Evolutionary Game Dynamics in Combinatorial Optimization: An Overview

Replicator equations are a class of dynamical systems developed and studied in the context of evolutionary game theory, a discipline pioneered by J. Maynard Smith which aims to model the evolution of animal behavior using the principles and tools of noncooperative game theory. Because of their dynamical properties, they have been recently applied with significant success to a number of combinatorial optimization problems. It is the purpose of this article to provide a summary and an up-to-date bibliography of these applications.

[1]  Marcello Pelillo,et al.  Relaxation labeling processes for the traveling salesman problem , 1993, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan).

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  F. Rendl,et al.  Replicator Dynamics for Evolution Towards the Maximum Clique: Variations and Experiments* , 1998 .

[4]  C. Rossi,et al.  A replicator equations-based evolutionary algorithm for the maximum clique problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[5]  Marcello Pelillo,et al.  Replicator Equations, Maximal Cliques, and Graph Isomorphism , 1998, Neural Computation.

[6]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[7]  Immanuel M. Bomze,et al.  Evolution towards the Maximum Clique , 1997, J. Glob. Optim..

[8]  Kishan G. Mehrotra,et al.  Replicators, Majorization and Genetic Algorithms: New Models and Analytical tools , 1996, FOGA.

[9]  M. Pelillo.  Relaxation labeling networks for the maximum clique problem , 1996 .

[10]  David S. Johnson.  The NP-Completeness Column: An Ongoing Guide , 1986, J. Algorithms.

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

[12]  Volker Stix,et al.  Genetic engineering via negative fitness:Evolutionary dynamics for global optimization , 1999, Ann. Oper. Res..

[13]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[14]  Marcello Pelillo,et al.  Parallelizable Evolutionary Dynamics Principles for Solving the Maximum Clique Problem , 1996, PPSN.

[15]  Heinz Mühlenbein,et al.  Evolution algorithms in combinatorial optimization , 1988, Parallel Comput..

[16]  Immanuel M. Bomze.  Global Escape Strategies for Maximizing Quadratic Forms over a Simplex , 1997, J. Glob. Optim..

[17]  T. Motzkin,et al.  Maxima for Graphs and a New Proof of a Theorem of Turán , 1965, Canadian Journal of Mathematics.

[18]  Marcello Pelillo,et al.  Evolutionary Approach to the Maximum Clique Problem: Empirical Evidence on a Larger Scale , 1997 .

[19]  A. Jagota,et al.  Feasible and infeasible maxima in a quadratic program for maximum clique , 1996 .

[20]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[21]  Kishan G. Mehrotra,et al.  Optimization Using Replicators , 1995, ICGA.

[22]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[23]  Volker Stix,et al.  Approximating the maximum weight clique using replicator dynamics , 2000, IEEE Trans. Neural Networks Learn. Syst..

[24]  Kaleem Siddiqi,et al.  Matching Hierarchical Structures Using Association Graphs , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Claudio Rossi,et al.  A new "annealed" heuristic for the maximum clique problem , 2000 .

[26]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[27]  Tibor Csendes,et al.  Developments in Global Optimization , 1997 .

[28]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[29]  Panos M. Pardalos,et al.  Continuous Characterizations of the Maximum Clique Problem , 1997, Math. Oper. Res..