Vincent T'Kindt

A Recovering Beam Search algorithm for the one-machine dynamic total completion time scheduling problem

This paper deals with the one-machine dynamic total completion time scheduling problem. This problem is known to be NP-hard in the strong sense. A polynomial time heuristic algorithm is proposed which applies the recently introduced Recovering Beam Search (RBS) approach. The algorithm is based on a beam search procedure with unitary beam width and includes a recovering subroutine that allows to overcome wrong decisions taken at higher levels of the beam search tree. It is shown that the total number of considered nodes is bounded by n where n is the jobsize. The proposed algorithm is able to solve in very short CPU time problems with up to 500 jobs outperforming the best state of the art heuristics.

Two-machine flowshop scheduling with a secondary criterion

This paper develops mathematical programming formulations, a branch-and-bound algorithm, and a heuristic algorithm for solving the two-machine flowshop scheduling problem with the objective of minimizing total completion time, subject to the constraint that the makespan is minimum. The proposed branch-and-bound algorithm uses several lower bounding schemes, which are based on problem relaxations. Several dominance conditions are used in the algorithm to limit the size of the search tree. Results of extensive computational tests show that the proposed branch-and-bound algorithm is effective in solving problems with up to 35 jobs. For problems containing larger number of jobs, the proposed heuristic algorithm, which is also used as an upper bound in the proposed branch-and-bound algorithm, is quite effective in finding an optimal or near-optimal schedule.

A recovering beam search algorithm for the single machine Just-in-Time scheduling problem

Abstract We consider the Just-in-Time scheduling problem where the Just-in-Time notion is captured by means of multiple conflicting criteria. The calculation of any non-dominated solution for these criteria is achieved by solving an extension of the single machine problem of minimising the mean weighted deviation from distinct due dates. In the extended problem each job to schedule is also constrained by a release date and a deadline. This problem is NP -Hard in the strong sense and we propose heuristic algorithms to solve it. Computational experiments show that, among those algorithms, the most effective heuristic, in terms of quality, is a Recovering Beam Search algorithm.

An Ant Colony Optimisation Algorithm for the Set Packing Problem

In this paper we consider the application of an Ant Colony Optimisation (ACO) metaheuristic on the Set Packing Problem (SPP) which is a NP-hard optimisation problem. For the proposed algorithm, two solution construction strategies based on exploration and exploitation of solution space are designed. The main difference between both strategies concerns the use of pheromones during the solution construction. The selection of one strategy is driven automatically by the search process. A territory disturbance strategy is integrated in the algorithm and is triggered when the convergence of the ACO stagnates. A set of randomly generated numerical instances, involving from 100 to 1000 variables and 100 to 5000 constraints, was used to perform computational experiments. To the best of our knowledge, only one other metaheuristic (Greedy Randomized Adaptative Search Procedure, GRASP) has been previously applied to the SPP. Consequently, we report and discuss the effectiveness of ACO when compared to the best known solutions and including those provided by GRASP. Optimal solutions obtained with Cplex on the smaller instances (up to 200 variables) are indicated with the calculation times. These experiments show that our ACO heuristic outperforms the GRASP heuristic. It is remarkable that the ACO heuristic is made up of simple search techniques whilst the considered GRASP heuristic is more evolved.

Solving a bicriteria scheduling problem on unrelated parallel machines occurring in the glass bottle industry

Abstract This paper deals with the resolution of a bicriteria scheduling problem connected with the glass bottles production. The shop is made up of unrelated parallel machines and the aim is to compute a schedule of orders that maximizes the total margin and that minimizes the difference in machines workload. An algorithm to compute the set of all strict Pareto optima is offered and later extended into an interactive algorithm.

Revisiting Branch and Bound Search Strategies for Machine Scheduling Problems

In the design of exact methods for NP-hard machine scheduling problems, branch and bound algorithms have always been widely considered. In this work we revisit the classic search strategies for branch and bound schemes. We consider a systematic application of the well known dynamic programming dominance property for machine scheduling problems. Several conditions concerning the application of the proposed property with respect to best first, depth first, breadth first search strategies and problem characteristics are presented. Computational testing on single machine and flow shop problems validate in practice the efficiency of the considered approach and suggest that the traditional choice of depth first search with respect to best first and breadth first is strongly questionable.

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.

Improving the preemptive bound for the one-machine dynamic total completion time scheduling problem

We consider the single machine dynamic total completion time scheduling problem. This problem is known to be NP-hard in the strong sense. The currently best available lower bound for the problem is known to be the optimal solution value of the corresponding preemptive problem which can be computed in O(nlogn) time. We propose an improvement on this bound by exploiting the properties of the preemptive solution. The proposed improvement reduces by approximately 44% on the average the gap between the preemptive solution value and the optimal solution value.

The e-OCEA project: towards an internet decision system for scheduling problems

This paper deals with an Internet decision support system for scheduling problems. This system, called e-OCEA, is being developed at the Laboratory of Computer Sciences of the University of Tours. It provides a user with tools to help create an effective algorithm to solve a scheduling problem. From the modelisation of the problem to the visualization of a computed schedule, the e-OCEA system offers software that can be used either by operations researchers or industrial engineers. In this paper, we present the current state of this system and provide future directions.

Counting and enumeration complexity with application to multicriteria scheduling

Abstract.In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results.