Dynamic Combinatorial Optimization Problems: A Fitness Landscape Analysis

The role of representations and variation operators in evolutionary computation is relatively well understood for the case of static optimization problems thanks to a variety of empirical studies as well as some theoretical results. In the field of evolutionary dynamic optimization very few studies exist to date that explicitly analyse the impact of these elements on the algorithm’s performance. In this chapter we utilise the fitness landscape metaphor to review previous work on evolutionary dynamic combinatorial optimization. This review highlights some of the properties unique to dynamic combinatorial optimization problems and paves the way for future research related to these important issues.

[1]  GUNAR E. LIEPINS,et al.  Representational issues in genetic optimization , 1990, J. Exp. Theor. Artif. Intell..

[2]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[3]  Von der Fakult Evolutionary Algorithms and Dynamic Optimization Problems , 2003 .

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

[5]  A. Sima Etaner-Uyar,et al.  A Critical Look at Dynamic Multi-dimensional Knapsack Problem Generation , 2009, EvoWorkshops.

[6]  Günther R. Raidl,et al.  Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem , 2005, Evolutionary Computation.

[7]  Xin Yao,et al.  Dynamic combinatorial optimisation problems: an analysis of the subset sum problem , 2011, Soft Comput..

[8]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[9]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[10]  Shengxiang Yang,et al.  Non-stationary problem optimization using the primal-dual genetic algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Ronald W. Morrison,et al.  Designing Evolutionary Algorithms for Dynamic Environments , 2004, Natural Computing Series.

[12]  Shengxiang Yang,et al.  PDGA: the Primal-Dual Genetic Algorithm , 2003, HIS.

[13]  Xin Yao,et al.  Population-Based Incremental Learning With Associative Memory for Dynamic Environments , 2008, IEEE Transactions on Evolutionary Computation.

[14]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[15]  Ivan Zelinka,et al.  Evolutionary Algorithms and Chaotic Systems , 2010, Evolutionary Algorithms and Chaotic Systems.

[16]  Helen G. Cobb,et al.  An Investigation into the Use of Hypermutation as an Adaptive Operator in Genetic Algorithms Having Continuous, Time-Dependent Nonstationary Environments , 1990 .

[17]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[18]  Gary G. Yen,et al.  Dynamic Evolutionary Algorithm With Variable Relocation , 2009, IEEE Transactions on Evolutionary Computation.

[19]  Xin Yao,et al.  A Note on Problem Difficulty Measures in Black-Box Optimization: Classification, Realizations and Predictability , 2007, Evolutionary Computation.

[20]  David E. Goldberg,et al.  Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy , 1987, ICGA.

[21]  Jürgen Branke,et al.  The Role of Representations in Dynamic Knapsack Problems , 2006, EvoWorkshops.

[22]  Riccardo Poli,et al.  Information landscapes , 2005, GECCO '05.

[23]  Kenneth A. De Jong,et al.  Evolving in a Changing World , 1999, ISMIS.

[24]  Dipankar Dasgupta,et al.  Nonstationary Function Optimization using the Structured Genetic Algorithm , 1992, PPSN.

[25]  Robert Schaefer Parallel Problem Solving from Nature - PPSN XI, 11th International Conference, Kraków, Poland, September 11-15, 2010. Proceedings, Part II , 2010, PPSN.

[26]  Shusaku Tsumoto,et al.  Foundations of Intelligent Systems, 15th International Symposium, ISMIS 2005, Saratoga Springs, NY, USA, May 25-28, 2005, Proceedings , 2005, ISMIS.

[27]  K. Yaniasaki,et al.  Dynamic optimization by evolutionary algorithms applied to financial time series , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[28]  Rolf Drechsler,et al.  Applications of Evolutionary Computing, EvoWorkshops 2008: EvoCOMNET, EvoFIN, EvoHOT, EvoIASP, EvoMUSART, EvoNUM, EvoSTOC, and EvoTransLog, Naples, Italy, March 26-28, 2008. Proceedings , 2008, EvoWorkshops.

[29]  Christoph F. Eick,et al.  Supporting Polyploidy in Genetic Algorithms Using Dominance Vectors , 1997, Evolutionary Programming.

[30]  C. R. Reeves,et al.  Landscapes, operators and heuristic search , 1999, Ann. Oper. Res..

[31]  Peter A. N. Bosman,et al.  Learning, anticipation and time-deception in evolutionary online dynamic optimization , 2005, GECCO '05.

[32]  Rajarshi Das,et al.  A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization , 1989, ICGA.

[33]  Thomas Jansen,et al.  A New Framework for the Valuation of Algorithms for Black-Box Optimization , 2002, FOGA.

[34]  Tim Jones Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[35]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[36]  T. Schnier,et al.  Using multiple representations in evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[37]  Shengxiang Yang,et al.  An Analysis of the XOR Dynamic Problem Generator Based on the Dynamical System , 2010, PPSN.

[38]  Ingo Wegener,et al.  Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions , 2003 .

[39]  Xin Yao,et al.  Attributes of Dynamic Combinatorial Optimisation , 2008, SEAL.

[40]  Hendrik Richter,et al.  Evolutionary Optimization and Dynamic Fitness Landscapes , 2010, Evolutionary Algorithms and Chaotic Systems.

[41]  C. Reeves,et al.  Properties of fitness functions and search landscapes , 2001 .

[42]  Philippe Collard,et al.  From GAs to artificial immune systems: improving adaptation in time dependent optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[43]  Shengxiang Yang,et al.  Memory-enhanced univariate marginal distribution algorithms for dynamic optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[44]  Jürgen Branke,et al.  Memory enhanced evolutionary algorithms for changing optimization problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[45]  Thomas Jansen,et al.  Optimization with randomized search heuristics - the (A)NFL theorem, realistic scenarios, and difficult functions , 2002, Theor. Comput. Sci..

[46]  Robert G. Reynolds,et al.  Evolutionary Programming VI , 1997, Lecture Notes in Computer Science.

[47]  Paul H. Calamai,et al.  Generalized benchmark generation for dynamic combinatorial problems , 2005, GECCO '05.

[48]  Peter A. N. Bosman,et al.  Learning and anticipation in online dynamic optimization with evolutionary algorithms: the stochastic case , 2007, GECCO '07.

[49]  Lee Altenberg,et al.  Fitness Distance Correlation Analysis: An Instructive Counterexample , 1997, ICGA.

[50]  A. Sima Etaner-Uyar,et al.  Towards an analysis of dynamic environments , 2005, GECCO '05.

[51]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[52]  R.W. Morrison,et al.  A test problem generator for non-stationary environments , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[53]  Shengxiang Yang,et al.  Adaptive Primal–Dual Genetic Algorithms in Dynamic Environments , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[55]  Shengxiang Yang,et al.  Continuous dynamic problem generators for evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.