search (see [Findler 1987]

 Successful search pattern transferrable to similar simulation models.

 Does not deal well with nonunimodality.

 Search moves in direction of increasing improvement of the objective function by “steps.” Step sizes vary depending on the sensitivity to change in the objective function until a user-defined convergence test or tolerance is satisfied.

 Feasible solution space is explored by moving from one candidate to its best neighbor. Movement occurs even if degradation in the objective function is a result. Tested solutions are considered “tabu” for a user defined number of iterations. Intensification and diversifications strategies are used to refine the search direction.

Method

General Advantages

General Disadvantages

Process

Genetic Algorithms [ Hopper 1999] [Collins 1998] [Aytug et al.1998] [Salzman and Breitenecker 1995] [Wellman and Gemmill 1995] [Michalewiez 1994] [Goldberg 1994, 1989] [Holland, 1975]

 Relatively fast compared to other search techniques.  Interface process with simulation models is easy due to the design of the algorithms.  Does a good job at identifying the global optimum in models with multiple local optima.  Algorithms are extensible.  Robust method.  Low computational complexity.  Good building block for hybrid methods.  Technique is efficient at moving from local optima.  Less computational time required for each search iteration however more computational time required overall because more iterations usually are needed.  Low computational complexity.  Process avoids cycling.  Good building block for hybrid methods.  Builds on established successful algorithmic procedures.  Expected lower computational complexity.  Expected higher accuracy.  Highly customizable for specific scenarios.  Usually designed to handle both discrete and continuous input parameters quite well.

 Genetic algorithms can be hard to analyze and design depending on the complexity of the manufacturing system being simulated.  Recognition of the need for more theoretical work in testing the accuracy of produced results.

 Based on the concept of evolution, genetic algorithms contain three operators: selection, crossover and mutation. The search process involves coding the parameter set and searching a population of points by means of probabilistic transition rules. The search ends when conditions of a termination rule are met.

 Process can require a great deal of computation time to find the optimal solution.  Attention must be paid to the proper selection of a seed solution or current state starting point.

 Search process involves three states: current state, neighboring state and optimal states. At each iteration, a change is made in the current state and evaluated against a neighboring state by means of cost function. Transitional probabilities and a temperature parameter dictate the likelihood of moving from one state to another. The search ends when a user-defined number of iterations or a user-defined number of optimal states is achieved.

 Lack of algorithmic validation.  Usually not extensible.  Interface code can become problematic depending on the hybrid technique.  Customization can preclude portability for other manufacturing scenarios.

 Process is dependent on the hybrid technique building blocks, whether evolutionary strategies, simulated annealing, deterministic searches, or other.

Simulated Annealing [ Liu, 1999] [Zolfaghari and Liang 1998] [ Bailey et al.1997] [Aarts and Korst, 1989] [Kirkpatrick et al. 1983]

Hybrid Techniques [ Alireza and Matsui 1999] [ Azadivar and Tompkins 1999] [Mason et al. 1999] [Fleury et al. 1999] [Shi et al. 1999] [Chen and Gen 1997] [Ahmed et al., 1998] [Emelyanov and Iassinovski 1997] [Gong et al.1997] [Dolgui and Ofitserov1997]

timal solution at time-specific points. Because of the size of the models and the time required to run the model, the process is undertaken as a static event in contrast to an integrated dynamic process. With the exception of some logistics optimization applications involving transportation scheduling, in most manufacturing and service settings, optimization is not implemented as a dynamic tool continuously running in the background and ultimately driving certain operating decisions. To be incorporated as a dynamic tool that contributes to intelligent system design, work must continue in further integrating the simulation modeling, optimization and improvement implementation processes. As optimization algorithms become more sophisticated, the simulation optimization process appears to be moving further away from the modeling process. This is further exacerbated by the three knowledge domains governing the three processes. For the most part, the large-scale system simulation modeling process is owned by the industrial engineers, operation researchers and simulationist community. Optimization algorithms and frameworks are driven by the computer science community and the improvement implementation processes are owned by the efficiency/managerial community. The optimization black box is becoming more and more removed from the ultimate modelers and especially users of the simulation’s results. The gap appears to be widening between research and theoretical development in optimization approaches and applications in contrast to narrowing. 2. Need for simulation optimization procedures to intelligently recognize input parameters. When modeling large-scale system problems, the use of off-the-shelf simulation packages is many times necessary. Most of the most popular discrete-event simulation packages have fast learning curves, are graphically realistic, affordable, and produce easy to read, customized analysis reports. In addition, add-on modules that allow for external code-writing and customization are common features of today’s off-the-shelf simulation packages. In most cases also, these packages have built-in optimization modules.

