Czesław Smutnicki

A fast tabu search algorithm for the permutation flow-shop problem

Abstract A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented. The algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion. Computational experiments (up to 500 jobs and 20 machines) show its excellent numerical properties.

An Advanced Tabu Search Algorithm for the Job Shop Problem

The job shop scheduling problem with the makespan criterion is a certain NP-hard case from OR theory having excellent practical applications. This problem, having been examined for years, is also regarded as an indicator of the quality of advanced scheduling algorithms. In this paper we provide a new approximate algorithm that is based on the big valley phenomenon, and uses some elements of so-called path relinking technique as well as new theoretical properties of neighbourhoods. The proposed algorithm owns, unprecedented up to now, accuracy, obtainable in a quick time on a PC, which has been confirmed after wide computer tests.

The flow shop with parallel machines: A tabu search approach

A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in a flow shop with parallel machines is presented. The algorithm is based on a tabu search technique with a specific neighborhood definition which employs notions of a critical path in a graph and a block of jobs. This is the first improvement algorithm for the considered problem. A special advanced method of implementation improves the local search significantly and increases the speed of the algorithm. Computational experiments (up to 3000 operations and 60 machines) show its excellent numerical properties. The proposed approach can be used for modeling and solving a broad class of flexible flow line scheduling problems.

Some aspects of scatter search in the flow-shop problem

Abstract The flow-shop scheduling problem with the makespan criterion is a certain strongly NP-hard case from the domain of OR. This problem, having simple formulation contrasting with its troublesome, complex and time-consuming solution methods, is ideal for testing the quality of advanced combinatorial optimization algorithms. Although many excellent approximate algorithms for the flow-shop problem have been provided, up till now, in the literature, some theoretical and experimental problems associated with an algorithm’s activity still remain unexamined. In this paper, we provide a new view on the solution space and the search process. Relying upon it, we are proposing the new approximate algorithm, which applies some properties of neighborhoods, refers to the big valley phenomenon, uses some elements of the scatter search as well as the path relinking technique. This algorithm shows up to now unprecedented accuracy, obtainable within a short time on a PC, which has been confirmed in a wide variety of computer tests. Good properties of the algorithm remain scalable if the size of instances increases.

Some results of the worst-case analysis for flow shop scheduling

Abstract Known approximation algorithms recommended for the permutation flow-shop problem with the weighted sum of completion times have a worst-case performance ratio which is unknown, or known but unlimited. We propose new algorithms with this ratio equal to [ m k]ϱ k , where ϱk is the worst-case performance ratio of an algorithm which solves an auxiliary k-machine problem. Worst-case analyses of other approximation algorithms for the mean completion time and the makespan criteria are also presented.

Worst-case analysis of an approximation algorithm for flow-shop scheduling

A worst-case analysis of an algorithm proposed by Campbell et al. for the m-machine permutation flow-shop problem is presented. The tight worst-case performance ratio [m/2] is found.

A two-machine permutation flow shop scheduling problem with buffers

Problems with “blocking” (limited intermediate storage space) are used frequently for modelling and scheduling just-in-time and flexible manufacturing systems. In this paper, an approximation algorithm is presented for the problem of finding the minimum makespan in a two-machine permutation flow-shop scheduling problem with the mediating buffer of finite capacity. The algorithm is based on the tabu search approach supported by the reduced neighborhood, search accelerator and technique of back jumps on the search trajectory. Due to some special properties, the proposed algorithm provides makespans very close to optimal in a short time. It has been shown that this algorithm outperforms all known approximation algorithms for the problem stated.ZusammenfassungIn dieser Arbeit wird eine Heuristik zur Ermittlung der minimalen Gesamtdurchlaufzeit in einem Zwei-Maschinen-Flow-Shop-Problem mit begrenzter Zwischenlagerkapazität vorgestellt. Solche Maschinenbelegungs-planungsprobleme werden häufig zur Modellierung von Justin-Time und Flexiblen Fertigungssytemen eingesetzt. Der Algorithmus basiert auf dem Tabu-Search-Verfahren mit eingeschränkter Nachbarschaft, beschleunigter Suche und Rücksprungtechnik auf der Suchtrajektorie. Aufgrund einiger spezieller Eigenschaften liefert das vorgestellte Verfahren in kurzer Zeit Lösungsqualitäten nahe dem Optimum.

Parallel tabu search algorithm for the hybrid flow shop problem

The paper deals with the parallel variant of the scheduling algorithm dedicated to the hybrid flow shop problem. The problem derives from practice of automated manufacturing lines, e.g. for printed packages. The overall goal is to design a new algorithm which merges the performance of the best known sequential approach with the efficient exploitation of parallel calculation environments. In order to fulfill the above aim, there are two methods proposed in this paper: the original fast method of parallel calculation of the criterion function and the local neighborhood parallel search method embedded in the tabu search approach. The theoretical analysis, as well as the original implementation, with the use of vector processing instructions SSE2 supported by suitable data organization, are presented below. Numerical properties of the proposed algorithm are empirically verified on the multi-core processor.

Some New Ideas in TS for Job Shop Scheduling

This paper deals with a classic job-shop scheduling problem with the makespan criterion. Some properties of the fast algorithm TSAB of Nowicki and Smutnicki, as well as properties of the solution space, have been discussed and examined. Next, by introducing the original method of diversification, TSAB has been embedded in more advanced algorithmic framework i-TSAB, which has far analogy to path relinking technique. Newly proposed algorithm is faster and has better accuracy than TSAB, runs within time of minutes on a PC and already in preliminary tests provides 23 new upper bounds among 35 unsolved yet common Taillards benchmarks.

New results in the worst-case analysis for flow-shop scheduling

Abstract The worst-case analysis of the approximation algorithm proposed by Palmer and the algorithm RAES (the best of algorithms proposed by Dannenbring) for m-machine permutation flow-shop problem are presented. The worst-case performance ratios equal approximately m 2 for each of the algorithms are found. An evaluation of the worst-case performance ratio of Nawazs algorithm N is shown. Proposed are a few modifications improving the speed of the algorithms RAES and N.