An efficient constraint handling scheme for a differential evolutionary algorithm
Systematic methods and tools for managing the complexity
Advances in Computational & Numerical Methods (T4-4P)
Keywords: Constraint handling, Differential evolution, Evolutionary optimization, Constrained optimization, Optimization technique
Recently, evolutionary algorithms (EAs) are receiving increasing attention in solving various engineering optimization problems. These problems are generally highly constrained, nonlinear and multi-modal objective functions, and involve inequality and/or equality constraints, resulting in a complex search space. Differential evolutionary algorithm (DE) is a novel evolutionary optimization algorithm being capable of handling non-differentiable, nonlinear and multi-modal objective functions. Unfortunately, constraint handling is one of the major drawbacks when applying DE to solve constrained optimization problems. Thus, an efficient constraint handling technique is required.
In this work, we presents a newly developed constraint handling scheme for a differential evolutionary algorithm. The developed approach does not use a traditional penalty function method and it does not require any extra parameters. It uses a repair algorithm based on the gradient information to correct infeasible solutions. All constraints are classified into equality and inequality. The reducible equality constraints are used to transform the original problem to the lower dimension optimization problem. While, the gradient information derived from the irreducible equality constraint set are applied to repair infeasible solutions. A dominance-based selection scheme are then applied to incorporate constraints into the objective function.
The performance of the proposed scheme and a conventional constraint handling techniques such as a penalty function method, are compared, both in terms of solution quality and convergence rate. We validate the proposed scheme using a number of test problems and chemical engineering optimization problems, including heat exchanger network design, reactor network design and PID controller tuning of continuous stirred tank reactor. The results obtained indicate that our approach is a viable alternative to a conventional penalty function method. It can effectively handle constraints encountered in both small and large scale optimization problems.
