A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with the best existing heuristic, as well as with optimal solutions for the smaller instance sizes. The computational results show that the performance of the proposed genetic approach is improved by the addition of a local search procedure, as well as by the insertion of simple heuristic solutions in the initial population. Indeed, the genetic versions that include either or both of these features not only provide significantly better results, but are also much faster. The genetic versions that use local search are clearly superior to the best existing heuristic, and the improvement in performance increases with both the size and difficulty of the instances. These procedures are also quite close to the optimum, and provided an optimal solution for most of the test instances.scheduling, single machine, linear earliness, quadratic tardiness, genetic algorithms

Greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we present greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomized schedules. On the other hand, these versions also differ on whether they employ only a final improvement step, or perform a local search after each greedy randomized construction. The proposed heuristics were compared with existing procedures, as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances, as well as a suitable alternative to the best existing procedure for the larger of the middle size instances.scheduling, single machine, early/tardy, quadratic penalties, greedy randomized dispatching rules

A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Hybrid Genetic Bees Algorithm applied to Single Machine Scheduling with Earliness and Tardiness Penalties

This paper presents a hybrid Genetic-Bees Algorithm based optimised solution for the single machine scheduling problem. The enhancement of the Bees Algorithm (BA) is conducted using the Genetic Algorithm's (GA's) operators during the global search stage. The proposed enhancement aims to increase the global search capability of the BA gradually with new additions. Although the BA has very successful implementations on various type of optimisation problems, it has found that the algorithm suffers from weak global search ability which increases the computational complexities on NP-hard type optimisation problems e.g. combinatorial/permutational type optimisation problems. This weakness occurs due to using a simple global random search operation during the search process. To reinforce the global search process in the BA, the proposed enhancement is utilised to increase exploration capability by expanding the number of fittest solutions through the genetical variations of promising solutions. The hybridisation process is realised by including two strategies into the basic BA, named as â\u80\u9creinforced global searchâ\u80\u9d and â\u80\u9cjumping functionâ\u80\u9d strategies. The reinforced global search strategy is the first stage of the hybridisation process and contains the mutation operator of the GA. The second strategy, jumping function strategy, consists of four GA operators as single point crossover, multipoint crossover, mutation and randomisation. To demonstrate the strength of the proposed solution, several experiments were carried out on 280 well-known single machine benchmark instances, and the results are presented by comparing to other well-known heuristic algorithms. According to the experiments, the proposed enhancements provides better capability to basic BA to jump from local minima, and GBA performed better compared to BA in terms of convergence and the quality of results. The convergence time reduced about 60% with about 30% better results for highly constrained jobs

Heuristic and Exact Algorithms for the Two-Machine Just in Time Job Shop Scheduling Problem

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithms proposed to find approximate solutions. Through computational experiments, the heuristic algorithms\u27 performance is evaluated with problems up to 500 jobs

Multiple neighborhoods in tabu search: successful applications for operations management problems

A metaheuristic is a refined solution method able to find a satisfying solution to a difficult problem in a reasonable amount of time. A local search metaheuristic works on a single solution and tries to improve it iteratively. Tabu search is one of the most famous local search, where at each iteration, a neighbor solution is generated from the current solution by performing a specific modification (called a move) on the latter. In contrast with most of the existing literature, the goal of this paper is to present tabu search approaches where different neighborhood structures (i.e., different types of moves) are jointly used. The discussion is illustrated for various operations management problems: truck loading, job scheduling, inventory management, and dimensioning of assembly lines

A genetic algorithm for assigning train arrival dates at a maintenance centre

© 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. The paper is concerned with planning heavy maintenance of train-sets at a maintenance centre. The heavy maintenance process is complex and, for each train-set, the actual duration of maintenance is uncertain at the time of planning. The allocation of the dates when train-sets should arrive at the maintenance centre is crucial phase of the planning procedure. The objective function is a weighted sum of two components, the expected total penalty for not meeting the required number of train-sets in active service and the total cost for the deviation (earliness and tardiness) from the desired dates of arrival. A genetic algorithm is presented for the considered problem and its effectiveness is demonstrated by the computational experiments that used real-world data provided by a big maintenance centre

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs