Metaheuristics and Scheduling

Abstract

Scheduling involves taking decisions regarding the allocation of available capacity or resources (equipment, labour and space) to jobs, activities, tasks or customers over time. Scheduling thus results in a time-phased plan, or schedule of activities. The schedule indicates what is to be done, when, by whom and with what equipment. Although the statement of a manufacturing organizational problem such as scheduling may seem simple, we must never underestimate the effort necessary to find its solution [WID 98]. Scheduling problems can be modeled as assignment problems, which represent a large class of combinatorial optimization problems. In most of these cases, finding the optimal solution is very difficult. In fact, except for a few exceptions, the only known method to solve the problem to optimality would be to enumerate an exponential number of possible solutions! Specialists in this case speak of NP-complete problems [CAR 88, GAR 79]. In these conditions, it is necessary to find a solution method providing solutions of good quality in a reasonable amount of time: this is what heuristic methods are all about. This chapter focuses on describing the three main heuristic classes, constructive methods, local search methods and evolutionary algorithms [COS 95c]. Since these methods are general enough to be applied to a multitude of combinatorial optimization problems, they are called metaheuristics.This chapter is organized as follows: the next two sections indicate how to model scheduling problems in terms of combinatorial optimization and briefly describe the Chapter written by Marino WIDMER, Alain HERTZ and Daniel COSTA.

8kaynak Kisitli Proje Çi̇zelgeleme Problemi̇nde Tekrarsiz Kromozom Destekli̇ Paralel Geneti̇k Algori̇tma Uygulamasi

“…Bu nedenle, problemin çözümü için sezgisel algoritmalar gerekli olmuştur. Sezgisel ve metasezgisel teknikler, makul bir süre içinde çözümler üretseler de, bunların etkililiğini ve verimliliğini arttırmak için daha fazla araştırma yapılması gerekmektedir (Widmer, Hertz, & Costa, 2008).…”

Automated Scheduling and Planning

“…Finding an exact solution may be very difficult due to searching an exponential number of possible solutions, and can be inappropriate because the problems may have large size, the dynamic character, constraints difficult to formulate in mathematical terms, contradictory objectives (Widmer and Costa, 2008). Exact algorithms are guaranteed to find an optimal solution, but they need exponential computation time in the worst-case for even small problem instances.…”

Minimizing Makespan in a Permutation Flow Shop Environment: Comparison of Scatter Search, Genetic Algorithm and Greedy Randomized Adaptive Search Procedures

“…Scheduling problems, which are combinatorial optimization problems, involve finding a schedule or assigning tasks to resources that optimize some objective function, subject to certain constraints. The higher the complexity, the harder it is to find the optimal solution to the problem (Widmer et al, 2008). Production scheduling problems have widespread coverage in the literature and have been addressed using different production systems, restrictions, source types, and objective functions.…”