A note on constrained multi-objective optimization benchmark problems

We investigate the properties of widely used constrained multi-objective optimization benchmark problems. A number of Multi-Objective Evolutionary Algorithms (MOEAs) for Constrained Multi-Objective Optimization Problems (CMOPs) have been proposed in the past few years. The C-DTLZ functions and Real-World-Like Problems (RWLPs) have frequently been used for evaluating the performance of MOEAs on CMOPs. In this paper, however, we show that the C-DTLZ functions and widely-used RWLPs have some unnatural problem features. The experimental results show that an MOEA without any Constraint Handling Techniques (CHTs) can successfully find well-approximated nondominated feasible solutions on the C1-DTLZ1, C1-DTLZ3, and C2-DTLZ2 functions. It is widely believed that RWLPs are MOEA-hard problems, and finding the feasible solutions on them is a very hard task. However, we show that the MOEA without any CHTs can find feasible solutions on widely-used RWLPs such as the speed reducer design problem, the two-bar truss design problem, and the water problem. Also, it is seldom that the infeasible solution simultaneously violates multiple constraints in the RWLPs. Due to the above reasons, we conclude that constrained multi-objective optimization benchmark problems need a careful reconsideration.

[1]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

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

[3]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  Kaisa Miettinen,et al.  On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization , 2016, PPSN.

[6]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[7]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[8]  Bishakh Bhattacharya,et al.  Practical Applications in Constrained Evolutionary Multi-objective Optimization , 2017, Recent Advances in Evolutionary Multi-objective Optimization.

[9]  Tapabrata Ray,et al.  Optimum Oil Production Planning Using Infeasibility Driven Evolutionary Algorithm , 2013, Evolutionary Computation.

[10]  Yong Wang,et al.  A comparative study of constraint-handling techniques in evolutionary constrained multiobjective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[11]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[12]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[13]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[14]  Tapabrata Ray,et al.  A Swarm Metaphor for Multiobjective Design Optimization , 2002 .

[15]  C. A. Coello Coello,et al.  Multiobjective structural optimization using a microgenetic algorithm , 2005 .

[16]  Thomas Stützle,et al.  Automatically Improving the Anytime Behaviour of Multiobjective Evolutionary Algorithms , 2013, EMO.

[17]  Michael G. Parsons,et al.  Formulation of Multicriterion Design Optimization Problems for Solution With Scalar Numerical Optimization Methods , 2004 .

[18]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

[19]  A. Oyama,et al.  New Constraint-Handling Method for Multi-Objective and Multi-Constraint Evolutionary Optimization , 2007 .

[20]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

[21]  Wenyin Gong,et al.  An efficient multiobjective differential evolution algorithm for engineering design , 2009 .

[22]  A. Osyczka,et al.  A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm , 1995 .

[23]  Hisao Ishibuchi,et al.  Selecting a small number of representative non-dominated solutions by a hypervolume-based solution selection approach , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[24]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm (IDEA) for Engineering Design Optimization , 2008, Australasian Conference on Artificial Intelligence.

[25]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[26]  Gary G. Yen,et al.  Constraint Handling in Multiobjective Evolutionary Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[27]  Kalyanmoy Deb,et al.  A Unified Evolutionary Optimization Procedure for Single, Multiple, and Many Objectives , 2016, IEEE Transactions on Evolutionary Computation.

[28]  Dimo Brockhoff,et al.  Benchmarking Numerical Multiobjective Optimizers Revisited , 2015, GECCO.

[29]  Tapabrata Ray,et al.  A Decomposition-Based Evolutionary Algorithm for Many Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[30]  Tapabrata Ray,et al.  Use of Infeasible Solutions During Constrained Evolutionary Search: A Short Survey , 2016, ACALCI.

[31]  Anne Auger,et al.  COCO: The Bi-objective Black Box Optimization Benchmarking (bbob-biobj) Test Suite , 2016, ArXiv.

[32]  Marco Laumanns,et al.  On Sequential Online Archiving of Objective Vectors , 2011, EMO.

[33]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[34]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[35]  Saúl Zapotecas Martínez,et al.  Constrained multi-objective aerodynamic shape optimization via swarm intelligence , 2014, GECCO.

[36]  R. Lyndon While,et al.  Multi-level Ranking for Constrained Multi-objective Evolutionary Optimisation , 2006, PPSN.

[37]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.