Evolutionary Algorithms and Multiple Objective Optimization

This chapter presents a review of the most important evolutionary multiobjective optimization techniques developed to date. Using as a basis a simple taxonomy of approaches, we briefly describe and analyze the advantages and disadvantages of each of them, together with some of their applications reported in the literature. Other important issues such as diversity and some of the main techniques developed to preserve it, as well as the need of suitable test functions and metrics that can properly evaluate the performance of these multiobjective optimization techniques are also addressed. We conclude this chapter with a brief outline of some potential paths of future research in this area.

[1]  Rob A. C. M. Broekmeulen Facility Management of Distribution Centres for Vegetables and Fruits , 1995 .

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  Michael Lahanas,et al.  Application of Multiobjective Evolutionary Algorithms for Dose Optimization Problems in Brachytherapy , 2001, EMO.

[4]  Alain Cardon,et al.  Genetic algorithms using multi-objectives in a multi-agent system , 2000, Robotics Auton. Syst..

[5]  Chung-Wei Feng,et al.  Using genetic algorithms to solve construction time-cost trade-off problems , 1997 .

[6]  Soroosh Sorooshian,et al.  Multi-objective global optimization for hydrologic models , 1998 .

[7]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[8]  Patrick D. Surry,et al.  A Multi-objective Approach to Constrained Optimisation of Gas Supply Networks: the COMOGA Method , 1995, Evolutionary Computing, AISB Workshop.

[9]  J. Periaux,et al.  Multi-point optimization using GAs and Nash/Stackelberg games for high lift multi-airfoil design in aerodynamics , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[10]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[11]  Marco Laumanns,et al.  Multi-objective Design Space Exploration of Road Trains with Evolutionary Algorithms , 2001, EMO.

[12]  R. Groppetti,et al.  On a Genetic Multiobjective Approach for the Integration and Optimization of Assembly Product Design and Process Planning , 1997 .

[13]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[14]  W. Stadler Multicriteria Optimization in Engineering and in the Sciences , 1988 .

[15]  Christian Mascle,et al.  Integrated Design and Manufacturing in Mechanical Engineering , 1997 .

[16]  Paolo Serafini Simulated Annealing for Multi Objective Optimization Problems , 1994 .

[17]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[18]  J. Eheart,et al.  Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem , 1995 .

[19]  L Rogers James,et al.  A Parallel Approach to Optimum Actuator Selection With a Genetic Algorithm , 2000 .

[20]  Thomas Hanne,et al.  Global Multiobjective Optimization Using Evolutionary Algorithms , 2000, J. Heuristics.

[21]  Volker Nissen,et al.  On Using Penalty Functions and Multicriteria Optimisation Techniques in Facility Layout , 1995 .

[22]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[23]  W. Cannon The Wisdom of the Body , 1932 .

[24]  Martin J. Oates,et al.  Advanced Multi-Objective Evolutionary Algorithms Applied to Two Problems in Telecommunications , 2000 .

[25]  Alan D. Christiansen,et al.  An empirical study of evolutionary techniques for multiobjective optimization in engineering design , 1996 .

[26]  Singiresu S Rao,et al.  Multiobjective optimization in structural design with uncertain parameters and stochastic processes , 1984 .

[27]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[28]  Shapour Azarm,et al.  On a new constraint handling technique for Multi-Objective Genetic Algorithms , 2001 .

[29]  Samir W. Mahfoud Niching methods for genetic algorithms , 1996 .

[30]  J. W. Hartmann,et al.  Optimal earth orbiting satellite constellations via a pareto genetic algorithm , 1998 .

[31]  Manuel Valenzuela-Rendón,et al.  A Non-Generational Genetic Algorithm for Multiobjective Optimization , 1997, ICGA.

[32]  Peter J. Fleming,et al.  Evolutionary Algorithms and Simulated Annealing for MCDM , 1999 .

[33]  Takao Terano,et al.  A Genetic Algorithm with Tabu Search for Multimodal and Multiobjective Function Optimization , 2000, GECCO.

[34]  Jonathan E. Rowe,et al.  An evolutionary approach to constructing prognostic models , 1999, Artif. Intell. Medicine.

