Metaheuristic Optimization Backgrounds: A Literature Review

Solving optimization problems becomes a central theme not only on operational research but also on several research areas like robotic, medicine, economic etc. The number of support decision problems that can be formalized as an optimization problem is growing rapidly. This study represents a literature revue of Metaheuristics optimization. Metaheuristics are applied to all kinds of combinatorial problems, and they can also be adapted to continuous problems. These approaches which include the simulated annealing method, genetic algorithms, taboo search method, the Ant Colony Algorithms, particle swarm optimization (PSO) etc. are for both mono-objective problems and multi-objective problems. The first area analyzes the inherent difficulties of each objective function, while the second treats the case of the simultaneous presence of several objectives. We will see that the tow aspects are often related in practice. Before focusing on the multi-objective optimization, it is necessary to explain the context of the mono-objective optimization. A special attention is given to the method of particle swarm optimization (PSO).

[1]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[2]  J. Dréo,et al.  Métaheuristiques pour l'optimisation difficile , 2003 .

[3]  Russell C. Eberhart,et al.  Particle swarm with extended memory for multiobjective optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[4]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[5]  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).

[6]  C. L. Valenzuela.  A simple evolutionary algorithm for multi-objective optimization (SEAMO) , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[7]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[8]  T. Friesz,et al.  The multiobjective equilibrium network design problem revisited: A simulated annealing approach , 1993 .

[9]  P. Siarry,et al.  Electronic component model minimization based on log simulated annealing , 1994 .

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

[11]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[12]  Riccardo Poli,et al.  Particle Swarm Optimisation , 2011 .

[13]  Xiaodong Li,et al.  A Non-dominated Sorting Particle Swarm Optimizer for Multiobjective Optimization , 2003, GECCO.

[14]  James Kennedy,et al.  The Behavior of Particles , 1998, Evolutionary Programming.

[15]  Jeffrey Horn,et al.  Multiobjective Optimization Using the Niched Pareto Genetic Algorithm , 1993 .

[16]  Marco Dorigo,et al.  Ant colony optimization theory: A survey , 2005, Theor. Comput. Sci..

[17]  J. S. F. Barker,et al.  Simulation of Genetic Systems by Automatic Digital Computers , 1958 .

[18]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

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

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

[21]  Tom Fearn,et al.  Particle Swarm Optimisation , 2014 .

[22]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[23]  E. Wilson,et al.  Sociobiology: The New Synthesis , 1975 .

[24]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[25]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

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

[27]  M.N. Vrahatis,et al.  Particle swarm optimizers for Pareto optimization with enhanced archiving techniques , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[28]  W. Renhart,et al.  Pareto optimality and particle swarm optimization , 2004, IEEE Transactions on Magnetics.

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

[30]  Konstantinos E. Parsopoulos,et al.  MULTIOBJECTIVE OPTIMIZATION USING PARALLEL VECTOR EVALUATED PARTICLE SWARM OPTIMIZATION , 2003 .

[31]  Tapabrata Ray,et al.  A Swarm Metaphor for Multiobjective Design Optimization , 2002 .

[32]  Andries Petrus Engelbrecht,et al.  Using neighbourhoods with the guaranteed convergence PSO , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[33]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[34]  J. Deneubourg,et al.  Self-organized shortcuts in the Argentine ant , 1989, Naturwissenschaften.

[35]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[36]  Marc Gravel,et al.  Optimisation Multi-Objectifs À L'Aide D'Un Algorithme De Colonie De Fourmis , 2004 .

[37]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[38]  A. Berro,et al.  Optimisation multiobjectif et stratégies d' évolution en environnement dynamique , 2001 .

[39]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[40]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[41]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[42]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[43]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[44]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[45]  John H. Holland,et al.  Genetic Algorithms and the Optimal Allocation of Trials , 1973, SIAM J. Comput..

[46]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[47]  M. N. Vrahatis,et al.  Particle swarm optimization method in multiobjective problems , 2002, SAC '02.

[48]  I. Loshchilov,et al.  A Comparison of Multiobjective Evolutionary Algorithms , 2009 .

[49]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[50]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[51]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

[52]  M. Schoenauer,et al.  Contrôle d'un algorithme génétique , 1996 .

[53]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[54]  Tian Hou Seow,et al.  Particle swarm inspired evolutionary algorithm (PS-EA) for multiobjective optimization problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[55]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

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

[57]  Russell C. Eberhart,et al.  Multiobjective optimization using dynamic neighborhood particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[58]  Prospero C. Naval,et al.  An effective use of crowding distance in multiobjective particle swarm optimization , 2005, GECCO '05.

[59]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[60]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

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

[62]  V. Cerný.  Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[63]  V. Pareto,et al.  Vilfredo Pareto. Cours d’Économie Politique , 1897 .

[64]  E. Ozcan,et al.  Particle swarm optimization: surfing the waves , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[65]  A. Rosa,et al.  Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes , 2005, nlin/0502057.

[66]  M. Gribaudo,et al.  2002 , 2001, Cell and Tissue Research.

[67]  El-Ghazali Talbi,et al.  A Taxonomy of Hybrid Metaheuristics , 2002, J. Heuristics.

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

[69]  Yongling Zheng,et al.  On the convergence analysis and parameter selection in particle swarm optimization , 2003, Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693).

[70]  Mordecai Avriel,et al.  Nonlinear programming , 1976 .

[71]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

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