Multi-Objective Optimization in Computational Intelligence

Transcription

1 Multi-Objective Optimization in Computational Intelligence Theory and Practice Lam Thu Bui University of New South Wales, Australia Sameer Alam University of New South Wales, Australia Information Science REFERENCE INFORMATION SCIENCE REFERENCE Hershey New York

2 Detailed Table of Contents Foreword Preface Acknowledgment xiv xv xix Section I Fundamentals Chapter I An Introduction to Multi-Objective Optimization 1 Lam Thu Bui, University o/new South Wales, Australia Sameer Alam, University of New South Wales, Australia This chapter is devoted to summarize all common concepts related to multiobjective optimization (MO). An overview ovtraditional" as well as Cl-based MO is given. Further, all aspects of Performance assessment for MO techniques are discussed. Finally, challenges facing MO techniques are addressed. All of these description and analysis give the readers basic knowledge for understandings the rest of the book. Chapter II Multi-Objective Particles Swarm Optimization Approaches 20 Konstantinos E. Parsopoulos, University ofpatras, Greece Michael N. Vrahatis, University ofpatras, Greece The multiple criteria nature of most real World problems has boosted research on multiobjective algorithms that can tackle such problems effectively, with the smallest possible computational bürden. Particle Swarm Optimization has attracted the interest of researchers due to its simplicity, effectiveness and efficiency in solving numerous Single-objective optimization problems. Up-to-date, there are a significant number of multiobjective Particle Swarm Optimization approaches and applications reported in the literature. This chapter aims at providing a review and discussion of the most established results on this field, as well as exposing the most active research topics that can give initiative for future research.

3 Chapter III Generalized Differential Evolution for Constrained Multi-Objective Optimization 43 Saku Kukkonen, Lappeenranta University of Technology, Finland Jouni Lampinen, University of Vaasa, Finland Multiobjective optimization with Evolutionary Algorithms has been gaining popularity recently because its applicability in practical problems. Many practical problems contain also constraints, which must be taken care of during optimization process. This chapter is about Generalized Differential Evolution, which is a general-purpose optimizer. It is based on a relatively recent Evolutionary Algorithm, Differential Evolution, which has been gaining popularity because of its simplicity and good observed Performance. Generalized Differential Evolution extends Differential Evolution for problems with several objectives and constraints. The chapter concentrates on describing different development phases and Performance of Generalized Differential Evolution but it also contains a brief review of other multiobjective DE approaches. Ability to solve multiobjective problems is mainly discussed, but constraint handling and the effect of control parameters are also covered. It is found that GDE versions, in particular the latest version, are effective and efücient for solving constrained multiobjective problems. Chapter IV Towards a More Efficient Multi-Objective Particle Swarm Optimizer 76 Luis V. Santana-Quintero, CINVESTAV-IPN, Evolutionary Computation Group (EVOCINV), Mexico Noel Ramirez-Santiago, CINVESTAV-IPN, Evolutionary Computation Group (EVOCINV), Mexico Carlos A. Coello Coello, CINVESTA V-IPN, Evolutionary Computation Group (EVOCINV), Mexico This chapter presents a hybrid between a particle swarm optimization (PSO) approach and scatter search. The main motivation for developing this approach is to combine the high convergence rate of the PSO algorithm with a local search approach based on scatter search, in order to have the main advantages of these two types of techniques. We propose a new leader selection scheine for PSO, which aims to accelerate convergence by increasing the selection pressure. However, this higher selection pressure reduces diversity. To alleviate that, scatter search is adopted after applying PSO, in order to spread the Solutions previously obtained, so that a better distribution along the Pareto front is achieved. The proposed approach can produce reasonably good approximations of multiobjective problems of high dimensionality, performing only 4,000 fitness function evaluations. Test problems taken from the specialized literature are adopted to validate the proposed hybrid approach. Results are compared with respect to the NSGA- II, which is an approach representative of the state-of-the-art in the area. Chapter V Multi-Objective Optimization Using Artificial Immune Systems 106 Licheng Jiao, Xidian University, RR. China Maoguo Gong, Xidian University, RR. China Wenping Ma, Xidian University, RR. China Ronghua Shang, Xidian University, RR. China