[35]  Min Qiu,et al.  Prioritising and scheduling road projects by genetic algorithm , 1997 .

[36]  Bernard De Baets,et al.  Bi-objective genetic algorithms for forest management: a comparative study. , 2001 .

[37]  W. Stadler NATURAL STRUCTURAL SHAPES (THE STATIC CASE) , 1978 .

[38]  K. Deb Solving goal programming problems using multi-objective genetic algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[39]  Kit Po Wong,et al.  Hybrid GA/SA algorithms for evaluating trade-off between economic cost and environmental impact in generation dispatch , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[40]  P. Reiser,et al.  Genetic algorithms in engineering systems: innovations and applications , 1996 .

[41]  Michael P. Fourman,et al.  Compaction of Symbolic Layout Using Genetic Algorithms , 1985, ICGA.

[42]  David E. Goldberg,et al.  Genetic algorithm design of Pareto optimal broadband microwave absorbers , 1996 .

[43]  Chisu Wu,et al.  Partitioning and allocation of objects in heterogeneous distributed environments using the niched Pareto genetic-algorithm , 1998, Proceedings 1998 Asia Pacific Software Engineering Conference (Cat. No.98EX240).

[44]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[45]  Hajime Kita,et al.  Multi-Objective Optimization by Means of the Thermodynamical Genetic Algorithm , 1996, PPSN.

[46]  Teodor Marcu A Multiobjective Evolutionary Approach to Pattern Recognition for Robust Diagnosis of Process Faults , 1997 .

[47]  Alan D. Christiansen,et al.  Multiobjective optimization of trusses using genetic algorithms , 2000 .

[48]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[49]  C. Mariano,et al.  MOAQ an Ant-Q algorithm for multiple objective optimization problems , 1999 .

[50]  Brian White,et al.  Fuzzy autopilot design using a multiobjective evolutionary algorithm , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[51]  Niraj K. Jha,et al.  MOGAC: a multiobjective genetic algorithm for hardware-software cosynthesis of distributed embedded systems , 1998, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[52]  Mark W. Thomas A Pareto frontier for full stern submarines via genetic algorithm , 1998 .

[53]  Alan D. Christiansen,et al.  Using a new GA-based multiobjective optimization technique for the design of robot arms , 1998, Robotica.

[54]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[55]  Masatoshi Sakawa,et al.  Interactive Decision Marking for Multiobjective Block Angular 0-1 Programming Problems with Fuzzy Parameters through Genetic Algorithms , 1997 .

[56]  Jürgen Teich,et al.  Multidimensional Exploration of Software Implementations for DSP Algorithms , 2000, J. VLSI Signal Process..

[57]  P. Hansen,et al.  Essays and surveys on multiple criteria decision making : proceedings of the Fifth International Conference on Multiple Criteria Decision Making, Mons, Belgium, August 9-13, 1982 , 1983 .

[58]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[59]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[60]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[61]  Ni-Bin Chang,et al.  Water pollution control in the river basin by fuzzy genetic algorithm-based multiobjective programming modeling , 1998 .

[62]  G. Rudolph On a multi-objective evolutionary algorithm and its convergence to the Pareto set , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[63]  Alan S. Perelson,et al.  Population Diversity in an Immune System Model: Implications for Genetic Search , 1992, FOGA.

[64]  R. J. Balling,et al.  The maximin fitness function for multi-objective evolutionary computation: application to city planning , 2001 .

[65]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[66]  Eric Michielssen,et al.  Integer coded Pareto genetic algorithm design of constrained antenna arrays , 1996 .

[67]  Thomas Hanne,et al.  On the convergence of multiobjective evolutionary algorithms , 1999, Eur. J. Oper. Res..

[68]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[69]  Wolfram Stadler,et al.  Fundamentals of Multicriteria Optimization , 1988 .

[70]  S. Ranjithan,et al.  Using genetic algorithms to solve a multiple objective groundwater pollution containment problem , 1994 .

