Multilocal programming and applications

Multilocal programming aims to identify all local maximizers of unconstrained or constrained nonlinear optimization problems. The multilocal programming theory relies on global optimization strategies combined with simple ideas that are inspired in deflection or stretching techniques to avoid convergence to the already detected local maximizers. The most used methods to solve this type of problems are based on stochastic procedures. In general, population-based methods are computationally expensive but rather reliable in identifying all local solutions. Stochastic methods based on point-to-point strategies are faster to identify the global solution, but sometimes are not able to identify all the optimal solutions of the problem. To handle the constraints of the problem, some penalty strategies are proposed. A well-known set of test problems is used to assess the performance of the algorithms. In this chapter, a review on recent techniques for both unconstrained and constrained multilocal programming is presented. Some real-world multilocal programming problems based on chemical engineering process design applications are described