Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit.

Area of Science:

• Optimization Algorithms
• Computational Intelligence
• Evolutionary Computation

Background:

• Multiobjective evolutionary algorithms (MOEAs) primarily address unconstrained problems, yet real-world scenarios often involve constraints.
• Existing MOEAs lack standardized benchmarks for evaluating performance on constrained multiobjective optimization problems (CMOPs).

Purpose of the Study:

• To propose a novel classification scheme for CMOPs based on feasibility-hardness, convergence-hardness, and diversity-hardness.
• To develop a toolkit for constructing difficulty-adjustable and scalable CMOPs (DAS-CMOPs) and many-objective CMOPs (DAS-CMaOPs).
• To provide a suite of nine DAS-CMOPs and nine DAS-CMaOPs for rigorous algorithm evaluation.

Main Methods:

• A problem classification scheme categorizing CMOP difficulty into feasibility, convergence, and diversity hardness.
• Development of a toolkit generating scalable CMOPs (DAS-CMOPs) with parameterized constraint functions reflecting the three hardness types.
• Evaluation of existing constrained multiobjective evolutionary algorithms (CMOEAs) on the newly proposed DAS-CMOPs and DAS-CMaOPs.

Main Results:

• Experimental results indicate varying algorithm performance based on CMOP difficulty types; MOEA/D-CDP excels in convergence-hard problems, while NSGA-II-CDP performs well on problems with combined hardness.
• C-NSGA-III shows effectiveness on feasibility-hard CMaOPs, and C-MOEA/DD is suitable for convergence-hard CMaOPs.
• Current algorithms demonstrate limitations in efficiently solving the proposed DAS-CMOPs and DAS-CMaOPs, highlighting the need for further algorithm development.

Conclusions:

• The proposed classification and test problems offer a standardized framework for advancing research in constrained multiobjective optimization.
• The study underscores the need for developing novel and more effective constrained multiobjective evolutionary algorithms.
• Further research is stimulated to address the challenges posed by the newly introduced scalable and difficulty-adjustable CMOPs.