[71]  P. M. Frank,et al.  Genetic evolving of dynamic neural networks with application to process fault diagnosis , 1999, 1999 European Control Conference (ECC).

[72]  Daisuke Sasaki,et al.  Multiobjective evolutionary computation for supersonic wing-shape optimization , 2000, IEEE Trans. Evol. Comput..

[73]  Hajime Kita,et al.  Multi-objective optimization by genetic algorithms: a review , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[74]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[75]  C. Darwin Charles Darwin The Origin of Species by means of Natural Selection or The Preservation of Favoured Races in the Struggle for Life , 2004 .

[76]  Tapan P. Bagchi,et al.  Multiobjective Scheduling by Genetic Algorithms , 1999 .

[77]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[78]  Srigiriraju Kishan Chetan,et al.  Noninferior Surface Tracing Evolutionary Algorithm (NSTEA) for Multiobjective optimization , 2000 .

[79]  Larry J. Eshelman,et al.  The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination , 1990, FOGA.

[80]  Jongsoo Lee,et al.  Constrained genetic search via schema adaptation: An immune network solution , 1996 .

[81]  Singiresu S. Rao Game theory approach for multiobjective structural optimization , 1987 .

[82]  E. Tunstel,et al.  Multiobjective evolutionary path planning via fuzzy tournament selection , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[83]  Carlos A. Coello Coello,et al.  Evolutionary multiobjective design of combinational logic circuits , 2000, Proceedings. The Second NASA/DoD Workshop on Evolvable Hardware.

[84]  Hajime Kita,et al.  Integration of multi-objective and interactive genetic algorithms and its application to animation design , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[85]  Dongkon Lee MULTIOBJECTIVE DESIGN OF A MARINE VEHICLE WITH AID OF DESIGN KNOWLEDGE , 1997 .

[86]  Ignacio J. Ramirez-Rosado,et al.  Reliability and Costs Optimization for Distribution Networks Expansion Using an Evolutionary Algorithm , 1989 .

[87]  Kalmanje Krishnakumar,et al.  Micro-Genetic Algorithms For Stationary And Non-Stationary Function Optimization , 1990, Other Conferences.

[88]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[89]  C. Coello,et al.  CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE , 2000 .

[90]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[91]  E. F. Khor,et al.  Evolutionary algorithms with goal and priority information for multi-objective optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[92]  Rudolf F. Albrecht,et al.  Artificial Neural Nets and Genetic Algorithms , 1995, Springer Vienna.

[93]  Zbigniew Michalewicz,et al.  Evolutionary Computation 2 , 2000 .

[94]  Michael Pilegaard Hansen,et al.  Metaheuristics for multiple objective combinatorial optimization , 1998 .

[95]  Larry J. Eshelman,et al.  Preventing Premature Convergence in Genetic Algorithms by Preventing Incest , 1991, ICGA.

[96]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[97]  Habib Youssef,et al.  Fuzzy Evolutionary Hybrid Metaheuristic for Network Topology Design , 2001, EMO.

[98]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

[99]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[100]  Jason R. Schott Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. , 1995 .

[101]  Paul M. Frank,et al.  Parallel Evolutionary Approach to System Identification for Process Fault Diagnosis , 1998 .

[102]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[103]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

[104]  S. Azarm,et al.  On improving multiobjective genetic algorithms for design optimization , 1999 .

[105]  Y. Yu,et al.  Multiobjective decision theory for computational optimization in radiation therapy. , 1997, Medical physics.

[106]  John H. Holland,et al.  Outline for a Logical Theory of Adaptive Systems , 1962, JACM.

[107]  Alan D. Christiansen,et al.  Two new GA-based methods for multiobjective optimization , 1998 .

[108]  W. Habenicht,et al.  Quad Trees, a Datastructure for Discrete Vector Optimization Problems , 1983 .

[109]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[110]  N.K. Jha,et al.  CORDS: hardware-software co-synthesis of reconfigurable real-time distributed embedded systems , 1998, 1998 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (IEEE Cat. No.98CB36287).

[111]  Hans-Paul Schwefel,et al.  Numerical optimization of computer models , 1981 .

