Improving efficiency of a multistart with interrupted hooke-and-jeeves filter search for solving MINLP problems

This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are sufficiently close to other points already used to invoke the local search is analyzed. A variant of the Hooke-and-Jeeves filter algorithm for MINLP is proposed with the goal of interrupting the iterative process if the accepted iterate falls inside an ϵ-neighborhood of an already computed minimizer. Preliminary numerical results are included.The authors wish to thank two anonymous referees for their comments and suggestions. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e Tecnologia, within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.