Time-varying external archive differential evolution algorithm with applications to parallel mechanisms

In this work, a time-varying external archive differential evolution algorithm is proposed, which can obtain the multiple roots for system of nonlinear equations for the forward dis-placement of parallel mechanisms. In time-varying external archive differential evolution three improvements are presented. At first, a time-varying subpopulation strategy is pro-posed to consider both global and local searching capabilities. Then, an individual judg-ment criterion is proposed, which employs the weighted basis vector mutation strategy for ordinary individuals and a hybrid mutation operator for locally optimal individuals. Fi-nally, the external archive strategy of neighborhood-based crowding differential evolution is improved to enhance the domain searching ability of the algorithm. To evaluate the per-formance of time-varying external archive differential evolution, twenty benchmark func-tions are selected as the test suite. Moreover, the solutions for forward displacements of four strongly coupled parallel mechanisms with different degrees of freedom are derived to test the generality of this method. From the acquired experimental results, it is demon-strated that fairly-competitive results can be provided compared to other methods, in both benchmark functions and forward displacement solutions of parallel mechanisms. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This work proposes a time-varying external archive differential evolution algorithm for obtaining multiple roots of the system of nonlinear equations for the forward displacement of parallel mechanisms. The algorithm improves the global and local searching capabilities through a time-varying subpopulation strategy and introduces an individual judgment criterion. The experimental results demonstrate the competitive performance of the proposed method compared to other methods in benchmark functions and forward displacement solutions of parallel mechanisms.