Genetic algorithms for single machine scheduling with quadratic earliness and tardiness costs

Abstract

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet and present several algorithms based on this approach. These versions differ on the generation of both the initial population and the individuals added in the migration step, as well as on the use of local search. The proposed procedures are compared with the best existing heuristics, as well as with optimal solutions for the smaller instance sizes. The computational results show that the proposed algorithms clearly outperform the existing procedures and are quite close to the optimum. The improvement over the existing heuristics increases with both the difficulty and the size of the instances. The performance of the proposed genetic approach is improved by the initialization of the initial population, the generation of greedy randomized solutions, and the addition of the local search procedure. Indeed, the more sophisticated versions can obtain similar or better solutions and are much faster. The genetic version that incorporates all the considered features is the new heuristic of choice for small and medium size instances. Keywords Scheduling. Single machine. Quadratic earliness and tardiness. Genetic algorithms j , subject to the constraint that no machine idle time is allowed. Even though scheduling models with a single processor may appear to arise infrequently in practice, this scheduling environment actually occurs in several activities (for a specific example in the chemical industry, see [1]). Also,

Solving the flexible job-shop just-in-time scheduling problem with quadratic earliness and tardiness costs

“…Two of the studies dealing with quadratic JIT costs were carried out by Hussain and Joshi [22] and Zambrano Rey et al [25], using GA. Other studies were designed for less complex problems such as the flow-shop-like problem [39] or the single machine problem [4,5]. In fact, in a recent study by Demir and Kürşat [10], out of the 23 papers reviewed, none targeted the FJSSP with quadratic earliness and tardiness costs.…”

“…JIT scheduling has been studied since the 1990s, but due to the intractable nature of the problem, the main focus has been on single machine problems [4,5], or specific cases of multiple machine problems: job shops with tardiness costs [6], identical parallel machines with earliness and tardiness costs [7], or problems with common due dates with earliness and tardiness penalties [8]. This paper focuses more particularly on flexible job-shop JIT scheduling.…”

Variable neighborhood search for the workload balancing problem in service enterprises

“…To practically solve the QIP, heuristic algorithms which find high quality solutions in short computation time have been proposed. Such heuristic algorithms are iterated local search [1], variable neighborhood search [2,3,4], simulated annealing [5,6,7], tabu search [8,9,10], genetic algorithms [11,12,13,14,15], evolution strategies [16,17], ant algorithms [18,19,20,21], and scatter search [22,13]. Among them, iterated local search (ILS) is a simple and powerful stochastic local search method for solving combinatorial problems.…”

Hybrid heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs

“…Among several beam search heuristic procedures proposed in this paper the recovering beam search (RBS) procedure produced the best results. Valente et al [16] proposed six random-key encoding [4] based elitist generational genetic algorithms. These genetic algorithms differ only slightly from one another.…”

“…As described in Sect. 2, the genetic algorithm used here is altogether different from those used in Valente et al [16], i.e., solution encoding, population replacement strategy, genetic operators viz. selection, mutation and crossover are all different.…”