Federico Della Croce

A genetic algorithm for the job shop problem

Scope and Purpoee--Job shop scheduling is a strongly NP-hard problem of combinatorial optimization and one of the most well-known machine scheduling problems. Scope of this paper is to present some improvements obtained in dealing with this problem using a heuristic technique based on Genetic Algorithms.

Minimizing tardy jobs in a flowshop with common due date

Abstract This paper considers the two-machine flowshop scheduling problem where the total time for which a shop is available to complete a given number of jobs is constrained to a known number. This problem is equivalent to the flowshop scheduling problem to minimize the total number of tardy jobs against a common due date. It has been recently proven to be NP-hard in the ordinary sense. A compact multidimensional knapsack problem formulation of the problem is introduced together with several structural properties. A branch and bound procedure is proposed to find an optimal solution to the problem. Computational results show that the proposed algorithm is capable of finding optimal solutions to problems with up to 900 jobs.

Generalized pairwise interchanges and machine scheduling

Abstract In this paper a generalization of pairwise interchanges is considered and applied to machine scheduling problems. It is shown how these swap operators can be used to compute bounds for Branch and Bound procedures, to prove dominance properties and to define a high-performance neighborhood for local search methods.

Complexity of single machine scheduling problems under scenario-based uncertainty

We present algorithmic and computational complexity results for several single machine scheduling problems where some job characteristics are uncertain. This uncertainty is modeled through a finite set of well-defined scenarios. We use here the so-called absolute robustness criterion to select among feasible solutions.

An improved general procedure for lexicographic bottleneck problems

In combinatorial optimization, the bottleneck (or minmax) problems are those problems where the objective is to find a feasible solution such that its largest cost coefficient elements have minimum cost. Here we consider a generalization of these problems, where under a lexicographic rule we want to minimize the cost also of the second largest cost coefficient elements, then of the third largest cost coefficients, and so on. We propose a general rule which leads, given the considered problem, to a vectorial version of the solution procedure for the underlying sum optimization (minsum) problem. This vectorial procedure increases by a factor of k (where k is the number of different cost coefficients) the complexity of the corresponding sum optimization problem solution procedure.

A heuristic approach for the max-min diversity problem based on max-clique

In this paper we discuss a heuristic approach for the solution to the max-min diversity problem. The approach relies on the equivalence between this problem and the classical max-clique: it solves different decision problems about the existence of cliques with a given size. The idea is rather simple but, according to the experiments and the comparison with the existing literature, appears as particularly promising and outperforms, both in quality and CPU time, the existing state of the art algorithms.

Minimizing the weighted sum of quadratic completion times on a single machine

This article discusses the scheduling problem of minimizing the weighted sum of quadratic completion times on a single machine. It establishes links between orderings of adjacent and nonadjacent jobs that lead to a powerful branch and bound method. Computational results show that this method clearly outperforms the state of the art algorithm.

Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria

We consider a two-machine flowshop-scheduling problem with an unknown common due date where the objective is minimization of both the number of tardy jobs and the unknown common due date. We show that the problem is NP-hard in the ordinary sense and present a pseudopolynomial dynamic program for its solution. Then, we propose an exact e-constraint approach based on the optimal solution of a related single-machine problem. For this latter problem a compact ILP formulation is explored: a powerful variable-fixing technique is presented and several logic cuts are considered. Computational results indicate that, with the proposed approach, the pareto optima can be computed, in reasonable time, for instances with up to 500 jobs.

A matheuristic approach for the two-machine total completion time flow shop problem

This paper deals with the two-machine total completion time flow shop problem. We present a so-called matheuristic post processing procedure that improves the objective function value with respect to the solutions provided by state of the art procedures. The proposed procedure is based on the positional completion times integer programming formulation of the problem with O(n2) variables and O(n) constraints.

A matheuristic approach for the total completion time two-machines permutation flow shop problem

This paper deals with the total completion time 2-machines flow shop problem. We present a so-called matheuristic post processing procedure that improves the objective function value with respect to the solutions provided by state of the art procedures. The proposed procedure is based on the positional completion times integer programming formulation of the problem with O(n2) variables and O(n) constraints.