4 This chapter focuses on extending Artificial Immune Systems (AIS) to solve multiobjective problems. It introduces two multiobjective optimization algorithms using AIS, the Immune Dominance Clonal Multi-objective Algorithm (IDCMA), and the Non-dominated Neighbour Immune Algorithm (NNIA). IDCMA is unique in that its fitness values of current dominated individuals are assigned as the values of a custom distance measure, termed as Ab-Ab affinity, between the dominated individuals and one of the nondominated individuals found so far. Meanwhile, NNIA solves multiobjective optimization problems by using a non-dominated neighbour-based selection technique, an immune inspired Operator, two heuristic search Operators and elitism. The unique selection technique of NNIAonly selects minority isolated nondominated individuals in population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. Chapter VI Lexicographic Goal Programming and Assessment Tools for a Combinatorial Production Problem 148 Seamus M. McGovern, U.S. DOTNational Transportation Systems Center, USA Surendra M. Gupta, Northeastern University, USA NP-complete combinatorial problems often necessitate the use of near-optimal Solution techniques including heuristics and metaheuristics. The addition of multiple optimization criteria can further complicate comparison of these Solution techniques due to the decision-maker's weighting schema potentially masking search limitations. In addition, many contemporary problems lack quantitative assessment tools, including benchmark data sets. This chapter proposes the use of lexicographic goal programming for use in comparing combinatorial search techniques. These techniques are implemented here using a recently formulated problem from the area of production analysis. The development of a benchmark data set and other assessment tools is demonstrated, and these are then used to compare the Performance of a genetic algorithm and an H-K general-purpose heuristic as applied to the production-related application. Chapter VII Evolutionary Population Dynamics and Multi-Objective Optimisation Problems 185 Andrew Lewis, Griffith University, Australia Sanaz Mostaghim, University of Karlsruhe, Germany Marcus Randall, Bond University, Australia Problems for which many objective functions are to be simultaneously optimised are widely encountered in science and industry. These multiobjective problems have also been the subject of intensive investigation and development recently for metaheuristic search algorithms such as ant colony optimisation, particle swarm optimisation and extremal optimisation. In this chapter, a unifying framework called evolutionary programming dynamics (EPD) is examined. Using underlying concepts of seif organised criticality and evolutionary programming, it can be applied to many optimisation algorithms as a Controlling metaheuristic, to improve Performance and results. We show this to be effective for both continuous and combinatorial problems.

5 Section II Applications Chapter VIII Multi-Objective Evolutionary Algorithms for Sensor Network Design 208 Ramesh Rajagopalan, Syracuse University, USA Chilukuri K. Mohan, Syracuse University, USA Kishan G. Mehrotra, Syracuse University, USA Pramod K. Varshney, Syracuse University, USA Many sensor network design problems are characterized by the need to optimize multiple conflicting objectives. However, existing approaches generally focus on a single objective (ignoring the others), or combine multiple objectives into a single function to be optimized, to facilitate the application of classical optimization algorithms. This restricts their ability and constrains their usefulness to the network designer. A much more appropriate and natural approach is to address multiple objectives simultaneously, applying recently developed multi-objective evolutionary algorithms (MOEAs) in solving sensor network design problems. This chapter describes and illustrates this approach by modeling two sensor network design problems (mobile agent routing and sensor placement), as multiobjective optimization problems, developing the appropriate objective functions and discussing the tradeoffs between them. Simulation results using two recently developed MOEAs, viz., EMOCA (Rajagopalan, Mohan, Mehrotra, & Varshney, 2006) and NSGA-II (Deb, Pratap, Agarwal, & Meyarivan, 2000), show that these MOEAs successfully discover multiple Solutions characterizing the tradeoffs between the objectives. Chapter IX Evolutionary Multi-Objective Optimization for DNA Sequence Design 239 Soo-Yong Shin, Seoul National University, Korea In-Hee Lee, Seoul National University, Korea Byoung-Tak Zhang, Seoul National University, Korea Finding reliable and efficient DNA sequences is one of the most important tasks for successful DNArelated experiments such as DNA Computing, DNA nano-assembly, DNA microarrays and polymerase chain reaction. Sequence design involves a number of heterogeneous and conflicting design criteria. Also, it is proven as a class of NP problems. These suggest that multiobjective evolutionary algorithms (MOEAs) are actually good candidates for DNA sequence optimization. In addition, the characteristics of MOEAs including simple addition/deletion of objectives and easy incorporation of various existing tools and human knowledge into the final decision process could increase the reliability of final DNA sequence set. In this chapter, we review multiobjective evolutionary approaches to DNA sequence design. In particular, we analyze the Performance of e-multiobjective evolutionary algorithms on three DNA sequence design problems and validate the results by showing superior Performance to previous techniques.

