Differential Evolution and Nelder-mead for Constrained Non-linear Integer Optimization Problems

We present a novel approach to solve constrained non-linear integer optimization problems based on Differential Evolution (DE) and Nelder-Mead (NM). DE is a promising technique used in non-differentiable and non-linear problems with continuous variables. It is used to identify promising regions in the search space. NM is a derivative-free technique used in non-linear continuous optimization problems. Since we are concerned with integer problems, then the NM is extended to handle with integer optimization problems. The constraints are treated by the Alpha Constrained method, where constraints values and fitness are compared using a lexicographical order. Since DE is used to continuous optimization and NM needs an initial starting point, we propose a method that use the best individual of DE as starting point to NM. Simulation results show the effectiveness of the proposed method.