. In this paper we show how the classical job-shop scheduling problem can be modeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to finding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniques for solving the optimization problem and, more importantly, it allows to model naturally more complex dynamic resource allocation problems which are not captured so easily in traditional models of operation research. We present several algorithms and heuristics for finding the shortest paths in timed automata and test their implementation in the tool Kronos on numerous benchmark examples. 1

In this paper we present an algorithm for efficiently computing the minimum cost of reaching a goal state in the model of Uniformly Priced Timed Automata (UPTA). This model can be seen as a submodel of the recently suggested model of linearly priced timed automata, which extends timed automata with prices on both locations and transitions. The presented algorithm is based on a symbolic semantics of UTPA, and an efficient representation and operations based on difference bound matrices. In analogy with Dijkstra's shortest path algorithm, we show that the search order of the algorithm can be chosen such that the number of symbolic states explored by the algorithm is optimal, to be optimal, in the sense that the number of explored states can not be reduced by any other search order. We also present a number of techniques inspired by branch-and-bound algorithms which can be used for limiting the search space and for quickly finding near-optimal solutions. The algorithm has been implemented in the verification tool Uppaal. When applied on a number of experiments the presented techniques reduced the explored state-space with up to 90%.

This document is based on the PhD thesis of the first author, defended at INPG Grenoble, November 2002

In this paper we show how the problem of job-shop scheduling where the jobs are preemptible can be modeled naturally as a shortest path problem defined on an extension of timed automata, namely stopwatch automata where some of the clocks might be freezed at certain states. Although standard verification problems on stopwatch automata are known to be undecidable, we show that due to well-known properties of optimal schedules, the shortest path in the automaton belongs to a finite class of acyclic paths where transitions occur at integer points in time, and hence the problem is solvable. We present several algorithms and heuristics for finding the shortest paths in such automata and test their implementation on numerous benchmark examples.

Tabu search algorithms are among the most effective approaches for solving the job-shop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP - complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating suboptimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very high-cost problem instances. Second, the model is significantly less accurate for structured, non-random JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP -complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than job-shop scheduling.

Abstract. In this paper we report a new SAT solver for difference logic, a propositional logic enriched with timing constraints. The main novelty of our solver is a tighter integration of the incremental analysis of numerical conflicts with the process of Boolean conflict analysis. This and other improvements lead to significant performance gains for some classes of problems. 1

Solution-Guided Multi-Point Constructive Search (SGMPCS) is a novel constructive search technique that performs a series of resource-limited tree searches where each search begins either from an empty solution (as in randomized restart) or from a solution that has been encountered during the search. A small number of these “elite ” solutions is maintained during the search. We introduce the technique and perform three sets of experiments on the job shop scheduling problem. First, a systematic, fully crossed study of SGMPCS is carried out to evaluate the performance impact of various parameter settings. Second, we inquire into the diversity of the elite solution set, showing, contrary to expectations, that a less diverse set leads to stronger performance. Finally, we compare the best parameter setting of SGMPCS from the first two experiments to chronological backtracking, limited discrepancy search, randomized restart, and a sophisticated tabu search algorithm on a set of well-known benchmark problems. Results demonstrate that SGMPCS is significantly better than the other constructive techniques tested, though lags behind the tabu search. 1.

Techniques that combine myopic problem specific methods and a meta-strategy, which guides the search out of local optimum, are currently providing the best results. Such hybrid methods are known as iterated local search algorithms or meta-heuristics. Despite the good results achieved by these methods the inability of many current meta-heuristics to provide a wide exploration of the search space in order to overcome strong local minima is highlighted here. Consequently in this work the evolutionary techniques of scatter search (SS) and its generalised form, path relinking (PR) are applied as they can provide the appropriate mixture of intensification (concentrate the search in promising areas) and diversification (search unvisited regions) and they can be integrated at various levels with intelligent search methods such as tabu search. The SS and PR strategies are embedded within a core and shell framework, in order to provide a wide exploration of the solution domain. Initiated from a ...

Over the last decade and a half, tabu search algorithms for machine scheduling have gained a near-mythical reputation by consistently equaling or establishing state-of-the-art performance levels on a range of academic and real-world problems. Yet, despite these successes, remarkably little research has been devoted to developing an understanding of why tabu search is so e#ective on this problem class. In this paper, we report results that provide significant progress in this direction. We consider Nowicki and Smutnicki's i-TSAB tabu search algorithm, which represents the current state-of-the-art for the makespan-minimization form of the classical jobshop scheduling problem. Via a series of controlled experiments, we identify those components of i-TSAB that enable it to achieve state-of-the-art performance levels. In doing so, we expose a number of misconceptions regarding the behavior and/or benefits of tabu search and other local search metaheuristics for the job-shop problem. Our results also serve to focus future research, by identifying those specific directions that are most likely to yield further improvements in performance.

We introduce BubbleSearch, a general approach for extending priority-based greedy heuristics.