This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual 'natural' permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multi-start implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighbourhood search methods which use the permutation and binary representations shows that the permutation-based methods have a higher likelihood of generating an optimal solution, but are less robust in that some poor solutions are obtained. Of the neighbourhood search methods, tabu search clearly dominates the others. Multi-start descent performs remarkably well relative to simulated annealing and threshold accepting.
Introduction
HistorySheet metal operations have been in existence since 8000 B.C. (Fries-Knoblach, 1999). Due to its long history, sheet metalworking is, unfortunately, often seen as archaic and uninteresting. That metal sheets can be transformed with the aid of robust machines into fancy consumer products with tight tolerances is inconceivable to many. Yet, sheet metal operations are used for producing both structural components and durable consumer goods. Nowadays, sheet metal parts are widely present in different daily life products. During the past decades, scientific research in the field of sheet metal operations has been booming and international conferences on different sheet metal topics attract numerous attendants. Both industry and the academic community recognize the importance of continuing improvement in sheet metal operations. Thirty years ago, the rapid advance of computer systems triggered the introduction of automation in manufacturing environments. Also for sheet metal operations the use of computer systems has become indispensable to survive. Computer aided design (CAD) and computer aided manufacturing (CAM) systems are widely present in sheet metal production environments. At the earliest design stage, CAD systems are used to computerize the whole process of drawing and redrawing the desired part. Most modern CAD systems allow to build up a part from several re-usable 3D components, thus automating to a large extent the time consuming design process. The use of computers has also entered the manufacturing stage through computer aided manufacturing. The CAD file is converted into a sequence of processes for manufacture on a numerically controlled (NC) machine. The use of computers helps operators in automating different steps of the production process. As far as planning is concerned, most attention is focused on the computerization of sheet metal process planning. Production planning proper received much less attention due to a long tradition of experience-based production planning.
Scope of the researchIf one queries the internet for sheet metal operations, numerous entries on processes are found, for instance on laser cutting, punching, deep drawing, bending, incremental forming,
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