Solving Dynamic Optimisation Problem with Variable Dimensions

Over the last two decades, dynamic optimisation problems DOPs have become a challenging research topic. In DOPs, at least one part of the problem changes as time passes. These changes may affect the objective functions and/or constraints. In this paper, we propose and define a novel type of DOP in which dimensions change as time passes. It is called DOP with variable dimensions DOPVD. We also propose a mask detection procedure to help algorithms in solving single objective unconstrained DOPVDs. This procedure is used to try to detect ineffective and effective dimensions while solving DOPVDs. In this paper, this procedure is added to Genetic Algorithms GAs to be tested. The results in this paper demonstrate that GAs which use the mask detection procedure outperform GA without it especially Periodic GA 5 PerGA5.

[1]  Enrique Alba,et al.  Metaheuristics for Dynamic Optimization , 2012, Metaheuristics for Dynamic Optimization.

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

[3]  Michel Gendreau,et al.  A Survey of Heuristics for the Vehicle Routing Problem Part II: Demand Side Extensions , 2008 .

[4]  Trung Thanh Nguyen,et al.  Continuous dynamic optimisation using evolutionary algorithms , 2011 .

[5]  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 .

[6]  Shigeyoshi Tsutsui,et al.  Advances in evolutionary computing: theory and applications , 2003 .

[7]  Jürgen Branke,et al.  Proceedings of the Workshop on Evolutionary Algorithms for Dynamic Optimization Problems (EvoDOP-2003) held in conjunction with the Genetic and Evolutionary Computation Conference (GECCO-2003), 12 July 2003, Chicago, USA [online] , 2003 .

[8]  Xin Yao,et al.  Benchmark Generator for CEC'2009 Competition on Dynamic Optimization , 2008 .

[9]  Shengxiang Yang,et al.  Evolutionary algorithms for dynamic optimization problems: workshop preface , 2005, GECCO '05.

[10]  Kamran Dadkhah Foundations of Mathematical and Computational Economics , 2006 .

[11]  Raymond Chiong,et al.  Dynamic Function Optimization: The Moving Peaks Benchmark , 2013, Metaheuristics for Dynamic Optimization.

[12]  Jing J. Liang,et al.  Novel composition test functions for numerical global optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[13]  Sanghamitra Bandyopadhyay,et al.  Some Single- and Multiobjective Optimization Techniques , 2013 .

[14]  Shengxiang Yang,et al.  Evolutionary computation for dynamic optimization problems , 2013, GECCO.

[15]  Krzysztof Trojanowski,et al.  Immune-based algorithms for dynamic optimization , 2009, Inf. Sci..

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

[17]  Hartmut Schmeck,et al.  Designing evolutionary algorithms for dynamic optimization problems , 2003 .

[18]  Shengxiang Yang,et al.  Evolutionary dynamic optimization: A survey of the state of the art , 2012, Swarm Evol. Comput..

[19]  Bruce L. Golden,et al.  The vehicle routing problem : latest advances and new challenges , 2008 .

[20]  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).

[21]  Shengxiang Yang,et al.  Evolutionary Dynamic Optimization: Methodologies , 2013 .

[22]  Shengxiang Yang,et al.  Genetic Algorithms with Memory- and Elitism-Based Immigrants in Dynamic Environments , 2008, Evolutionary Computation.

[23]  Changhe Li,et al.  Evolutionary Dynamic Optimization: Test and Evaluation Environments , 2013 .

[24]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[25]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.