A Constructive Heuristics and an Iterated Neighborhood Search Procedure to Solve the Cost-Balanced Path Problem

This paper presents a new heuristic algorithm tailored to solve large instances of an NP-hard variant the shortest path problem, denoted cost-balanced recently proposed in literature. The problem consists finding origin–destination direct graph, having both negative and positive weights associated with arcs, such that total sum selected arcs is as close zero possible. At least authors’ knowledge, there are no solution algorithms for facing this problem. integrates constructive procedure improvement procedure, it validated thanks implementation iterated neighborhood search procedure. reported numerical experimentation shows computationally very efficient. In particular, most suitable case where possible prove existence perfectly balanced thus optimality by good percentage optimal solutions negligible computational time.