A Feature-based analysis on the impact of linear constraints for ε-constrained differential evolution

Feature-based analysis has provided new insights into what characteristics make a problem hard or easy for a given algorithms. Studies, so far, considered unconstrained continuous optimisation problem and classical combinatorial optimisation problems such as the Travelling Salesperson problem. In this paper, we present a first feature-based analysis for constrained continuous optimisation. To start the feature-based analysis of constrained continuous optimization, we examine how linear constraints can influence the optimisation behaviour of the well-known ε-constrained differential evolution algorithm. Evolving the coefficients of a linear constraint, we show that even the type of one linear constraint can make a difference of 10-30% in terms of function evaluations for well-known continuous benchmark functions.

[1]  Zbigniew Michalewicz,et al.  Test-case generator for nonlinear continuous parameter optimization techniques , 2000, IEEE Trans. Evol. Comput..

[2]  Tetsuyuki Takahama,et al.  Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation , 2010, IEEE Congress on Evolutionary Computation.

[3]  Jano I. van Hemert,et al.  Understanding TSP Difficulty by Learning from Evolved Instances , 2010, LION.

[4]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[5]  Tetsuyuki Takahama,et al.  Solving Difficult Constrained Optimization Problems by the ε Constrained Differential Evolution with Gradient-Based Mutation , 2009 .

[6]  Bernd Bischl,et al.  A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem , 2012, Annals of Mathematics and Artificial Intelligence.

[7]  Tetsuyuki Takahama,et al.  Constrained Optimization by the ε Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[8]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

[9]  Bernd Bischl,et al.  Exploratory landscape analysis , 2011, GECCO '11.

[10]  N. Hansen,et al.  Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem , 2015, Evolutionary Computation.

[11]  Tetsuyuki Takahama,et al.  Constrained Optimization by ε Constrained Differential Evolution with Dynamic ε-Level Control , 2008 .

[12]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

[13]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[14]  Z. Michalewicz,et al.  Test-case generator TCG-2 for nonlinear parameter optimisation , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[15]  Carlos A. Coello Coello,et al.  What Makes a Constrained Problem Difficult to Solve by an Evolutionary Algorithm , 2004 .

[16]  Tetsuyuki Takahama,et al.  Efficient constrained optimization by the ε constrained adaptive differential evolution , 2010, IEEE Congress on Evolutionary Computation.

[17]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

[18]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[19]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[20]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[21]  Markus Wagner,et al.  Ant colony optimisation and the traveling salesperson problem: hardness, features and parameter settings , 2013, GECCO '13 Companion.

[22]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[23]  Bernd Bischl,et al.  A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem , 2013, FOGA XII '13.