Characterization of Constrained Continuous Multiobjective Optimization Problems: A Feature Space Perspective

TL;DR

This paper extends landscape analysis to constrained multiobjective optimization problems, introducing 29 features to better characterize and compare artificial and real-world CMOPs, aiding benchmark selection.

Contribution

It proposes 29 novel landscape features for CMOPs and evaluates how well artificial test suites represent real-world problem characteristics.

Findings

Artificial test problems often lack realistic features like negative objective correlation.

No single test suite perfectly captures all real-world CMOP characteristics.

Landscape features can guide the selection or creation of more representative benchmark problems.

Abstract

Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still unsatisfactory understood and characterized. For this reason, the selection of appropriate CMOPs for benchmarking is difficult and lacks a formal background. We address this issue by extending landscape analysis to constrained multiobjective optimization. By employing four exploratory landscape analysis techniques, we propose 29 landscape features (of which 19 are novel) to characterize CMOPs. These landscape features are then used to compare eight frequently used artificial test suites against a recently proposed suite consisting of real-world problems based on physical models. The experimental results reveal that the artificial test problems fail to adequately represent some realistic characteristics, such as strong negative correlation between the objectives and constraints. Moreover, our findings show that all the studied artificial test suites have advantages and limitations, and that no "perfect" suite exists. Benchmark designers can use the obtained results to select or generate appropriate CMOP instances based on the characteristics they want to explore.