One of the greatest drawbacks however of these off-the-shelf simulation packages is the lack of flexibility in altering the resident optimization algorithms. Unless customized code is developed external to the simulation package and then integrated into the simulation, the user must take what the vendor provides. Depending on the desired optimization function and input parameters, the vendor resident procedure may be wholly inadequate for the situation under study. Furthermore, discrete-event package vendors closely guard as proprietary knowledge, the exact code used to optimize their products. Selection of a specific procedure should be dependent on unique characteristics of the optimization problem and not necessarily what is included in the offthe-shelf simulation software. This is perhaps one reason why the move toward metaheuristic frameworks has occurred. These general purpose approaches are evaluated as effective and efficient over a range of problems. To address this shortfall, some type of intelligent interface is suggested. This interface could be designed to choose from among a number of algorithmic optimization procedures based on the objective function and input parameters under evaluation at any particular moment. This implies perhaps an additional layer of AI/neural code that could be incorporated into the optimization process. Ultimately, this intelligent interface could “learn” to recognize common optimization scenarios, select starting and stopping rules, and potentially also interface with the system improvement framework. As a further extension to the intelligent interface, dynamic algorithmic visualization capabilities could be incorporated into the optimization procedures. Immersive technologies are used in many simulation arenas. Incorporating immersive visualization into optimization would serve to bring a transparency between the modeling and optimization processes. This would allow users and decision makers to interactively view, and potentially redirect the optimization process. In essence, this feature would provide the decision maker the ability to immerse him or herself into the model, thus “directing” both the simulation and optimization processes.

4. CONCLUSION As a tool to design and improve large-scale systems, discrete-event simulation optimization is ideally suited for addressing the complexity associated with systems characterized as discreteevent and stochastic in nature. With the variety and robustness of algorithmic optimization procedures, virtually all types of system problems can be modeled and optimized. Yet, even though the algorithmic development in optimization has been well researched, there appears to be widening gaps between the modeling, optimization and implementation communities. Furthermore, due to lack of transparency among the work of these three groups, development of integrative frameworks has been lacking. For optimization work to advance in discrete-event modeling, it is proposed that movement toward the design of dynamically integrated simulation/optimization/implementation products be furthered explored. In addition, intelligent optimization interfaces are also proposed for off-the-shelf discrete-event simulation packages. Advances in the area of discrete-event simulation optimization should move in the direction of blurring the boundaries between simulation modeling, optimization and change implementation instead of widening the gaps. REFERENCES Aarts, E. and Korst, J. (1989) Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. John Wiley and Sons, Chichester, U.K.

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tion of Associate Department Head for the Department of Industrial Engineering at New Mexico State University (NMSU). In addition, she served as the founder and Director of the Advanced Modeling and Simulation Laboratory at NMSU and Director of a university-wide economic development research center. Dr. Riley has extensive business and engineering consulting experience. As well, she is an active researcher, teacher and author in the area of simulation modeling and large-scale system optimization. She has taught over 30 different courses in her career, many of them simulation focused and has written or co-authored over 120 academic/research publications and over 150 research proposals. Dr. Riley earned an M.S. in Industrial Engineering as well as a Ph.D. in Logistics from New Mexico State University, completed a two-year post graduate fellowship at Brown University, earned an MBA from Suffolk University and an undergraduate degree from Boston University.