A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem

We consider the single-machine total weighted tardiness problem (TWT) where a set of n jobs with general weights w_1,…, w_n, integer processing times p_1,…, p_n, and integer due dates d_1,…, d_n has to be scheduled non-preemptively. If C_j is the completion time of job j then T_j = max(0, C_j - d_j) denotes the tardiness of this job. The objective is to find a schedule S^{*}_{WT} that minimizes the weighted sum of the tardiness costs of all jobs computed as \sum_{j=1}^{n} w_j T_j. This problem is known to be unary NP-hard. Our goal is to design a constructive heuristic for this problem that yields excellent feasible solutions in short computational times by exploiting the structural properties of a preemptive relaxation

Dominance-Based Heuristics for One-Machine Total Cost Scheduling Problems

International audienceWe study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria

Evaluación de funciones de utilidad de GRASP en la programación de producción para minimizar la tardanza total ponderada en una máquina

This paper considers the total weighted tardiness minimization in a single machineenvironment (1|| wj Tj ) a scheduling problem which has been proved to be NP-Hard. The solution approach uses the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic known for the quality of the solutions it can generate and the selective ability of its utility function during the construction phase. This work proposes and analyses three different utility functions for the problem in question. A statistical study showed significant differences between the mean values obtained from the proposed utility functions. The computational experiments were carried out using problems instances found in the OR-LIBRARY, and the outcome of these experiments were competitive solutions compared to the best known values of the instances involved. This work also shows the ease of developing GRASP methods for solving scheduling problems in a simple spreadsheet software such as MS Excel.Este artículo aborda la minimización de la tardanza total ponderada en un entorno de producción (1|| wj Tj ) que es conocido en complejidad como de tipo NP-hard. El enfoque de solución propuesto utiliza la metaheurística Greedy Randomized Adaptive Search Procedure (GRASP), la cual es reconocida por la correlación existente entre la calidad de las soluciones y la capacidad discriminante de la función de utilidad empleada en su fase constructiva. Este trabajo propone y analiza tres diferentes funciones de utilidad para este problema en particular. El desempeño de estas funciones se evaluó mediante un estudio estadístico que evidenció diferencias significativas en los valores medios de tardanza total ponderada, explicadas por el factor función de utilidad. La fase experimental se desarrolló usando instancias de la librería OR-LIBRARY y permitió obtener soluciones competitivas en calidad con respecto a los mejores valores conocidos para las instancias de este problema. Este trabajo ilustra la potencialidad de uso de métodos GRASP implementados en una hoja de cálculo normal para hallar soluciones a problemas de programación de la producción

On Neighborhood Tree Search

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by exploring different paths of the tree in a heuristic way. We show that allowing the search to 'backtrack' to a previously visited solution and resuming the iterative variable neighborhood descent by 'pruning' the already explored neighborhood branches leads to the design of effective and efficient search heuristics. We describe this idea by discussing its basic design components within a generic algorithmic scheme and we propose some simple and intuitive strategies to guide the search when traversing the neighborhood tree. We conduct a thorough experimental analysis of this approach by considering two different problem domains, namely, the Total Weighted Tardiness Problem (SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show that independently of the considered domain, the approach is highly competitive. In particular, we show that using different branching and backtracking strategies when exploring the neighborhood tree allows us to achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012

A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem

We consider the non-preemptive single-machine total weighted tardiness (TWT) problem with general weights, processing times, and due dates. We first develop a family of preemptive lower bounds for this problem and explore their structural properties. Then, we show that the solution corresponding to the least tight lower-bound among those investigated features some desirable properties that can be exploited to build excellent feasible solutions to the original non-preemptive problem in short computational times. We present results on standard benchmark instances from the literature

Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Analysis of the stagnation behavior of the interacted multiple ant colonies optimization framework

Search Stagnation is a common problem that all Ant Colony Optimization (ACO) algorithms suffer from regardless of their application domain. The framework of Interacted Multiple Ant Colonies Optimization (IMACO) is a recent proposition.It divides the ants’ population into several colonies and employs certain techniques to organize the work of these colonies.This paper conducts experimental tests to analyze the stagnation behavior of IMACO.It also proposes the idea that different ant colonies use different types of problem dependent heuristics.The performance of IMACO was demonstrated by comparing it with the Ant Colony System (ACS) the best performing ant algorithm.The Computational results show the superiority of IMACO. The results show that IMACO suffers less from stagnation than ACS