Multi-objective optimization of a leg mechanism using genetic algorithms

Many engineering optimal design problems involve multiple conflicting objectives and often they are attempted to be solved by converting them into a single composite objective. Moreover, to be able to use standard classical optimization methods, often such problems are divided into suitable subproblems and solved in stages. A leg mechanism design problem which received some attention in the past involves link length and spring characteristics as decision variables and as many as three objectives and 17 inequality constraints. The problem is difficult to optimize because of strict geometric constraints which make only a tiny fraction of the search space feasible. This article applies an evolutionary multi-objective optimization (EMO) methodology to solve the complete leg mechanism optimization problem for all three objectives simultaneously. The way of solving the complete problem demonstrates how such a complex engineering design problem can be solved by evolutionary algorithms and shows that useful insights into the design problem can be obtained by systematically starting with fewer objectives and gradually adding more objectives. Several optimization concepts are introduced to gain confidence in the obtained solutions. Results of this study are compared with that of an earlier study and in all cases the superiority and flexibility of the EMO approach is demonstrated. The ease and efficiency of the EMO methodology demonstrated in this article should encourage similar studies involving other mechanical component design problems.