Penalty-Based Heuristic DIRECT Method for Constrained Global Optimization

Abstract

This paper is concerned with an extension of the heuristic DIRECT method, presented in [ 8 ], to solve nonlinear constrained global optimization (CGO) problems. Using a penalty strategy based on a penalty auxiliary function, the CGO problem is transformed into a bound constrained problem. We have analyzed the performance of the proposed algorithm using fixed values of the penalty parameter, and we may conclude that the algorithm competes favourably with other DIRECT-type algorithms in the literature.

A Dynamically Dimensioned Search Allowing a Flexible Search Range and Its Application to Optimize Discrete Hedging Rule Curves

“…A simple way to optimize constrained problems using the DDS is the penalty methods, which seek the solution by replacing the original constrained problem with a sequence of unconstrained sub-problems, where the constraint functions are combined with the objective function to define a penalty function. In other words, the penalty method is to discard an infeasible solution by imposing a big number on the objective function if the candidate solution violates the constraints in the optimization problem seek to minima [54,55]. When solving the constrained optimization problem using the DDS, one can formulate the problem as follows:…”