Philippe Michelon

LSSPER: Solving the Resource-Constrained Project Scheduling Problem with Large Neighbourhood Search

This paper presents the Local Search with SubProblem Exact Resolution (LSSPER) method based on large neighbourhood search for solving the resource-constrained project scheduling problem (RCPSP). At each step of the method, a subpart of the current solution is fixed while the other part defines a subproblem solved externally by a heuristic or an exact solution approach (using either constraint programming techniques or mathematical programming techniques). Hence, the method can be seen as a hybrid scheme. The key point of the method deals with the choice of the subproblem to be optimized. In this paper, we investigate the application of the method to the RCPSP. Several strategies for generating the subproblem are proposed. In order to evaluate these strategies, and, also, to compare the whole method with current state-of-the-art heuristics, extensive numerical experiments have been performed. The proposed method appears to be very efficient.

Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem

We propose a cooperation method between constraint programming and integer programming to compute lower bounds for the resource-constrained project scheduling problem (RCPSP). The lower bounds are evaluated through linear-programming (LP) relaxations of two different integer linear formulations. Efficient resource-constraint propagation algorithms serve as a preprocessing technique for these relaxations. The originality of our approach is to use additionally some deductions performed by constraint propagation, and particularly by the shaving technique, to derive new cutting planes that strengthen the linear programs. Such new valid linear inequalities are given in this paper, as well as a computational analysis of our approach. Through this analysis, we also compare the two considered linear formulations for the RCPSP and confirm the efficiency of lower bounds computed in a destructive way.

Lagrangian decomposition for integer nonlinear programming with linear constraints

We present a Lagrangean decomposition to study integer nonlinear programming problems. Solving the dual Lagrangean relaxation we have to obtain at each iteration the solution of a nonlinear programming with continuous variables and an integer linear programming. Decreasing iteratively the primal—dual gap we propose two algorithms to treat the integer nonlinear programming.

Generalized Assignment Type Goal Programming Problem: Application to Nurse Scheduling

The notion of the Generalized Assignment Type Goal Programming Problem is introduced to consider the additional side constraints of an Assignment Type problem as goal functions. A short term Tabu Search method together with diversification strategies are used to deal with this model. The methods are tested on real-world Nurse Scheduling Problems.

Crop rotation scheduling with adjacency constraints

In this article we propose a 0-1 optimization model to determine a crop rotation schedule for each plot in a cropping area. The rotations have the same duration in all the plots and the crops are selected to maximize plot occupation. The crops may have different production times and planting dates. The problem includes planting constraints for adjacent plots and also for sequences of crops in the rotations. Moreover, cultivating crops for green manuring and fallow periods are scheduled into each plot. As the model has, in general, a great number of constraints and variables, we propose a heuristics based on column generation. To evaluate the performance of the model and the method, computational experiments using real-world data were performed. The solutions obtained indicate that the method generates good results.

An exact method with variable fixing for solving the generalized assignment problem

We propose a simple exact algorithm for solving the generalized assignment problem. Our contribution is twofold: we reformulate the optimization problem into a sequence of decision problems, and we apply variable-fixing rules to solve these effectively. The decision problems are solved by a simple depth-first lagrangian branch-and-bound method, improved by our variable-fixing rules to prune the search tree. These rules rely on lagrangian reduced costs which we compute using an existing but little-known dynamic programming algorithm.

A constraint programming approach for the resource-constrained project scheduling problem

AbstractnA “pure” Constraint Programming approach for the Resource-Constrained Project Scheduling Problem (RCPSP) is presented. Our basic idea was to substitute the resource constraints by a set of “sub-constraints” generated as needed. Each of these sub-constraints corresponds to a set of tasks that cannot be executed together without violating one of the resource constraints. A filtering algorithm for these sub-constraints has been developed. When applied to the initial resource constraints together with known filtering algorithms, this new filtering algorithm provides very good numerical results.n

The Euclidean Steiner tree problem in Rn: A mathematical programming formulation

A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in Rn is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to evaluate a subgradient at each iteration we have to solve three optimization problems, two in polynomial time, and one is a special convex nondifferentiable programming problem.

Scheduling the flying squad nurses of a hospital using a multi-objective programming model

In this paper, we address the problem of scheduling nurses working on the flying squad of a hospital. Considering the large number of constraints, many of them being conflicting, the problem is formulated as a multi-objective programming problem with binary variables, where the objective function consists of a vector of objectives and penalty variables (deviation measures) provided by the soft constraints. Two approaches are considered to solve the problem: the weighted method and the sequential method. The best results are obtained with a mix of the two solving methods. Numerical results are presented.

An exact cooperative method for the uncapacitated facility location problem

In this paper, we present a cooperative primal-dual method to solve the uncapacitated facility location problem exactly. It consists of a primal process, which performs a variation of a known and effective tabu search procedure, and a dual process, which performs a lagrangian branch-and-bound search. Both processes cooperate by exchanging information which helps them find the optimal solution. Further contributions include new techniques for improving the evaluation of the branch-and-bound nodes: decision-variable bound tightening rules applied at each node, and a subgradient caching strategy to improve the bundle method applied at each node.