Pierre Lopez

Discrepancy search for the flexible job shop scheduling problem

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop problem in which each operation must be processed on a given machine chosen among a finite subset of candidate machines. The aim is to find an allocation for each operation and to define the sequence of operations on each machine, so that the resulting schedule has a minimal completion time. We propose a variant of the climbing discrepancy search approach for solving this problem. We also present various neighborhood structures related to assignment and sequencing problems. We report the results of extensive computational experiments carried out on well-known benchmarks for flexible job shop scheduling. The results demonstrate that the proposed approach outperforms the best-known algorithms for the FJSP on some types of benchmarks and remains comparable with them on other ones.

Schedule generation schemes for the job-shop problem with sequence-dependent setup times: dominance properties and computational analysis

We consider the job-shop problem with sequence-dependent setup times. We focus on the formal definition of schedule generation schemes (SGSs) based on the semi-active, active, and non-delay schedule categories. We study dominance properties of the sets of schedules obtainable with each SGS. We show how the proposed SGSs can be used within single-pass and multi-pass priority rule based heuristics. We study several priority rules for the problem and provide a comparative computational analysis of the different SGSs on sets of instances taken from the literature. The proposed SGSs significantly improve previously best-known results on a set of hard benchmark instances.

On Not-First/Not-Last conditions in disjunctive scheduling

Abstract This paper is concerned with the development of constraint propagation techniques for the characterization of feasible solutions in disjunctive scheduling. In disjunctive scheduling, a set of uninterruptible tasks is to be performed on a set of resources. Each task has a release date, a deadline, and a fixed processing time; each resource can handle only one task at a time. Some of these propagation techniques are implemented by rules that deduce either mandatory or forbidden sequences between tasks or sets of tasks. For instance, certain rules indicate whether a given task must or cannot be performed before or after a set of other competing tasks. We focus our attention on the latter problem, known as the “Not-First/Not-Last” (NF/NL) problem. The genericity of propagation rules is a question of major importance. It induces that the result of the overall propagation must not depend on the order in which the inference rules are applied. Hence, one must search for completeness in the time-windows narrowing, in order to ensure the convergence of the propagation towards a unique fix-point. An efficient algorithm is proposed. It guarantees the completeness of time-windows narrowing due to NF/NL conditions. It has been integrated in a branch and bound procedure to solve job-shop instances. It has also been tested within several lower bounding procedures. Computational results are reported and the power and complementarity of NF/NL rules with other classical inference rules are discussed.

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. These problems are strongly NP-hard and it is even conjectured that no list scheduling algorithm can be defined without explicitly considering jointly scheduling and resource allocation. We propose dominance conditions based on the analysis of the problem structure and an extension to setup times of the energetic reasoning constraint propagation algorithm. An exact branch-and-bound procedure and a climbing discrepancy search (CDS) heuristic based on these components are defined. We show how the proposed dominance rules can still be valid in the CDS scheme. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases.

A multi-objective local search heuristic for scheduling Earth observations taken by an agile satellite

This paper presents an indicator-based multi-objective local search (IBMOLS) to solve a multi-objective optimization problem. The problem concerns the selection and scheduling of observations for an agile Earth observing satellite. The mission of an Earth observing satellite is to obtain photographs of the Earth surface to satisfy user requirements. Requests from several users have to be managed before transmitting an order, which is a sequence of selected acquisitions, to the satellite. The obtained sequence has to optimize two objectives under operation constraints. The objectives are to maximize the total profit of the selected acquisitions and simultaneously to ensure the fairness of resource sharing by minimizing the maximum profit difference between users. Experiments are conducted on realistic instances. Hypervolumes of the approximate Pareto fronts are computed and the results from IBMOLS are compared with the results from the biased random-key genetic algorithm (BRKGA).

Climbing depth-bounded discrepancy search for solving hybrid flow shop problems

This paper investigates how to adapt some discrepancy-based search methods to solve Hybrid Flow Shop (HFS) problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimises the makespan. We present here an adaptation of the Depth-bounded Discrepancy Search (DDS) method to obtain near-optimal solutions with makespan of high quality. This adaptation for the HFS contains no redundancy for the search tree expansion. To improve the solutions of our HFS problem, we propose a local search method, called Climbing Depth-bounded Discrepancy Search (CDDS), which is a hybridisation of two existing discrepancy-based methods: DDS and Climbing Discrepancy Search (CDS). CDDS introduces an intensification process around promising solutions. These methods are tested on benchmark problems. Results show that discrepancy methods give promising results and CDDS method gives the best solutions. [Received 27 October 2006; Revised 27 February 2007; Accepted 8 March 2007].

Generalized disjunctive constraint propagation for solving the job shop problem with time lags

This paper addresses the job-shop scheduling problem with time-lags. We propose an insertion heuristic and generalized resource constraint propagation mechanisms. Our propositions are embedded in a branch-and-bound algorithm to provide an experimental evaluation on some benchmark instances. The results obtained conclude that our heuristic achieves the best solutions on the instances, especially when problems involve tightened time lags. The results also prove the interest of the constraint propagation generalization when time lags are considered.

Multi-objective optimization for selecting and scheduling observations by agile earth observing satellites

This paper presents a biased random-key genetic algorithm for solving a multi-objective optimization problem concerning the management of agile Earth observing satellites. It addresses the selection and scheduling of a subset of photographs from a set of candidates in order to optimize two objectives: maximizing the total profit, and ensuring fairness among users by minimizing the maximum profit difference between users. Two methods, one based on dominance, the other based on indicator, are compared to select the preferred solutions. The methods are evaluated on realistic instances derived from the 2003 ROADEF challenge.

YIELDS: A Yet Improved Limited Discrepancy Search for CSPs

In this paper, we introduce a Yet ImprovEd Limited Discrepancy Search (YIELDS), a complete algorithm for solving Constraint Satisfaction Problems. As indicated in its name, YIELDS is an improved version of Limited Discrepancy Search (LDS). It integrates constraint propagation and variable order learning. The learning scheme, which is the main contribution of this paper, takes benefit from failures encountered during search in order to enhance the efficiency of variable ordering heuristic. As a result, we obtain a search which needs less discrepancies than LDS to find a solution or to state a problem is intractable. This method is then less redundant than LDS. The efficiency of YIELDS is experimentally validated, comparing it with several solving algorithms: Depth-bounded Discrepancy Search, Forward Checking, and Maintaining Arc-Consistency. Experiments carried out on randomly generated binary CSPs and real problems clearly indicate that YIELDS often outperforms the algorithms with which it is compared, especially for tractable problems.

Solving two-stage hybrid flow shop using climbing depth-bounded discrepancy search

This paper investigates how to adapt a discrepancy-based search method to solve two-stage hybrid flowshop scheduling problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimizes the makespan. We present an adaptation of the Climbing Depth-bounded Discrepancy Search (CDDS) method based on Johnsons rule and on dedicated lower bounds for the two-stage hybrid flow shop problem. We report the results of extensive computational experiments, which show that the proposed adaptation of the CDDS method solves instances in restrained CPU time and with high quality of makespan.