Order-based neighborhoods for project scheduling with nonregular objective functions

Abstract

This paper is concerned with project scheduling where scarce resources are taken into account and some nonregular objective function is to be minimized. The activities of the project are linked by general temporal constraints. For a variety of nonregular objective functions, the search for optimal solutions can be restricted to special types of schedules which correspond to specific points of the feasible region. Each of those schedules can be associated with some strict order in the activity set. We study three neighborhoods on the set of spanning forests and spanning trees, respectively, of order networks arising from such strict orders in the activity set. The first neighborhood is dedicated to objective functions for which any local minimizer on an order-induced subset of the feasible region is a global minimizer on this subset as well. The second and the third neighborhoods cope with the case of objective functions which are minimized by vertices and minimal points, respectively, of order-induced subsets of the feasible region. For all neighborhoods, weak optimal connectivity of the corresponding neighborhood graph is shown.