A Modified Matrix Adaptation Evolution Strategy with Restarts for Constrained Real-World Problems

In combination with successful constraint handling techniques, a Matrix Adaptation Evolution Strategy (MA-ES) variant (the $\epsilon$MAg-ES) turned out to be a competitive algorithm on the constrained optimization problems proposed for the CEC 2018 competition on constrained single objective real-parameter optimization. A subsequent analysis points to additional potential in terms of robustness and solution quality. The consideration of a restart scheme and adjustments in the constraint handling techniques put this into effect and simplify the configuration. The resulting BP-$\epsilon$MAg-ES algorithm is applied to the constrained problems proposed for the IEEE CEC 2020 competition on Real-World Single-Objective Constrained optimization. The novel MA-ES variant realizes improvements over the original $\epsilon$MAg-ES in terms of feasibility and effectiveness on many of the real-world benchmarks. The BP-$\epsilon$MAg-ES realizes a feasibility rate of 100% on 44 out of 57 real-world problems and improves the best-known solution in 5 cases.

[1]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[2]  Hans-Georg Beyer,et al.  Comparison of contemporary evolutionary algorithms on the rotated Klee-Minty problem , 2019, GECCO.

[3]  Nikolaus Hansen,et al.  Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed , 2009, GECCO '09.

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

[5]  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.

[6]  Guohua Wu,et al.  A test-suite of non-convex constrained optimization problems from the real-world and some baseline results , 2020, Swarm Evol. Comput..

[7]  Zhun Fan,et al.  LSHADE44 with an Improved $\epsilon$ Constraint-Handling Method for Solving Constrained Single-Objective Optimization Problems , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[8]  Hans-Georg Beyer,et al.  A Matrix Adaptation Evolution Strategy for Constrained Real-Parameter Optimization , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[9]  Bernhard Sendhoff,et al.  Simplify Your Covariance Matrix Adaptation Evolution Strategy , 2017, IEEE Transactions on Evolutionary Computation.

[10]  Ilya Loshchilov,et al.  CMA-ES with restarts for solving CEC 2013 benchmark problems , 2013, 2013 IEEE Congress on Evolutionary Computation.