Time and multiple objectives in scheduling and routing problems

Many optimization problems encountered in practice are multi-objective by nature, i.e., different objectives are conflicting and equally important. Many times, it is not desirable to drop some of them or to optimize them in a composite single objective or hierarchical manner. Furthermore, cost parameters change over time which makes optimization problems harder. For instance, in the transport sector, travel costs are a function of travel time which changes depending on the time of the day a vehicle is travelling (e.g., due to road congestion). Road congestion results in tremendous delays which lead to a decrease in the service quality and the responsiveness of logistic service providers. In Chapter 2, we develop a generic approach to deal with Multi-Objective Scheduling Problems (MOSPs) with State-Dependent Cost Parameters. The aim is to determine the set of Pareto solutions that capture the trade offs between the different conflicting objectives. Due to the complexity of MOSPs, an efficient approximation based on dynamic programming is developed. The approximation has a provable worse case performance guarantee. Even though the generated approximate Pareto front consist of fewer solutions, it still represents a good coverage of the true Pareto front. Furthermore, considerable gains in computation times are achieved. In Chapter 3, the developed methodology is validated on the multi-objective timedependent knapsack problem. In the classical knapsack problem, the input consists of a knapsack with a finite capacity and a set of items, each with a certain weight and a cost. A feasible solution to the knapsack problem is a selection of items such that their total weight does not exceed the knapsack capacity. The goal is to maximize the single objective function consisting of the total pro t of the selected items. We extend the classical knapsack problem in two ways. First, we consider time-dependent profits (e.g., in a retail environment profit depends on whether it is Christmas or not)

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM