This paper investigates, for the first time in the literature, the approximation of minmax (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a constant number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Us...

This paper investigates, for the first time in the literature, the approximation of min-max (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a bounded number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Us...

When facing a real world, optimization problems mainly become multiobjective i.e. they have several criteria of excellence. A multi-criteria problem submitted for multi-criteria evaluation is a complex problem, as usually there is no optimal solution, and no alternative is the best one according to all criteria. However, if a metaheuristic algorithm is combined with a Multi-Criteria Decision-Ma...

Abstract In this paper a class of robust two-stage combinatorial optimization problems is discussed. It assumed that the uncertain second-stage costs are specified in form convex uncertainty set, particular polyhedral or ellipsoidal ones. shown versions basic network and selection NP-hard, even very restrictive cases. Some exact approximation algorithms for general problem constructed. Polynomi...

We consider a stochastic shortest path problem with associative criteria in which for each node of a graph we choose a probability distribution over the set of successor nodes so as to reach a given target node optimally. We formulate such a problem as an associative Markov decision processes. We show that an optimal value function is a unique solution to an optimality equation and find an opti...

The Internet is constantly growing but the available resources, i.e. bandwidth, are limited. Using bandwidth efficiently to provide high quality of service to users is referred to as traffic engineering. This is of utmost importance. Traffic in IP networks is commonly routed along shortest paths with respect to auxiliary link weights, e.g. using the OSPF or IS-IS protocol. Here, shortest path r...

a shortest path problem is a practical issue in networks for real-world situations. this paper addresses the fuzzy shortest path (fsp) problem to obtain the best fuzzy path among fuzzy paths sets. for this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (ifss) in order to determine the fuzzy shortest path. moreover, this algorithm is developed for ...

The aim of the paper is to show an example of interaction between the AI and OR elds of research using the Constraint Programming (CP) framework to glue them together. We solve a shortest path problem using the c-semiring-based framework for programming over soft constraints (SCLP), which is an extension of classical constraint solving and programming. The SCLP approac handle uniformly several ...