Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Multi-objective test problems, linkages, and evolutionary methodologies
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Multi-objective genetic algorithms: Problem difficulties and construction of test problems
Evolutionary Computation
Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II
IEEE Transactions on Evolutionary Computation
Quantifying the effects of objective space dimension in evolutionary multiobjective optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
On the Evolutionary Optimization of Many Conflicting Objectives
IEEE Transactions on Evolutionary Computation
RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm
IEEE Transactions on Evolutionary Computation
A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA
IEEE Transactions on Evolutionary Computation
Recent advances in problem understanding: changes in the landscape a year on
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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Test problems have played a fundamental role in understanding the strengths and weaknesses of the existing Evolutionary Multiobjective Optimization (EMO) algorithms. A range of test problems exist which have enabled the research community to understand how the performance of EMO algorithms is affected by the geometrical shape of the Pareto front (PF), i.e., PF being convex, concave or mixed. However, the shapes of the Pareto Set (PS) of most of these test problems are rather simple (linear or quadratic), even though the real-world engineering problems are expected to have complicated PS shapes. The state-of-the-art in many-objective optimization problems (those involving four or more objectives) is rather worse. There is a dearth of test problems (even those with simple PS shapes) and the algorithms that can handle such problems. This paper proposes a framework for continuous many-objective test problems with arbitrarily prescribed PS shapes. The behavior of two popular EMO algorithms namely NSGAII and MOEA/D has also been studied for a sample of the proposed test problems. It is hoped that this paper will promote an integrated investigation of EMO algorithms for their scalability with objectives and their ability to handle complicated PS shapes with varying nature of the PF.