This report discusses the design of computational experiments to test heuristic methods and provides reporting guidelines for such experimentation. The goal is to promote thoughtful, well-planned, and extensive testing of heuristics, full disclosure of experimental conditions, and integrity in and reproducibility of the reported results. 1

:- Due to the stubborn nature of the deterministic job-shop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS:- Scheduling Theory; Job-Shop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...

Scheduling in an environment with constraints of many different types is known to be a hard problem. We tackle this problem for an integrated steel plant in Ghent, Belgium, using UPPAAL, a model checker for networks of timed automata. We show how to translate schedulability to reachability, enabling us to use UPPAAL's model checking algorithms. 1. Introduction This report is a result of the participation of CSI Nijmegen in the European Union Esprit long term research project Verification of Hybrid Systems (http://wwwverimag. imag.fr//VHS/). The Esprit program was set up to improve the take-up of modern information technologies in industry. The VHS project in particular is meant to stimulate research in the area of hybrid systems. These systems typically consist of digital components in a continuous environment. The correct behavior depends strongly on the interaction between the digital components, say the controller, and the controlled process. Hybrid systems are important in numero...

Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Systematic techniques such as chronological backtracking can be applied to these problems, but the order in which they examine nodes makes them unlikely to find a solution in the explored fraction of the space. Nonsystematic techniques have been proposed to alleviate the problem by searching nodes in a random order. A technique known as iterative sampling follows random paths from the root of the tree to the fringe, stopping if a path ends at a goal node. Although the nonsystematic techniques do not suffer from the problem of exploring nodes in a bad order, they do reconsider nodes they have already ruled out, a problem that is serious when the density of solutions in the tree is low. Unfortunately, for many practical problems the order of examing nodes matters and the density of solutions is low. Consequently, neither chronological backtracking...

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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%.

Abstract. In this paper, we present a major improvement in the search procedures in constraint programming. First, we integrate various search procedures from AI and OR. Second, we parallelize the search on shared-memory computers. Third, we add an object-oriented extensible control language to implement complex complete and incomplete search procedures. The result is a powerful set of tools which offers both brute force search using simple search procedures and parallelism, and finely tuned search procedures using that expressive control language. With this, we were able both to solve difficult and open problems using complete search procedures, and to quickly produce good results using incomplete search procedures. 1

: The Job-Shop Scheduling Problem (JSSP) is one of the most difficult NP-hard combinatorial optimization problems. This paper proposes a new method for solving JSSPs based on simulated annealing (SA), a stochastic local search, enhanced by shifting bottleneck (SB), a problem specific deterministic local search. In our method new schedules are generated by a variant of Giffler and Thompson's active scheduler with operation permutations on the critical path. SA selects a new schedule and probabilistically accepts or rejects it. The modified SB is applied to repair the rejected schedule; the new schedule is accepted if an improvement is made. Experimental results showed the proposed method found near optimal schedules for the difficult benchmark problems and outperformed other existing local search algorithms. Key Words: Simulated annealing, shifting bottleneck, job-shop scheduling, heuristics, local search 1. Background Scheduling is allocating shared resources over time to competi...

A great deal of research has been focused on solving the job-shop problem (P J ), over the last forty years, resulting in a wide variety of approaches. Recently, much effort has been concentrated on hybrid methods to solve P J as a single technique cannot solve this stubborn problem. As a result much effort has recently been concentrated on techniques that combine myopic problem specific methods and a meta-strategy which guides the search out of local optima. These approaches currently provide the best results. Such hybrid techniques are known as iterated local search algorithms or meta-heuristics. In this paper we seek to assess the work done in the job-shop domain by providing a review of many of the techniques used. The impact of the major contributions is indicated by applying these techniques to a set of standard benchmark problems. It is established that methods such as Tabu Search, Genetic Algorithms, Simulated Annealing should be considered complementary rather than competitive...

We present constraint-based optimization algorithms and a constraintbased approximation algorithm for the job-shop scheduling problem. An empirical performance analysis shows that both the optimization algorithms and the approximation algorithm perform well. Especially the approximation algorithm is among the best algorithms known to date. We, furthermore, show that we can improve the performance of the optimization algorithms by combining them with the approximation algorithm.