Towards generating diverse topologies of path tracing compliant mechanisms using a local search based multi-objective genetic algorithm procedure

Abstract

A new bi-objective optimization problem is formulated for generating the diverse topologies of compliant mechanisms tracing a user-defined path. Motivation behind the present study is to generate the compliant mechanisms which perform the same task of tracing a prescribed trajectory near minimum-weight solution. Therefore, the constraint are imposed at each precision point representing a prescribed path for accomplishing the tracing task. An additional constraint on stress is also included for the feasible designs. The study starts with a single objective analysis of minimum-weight of compliant mechanism and the obtained topology is referred as the reference design. Thereafter, a bi-objective optimization problem is solved by considering the objectives as minimization of weight of structure and maximization of diversity of structure with respect to the reference design. Here, the diversity is evaluated by finding the dissimilarity in the bit value at each gene position of the binary strings of the reference design and a structure evolved from the GA population. A local search based multi-objective genetic algorithm (MOGA) optimization procedure is used in which the NSGA-II is used as a global search and optimization algorithm. A parallel computing is employed in the study for evaluating nonlinear geometric FE analysis and also for the NSGA-II operations. After the NSGA-II run, a few solutions are selected from the non-dominated front and the local search is applied on them. With the help of a given optimization procedure, compliant mechanism designs tracing curvilinear and straight line trajectories are evolved and presented in the study. In both examples, compliant mechanisms are designed to have any arbitrary support and loading regions.