Agnès Plateau

A path relinking algorithm for the generalized assignment problem

The Generalized Assignment Problem (GAP) consists in finding a maximum-profit assignment of tasks to agents with capacity constraints. In this paper, a path relinking heuristic is proposed for the GAP. The main feature of our path relinking is that both feasible and infeasible solutions are inserted in the reference set of elite solutions, trade-off between feasibility and infeasibility being ruled through a penalty coefficient for infeasibility. Since exploration of the solution space is very sensitive to this penalty coefficient, the coefficient is dynamically updated at each round of combinations so that a balance is kept between feasible and infeasible solutions in the reference set. Numerical experiments reported on classical testbed instances of the OR-library show that the algorithm compares favorably to several other methods in the literature. In particular, more than 95% of the instances in the test-file were solved to optimality with short computation time.

A branch-and-price-and-cut approach for sustainable crop rotation planning

In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received increased attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly NP-hard. We propose a 0-1 linear programming compact formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Priceand- Cut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the effectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound.

A hybrid search combining interior point methods and metaheuristics for 0–1 programming

Our search deals with methods hybridizing interior point processes and metaheuristics for solving 0-1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0-1 multiconstraint knapsack problems.

Hybrid column generation for large-size Covering Integer Programs: Application to transportation planning

The well-known column generation scheme is often an efficient approach for solving the linear relaxation of large-size Covering Integer Programs (CIP). In this paper, this technique is hybridized with an extension of the best-known CIP approximation heuristic, taking advantage of distinct criteria of columns selection. This extension uses fractional optimization for solving pricing subproblems. Numerical results on a real-case transportation planning problem show that the hybrid scheme accelerates the convergence of column generation both in terms of number of iterations and computational time. The integer solutions generated at the end of the process can also be improved for a significant proportion of instances, highlighting the potential of diversification of the approximation heuristic.

A computational study for the p-median Problem

Abstract Given a set of clients and a set of potential sites for facilities, the p -median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. In [Elloumi, S., A tighter formulation of the p-median problem , J. Comb. Optim., 19 (2004), 69–83], a new formulation of this problem was proposed that takes benefit from identical values in the distance matrix. This formulation, when directly used in a mixed integer linear programming software, was proved to perform better than other known formulations, on a large number of instances. Here, we propose to improve the performances of the new formulation by taking benefit from its structure in the solution of its LP-relaxation. Rows and columns are gradually added to the linear program until a condition on the optimal values of the variables is reached. A computational comparison is carried out on many classes of instances.