A Scatter Search Heuristic for the Fixed-Charge Capacitated Network Design Problem

Abstract

The Fixed-Charge Capacitated Multi-commodity Network Design (CMND) problem consists in finding the optimal configuration, i.e., the arcs to include in the final design, of a network on which the flows of several products (“commodities”) must be routed to satisfy given demands between origin-destination pairs. Each of the arcs that can possibly be included in the design is characterized by its capacity (the maximum amount of flow of all commodities it can support), a fixed cost to be incurred if the arc is selected, and a variable cost for each unit of flow that uses the arc. The objective of the problem is to minimize the total system cost (the sum of the fixed costs of selected arcs and routing costs), while respecting capacity limits.