An Extension of the Welded Beam Problem that Includes Multiple Interacting Design Concepts

Angus Kenny, Tapabrata Ray, Hemant Kumar Singh

Abstract: Multi-objective multi-concept (MOMC) problems address the simultaneous optimization of diverse design concepts to identify solutions that are optimal for the objectives across all concepts. This paper presents a MOMC formulation of the classic welded beam problem, updated with contemporary cost estimates and metric units. Unlike the original model, which assumes a fixed cross-section, the proposed formulation incorporates multiple design concepts, each featuring distinct cross-sectional geometries and corresponding design variables. The formulation is validated through comparison with existing welded beam problem formulations, and an in-depth analysis of the objective space is conducted for both individual concepts and the combined multi-concept case. Baseline results are presented using two evolutionary algorithms—NSGA-II and IDEA—applied to each design concept separately. Their effectiveness on the multi-concept problem was also evaluated by merging the results from each individual concept. Both algorithms successfully identified near-optimal solutions for the individual concepts; however, their performance declined for the multi-concept case, especially under limited computational budgets. These findings highlight the unique complexities inherent in MOMC problems and emphasize the need for more dedicated optimization approaches to address this class of problems.

External IDs:dblp:conf/emo/KennyRS25