[112]  Tapabrata Ray,et al.  A global optimization model for ship design , 1995 .

[113]  Singiresu S Rao,et al.  Genetic algorithmic approach for multiobjective optimization of structures , 1993 .

[114]  J. Nash THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[115]  P. Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[116]  Carlos A. Coello Coello,et al.  A Micro-Genetic Algorithm for Multiobjective Optimization , 2001, EMO.

[117]  John W. Fowler,et al.  Comparison of Multiple Objective Genetic Algorithms for Parallel Machine Scheduling Problems , 2001, EMO.

[118]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[119]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[120]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[121]  Jongsoo Lee,et al.  GA BASED SIMULATION OF IMMUNE NETWORKS APPLICATIONS IN STRUCTURAL OPTIMIZATION , 1997 .

[122]  Geoffrey T. Parks Multiobjective Pressurised Water Reactor Reload Core Design using a Genetic Algorithm , 1997, ICANNGA.

[123]  Peter J. Bentley,et al.  Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms , 1998 .

[124]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

[125]  H. P. Schwefel,et al.  Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie , 1977 .

[126]  Xiaojian Liu,et al.  Genetic approach to optimal topology/controller design of adaptive structures , 1998 .

[127]  P. K. Chawdhry,et al.  Soft Computing in Engineering Design and Manufacturing , 1998, Springer London.

[128]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[129]  A. Dhingra,et al.  A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables , 1994 .

[130]  Joel N. Morse,et al.  Reducing the size of the nondominated set: Pruning by clustering , 1980, Comput. Oper. Res..

[131]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[132]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

[133]  D.A. Van Veldhuizen,et al.  Finding improved wire-antenna geometries with genetic algorithms , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[134]  Torsten Schaub The Automation of Reasoning with Incomplete Information , 1997, Lecture Notes in Computer Science.

[135]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[136]  C. Coello TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[137]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[138]  Ester Bernadó-Mansilla,et al.  MOLeCS: Using Multiobjective Evolutionary Algorithms for Learning , 2001, EMO.

[139]  El-Ghazali Talbi,et al.  A multiobjective genetic algorithm for radio network optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[140]  Charles J. Petrie,et al.  Using Pareto optimality to coordinate distributed agents , 1995, Artif. Intell. Eng. Des. Anal. Manuf..

[141]  Godfrey A. Walters,et al.  Multiobjective Genetic Algorithms for Pump Scheduling in Water Supply , 1997, Evolutionary Computing, AISB Workshop.

[142]  Lashon B. Booker,et al.  Proceedings of the fourth international conference on Genetic algorithms , 1991 .

[143]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[144]  Sushil J. Louis,et al.  Multi-criteria search and optimization: an application to X-ray plasma spectroscopy , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[145]  Volker Nissen,et al.  Evolutionary Algorithms in Management Applications , 1995 .

[146]  Peter J. Fleming,et al.  Accelerating multi-objective control system design using a neuro-genetic approach , 2000 .

[147]  A. P.-St Boganmeldelse. Vilfredo Pareto: Cours d'économie politique. Professe a l'Université de Lausanne. I—II. Lausanne, F. Rouge. , .

[148]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[149]  Hojjat Adeli,et al.  Advances in Design Optimization , 1994 .

[150]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithm test suites , 1999, SAC '99.

[151]  C. B. Lucasius,et al.  Multicriteria target vector optimization of analytical procedures using a genetic algorithm: Part I. Theory, numerical simulations and application to atomic emission spectroscopy , 1992 .

[152]  E. L. Ulungu,et al.  MOSA method: a tool for solving multiobjective combinatorial optimization problems , 1999 .

[153]  John J. Grefenstette,et al.  Genetic algorithms and their applications , 1987 .

[154]  Michael G.H. Bell,et al.  Optimisation of a fuzzy logic traffic signal controller by a multiobjective genetic algorithm , 1998 .

[155]  Dongkyung Nam,et al.  Parameter optimization of a voltage reference circuit using EP , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[156]  C.C.H. Borges,et al.  A non-generational genetic algorithm for multiobjective optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[157]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.