An archive-based multi-objective evolutionary algorithm with adaptive search space partitioning to deal with expensive optimization problems: Application to process eco-design

•Optimal Pareto fronts were achieved with 200 and 300 function calls (2D, 3D problems).•Convergence accuracy was improved by a factor of 50 for most test functions.•Convergence improvements were attained for both unimodal and multimodal problems.•Proposed algorithm outperformed ParEGO in both convergence accuracy and speed.

In eco-design, the integration of environmental aspects into the earliest stage of design is considered with the aim of reducing adverse environmental impacts throughout a product's life cycle. An eco-design problem is therefore multi-objective, where several objectives (environmental, economic, and technological) are to be simultaneously optimized.The optimization of industrial processes usually requires solving expensive multi-objective optimization problems (MOPs). Aiming to solve efficiently MOPs, with a limited computational budget, this paper proposes a new framework called AMOEA-MAP. The framework relies on the structure of the NSGAII algorithm and possesses two novel operators: a memory-based adaptive partitioning strategy, which provides an adaptive reticulation of the search space for a quick identification of optimal zones with less computational effort; and a bi-population evolutionary algorithm, tailored for expensive optimization problems.To ascertain its generality, the framework is first tested on several tough benchmarks. Its performance is subsequently validated on a real-world eco-design problem.

Graphical abstractWhen dealing with expensive multi-objective optimization problems, the AMOEA-MAP algorithm (this work) allowed the granting of a better identification of globally optimal zones and a better distribution of optimal solutions in the optimal Pareto sets, compared to the ParEGO algorithm. In the following graphics, the comparisons have been made through several three-dimensional benchmarks (DTLZ1-6), where a limited computational budget of 300 function evaluations has been set for each run.Figure optionsDownload full-size imageDownload as PowerPoint slide