REPOSITORY > RESULTS

Abstract

Despite the large volume of recently published papers in the field of constrained multiobjective
optimization, the understanding and characterization of constrained multiobjective
optimization problems (CMOPs) for benchmarking multiobjective evolutionary algorithms
(MOEAs) and the related constraint handling techniques (CHTs) remain unsatisfactory.
Therefore, selecting appropriate CMOPs for benchmarking is challenging and lacks a formal
basis. Under such conditions, preparing a robust and well-designed experimental setup for
constrained multiobjective optimization becomes a difficult task. An inadequately designed
benchmark could result in improper conclusions about CMOP landscapes and MOEA
performance. This thesis takes a step towards resolving this issue by examining CMOPs
from both the feature and the performance space perspective.
Regarding the feature space perspective, we expand the landscape analysis to constrained
multiobjective optimization. Using four exploratory landscape analysis techniques, we
propose various landscape features to characterize CMOPs. These features are then
employed to compare eight commonly 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 do not sufficiently represent certain realistic
characteristics, such as strong negative correlation between the objectives and constraints.
Furthermore, our results show that all the studied artificial test suites have advantages and
limitations, and no “perfect” suite exists. Additionally, the effectiveness of the proposed
features at predicting algorithm performance is demonstrated for two MOEAs.
Concerning the performance space perspective, the thesis initially presents a novel performance
assessment method designed specifically for constrained multiobjective optimization.
This methodology provides a first attempt at measuring performance in approximating the
Pareto front and constraint satisfaction simultaneously. Moreover, it proposes an approach
to measure the capability of the given optimization problem to differentiate among algorithm
performances. Additionally, this approach is used to compare eight commonly used artificial
test suites of CMOPs. The experimental results reveal which suites are more effective at
distinguishing between three well-known MOEAs.
Finally, we illustrate how the proposed methodology can be used in two real-world
scenarios: design of cyclone dust separators and elevator group control. Both problems
are characterized with seven landscape features proposed in this thesis, providing insights
into their complexity. The analysis shows that the design of elevator group control is more
challenging, which is additionally confirmed by a performance space study.