6 Chapter X Computational Intelligence to Speed-Up Multi-Objective Design Space Exploration of Embedded Systems 265 Giuseppe Ascia, Universitä degli Studi di Catania, Italy Vincenzo Catania, Universitä degli Studi di Catania, Italy Alessandro G Di Nuovo, Universitä degli Studi di Catania, Italy Maurizio Palesi, Universitä degli Studi di Catania, Italy Davide Patti, Universitä degli Studi di Catania, Italy Multi-Objective Evolutionary Algorithms (MOEAs) have received increasing interest in industry, because they have proved to be powerful optimizers. Despite the great success achieved, MOEAs have also encountered many challenges in real-world applications. One of the main difficulties in applying MOEAs is the large number of fitness evaluations (objective calculations) that are often needed before a well acceptable Solution can be found. In fact, there are several industrial situations in which both fitness evaluations are computationally expensive and, meanwhile, time available is very low. In this applications efücient strategies to approximate the fitness function have to be adopted, looking for a trade-off between optimization Performances and efficiency. This is the case of a complex embedded System design, where it is needed to define an optimal architecture in relation to certain Performance indexes respecting strict time-to-market constraints. This activity, known as Design Space Exploration (DSE), is still a great challenge for the EDA (Electronic Design Automation) Community. One of the most important bottlenecks in the overall design flow of an embedded System is due to the Simulation. Simulation occurs at every phase of the design flow and it is used to evaluate a system candidate to be implemented. In this chapter we focus on System level design proposing an hybrid computational intelligence approach based on fuzzy approximation to speed up the evaluation ofa candidate System. The methodology is applied to a real case study: optimization of the Performance and power consumption of an embedded architecture based on a Very Long Instruction Word (VLIW) microprocessor in a mobile multimedia application domain. The results, carried out on a multimedia benchmark suite, are compared, in terms of both Performance and efficiency, with other MOGAs strategies to demonstrate the scalability and the accuracy of the proposed approach. Chapter XI Walking with EMO: Multi-Objective Robotics for Evolving Two, Four, and Six-Legged Locomotion 300 Jason Teo, Universiti Malaysia Sabah, Malaysia Lynnie D. Neri, Universiti Malaysia Sabah, Malaysia Minh H. Nguyen, University o/new South Wales, Australia Hussein A. Abbass, University ofnew South Wales, Australia This chapter will demonstrate the various robotics applications that can be achieved using evolutionary multiobjective optimization (EMO) techniques. The main objective of this chapter is to demonstrate practica! ways of generating simple legged locomotion for simulated robots with two, four and six legs using EMO. The operational Performance as well as complexities of the resulting evolved Pareto solu-

7 tions that act as Controllers for these robots will then be analyzed. Additionally, the operational dynamics of these evolved Pareto Controllers in noisy and uncertain environments, limb dynamics and effects of using a different underlying EMO algorithm will also be discussed. Chapter XII Evolutionary Multi-Objective Optimization in Energy Conversion Systems: From Component Detail to System Configuration Andrea Toffolo, University ofpadova, Italy 333 The research field on energy conversion Systems presents a large variety of multiobjective optimization problems that can be solved taking füll advantage of the features of evolutionary algorithms. In fact, design and Operation of energy Systems can be considered in several different perspectives (e.g., Performance, efficiency, costs, environmental aspects). This results in a number of objective functions that should be simultaneously optimized, and the knowledge of the Pareto optimal set of Solutions is of fundamental importance to the decision maker. This chapter proposes a brief survey of typical applications at different levels, ranging from the design of component detail to the challenge about the synthesis of the configuration of complex energy conversion Systems. For sake of simplicity, the proposed examples are grouped into three main categories: design of components/component details, design of overall energy System and Operation of energy Systems. Each multiobjective optimization problem is presented with a short background and some details about the formulation. Future research directions in the field of energy Systems are also discussed at the end of the chapter. Chapter XIII Evolutionary Multi-Objective Optimization for Assignment Problems Mark P. Kleeman, Air Force Institute of Technology, USA Gary B. Lamont, Air Force Institute of Technology, USA 364 Assignment problems are used throughout many research disciplines. Most assignment problems in the literature have focused on solving a single objective. This chapter focuses on assignment problems that have multiple objectives that need to be satisfied. In particular, this chapter looks at how multiobjective evolutionary algorithms have been used to solve some of these problems. Additionally, this chapter examines many of the Operators that have been utilized to solve assignment problems and discusses some of the advantages and disadvantages of using specific Operators. Chapter XIV Evolutionary Multi-Objective Optimization in Military Applications Mark P. Kleeman, Air Force Institute of Technology, USA Gary B. Lamont, Air Force Institute of Technology, USA 388 This chapter attempts to provide a spectrum of military multiobjective optimization problems whose characteristics imply that an MOEA approach is appropriate. The choice of selected Operators indicates that good results can be achieved for these problems. Selection and testing of other Operators and associated Parameters may generate "better" Solutions. It is not intended that these problems represent the totality

8 or even the complete spectrum of all military optimization problems. However, the examples discussed are very complex with high-dimensionality and therefore reflect the many difficulties the military faces in achieving their goals. MOEAs with local search are another method of attacking theslems that should provide effective and eflicient Solutions. Compilation ofreferences 430 About the Contributors 461 Index 469