Parallel evolutionary algorithm for single and multi-objective optimisation: Differential evolution and constraints handling

This paper presents an evolutionary algorithm employing differential evolution to solve nonlinear optimisation problems with (or without) constraints and multiple objectives. New decision strategies to compare candidate solutions are developed that take into account all constraints and objective functions. The new constraint handling strategy uses the concept of Pareto dominance to rank the candidate solutions based on their constraint violation value. In order to improve the performance of the algorithm, a set of genetic operators and differential evolution operators are combined. In addition, the paper proposes an algorithm to perform parallel evolution in a way that the diversity of the final population is preserved after migrations. Another goal of the algorithm is to handle problems with a mix of integers and real-valued variables. Numerical experiments investigate the robustness and the performance of the algorithm through multiple benchmark optimisation problems. Finally, two engineering applications are studied, namely: (1) the topology optimisation of trusses; and (2) the economical dispatch problem in power generation. Results show that the algorithm is capable of handling optimisation problems with a mix of integer and real-valued variables with constraints and multiple objectives