A new hybrid meta-heuristic algorithm for solving single machine scheduling problems

A dissertation submitted in partial ful lment of the degree of Master of Science in Engineering (Electrical) (50/50) in the Faculty of Engineering and the Built Environment Department of Electrical and Information Engineering May 2017Numerous applications in a wide variety of elds has resulted in a rich history of research into optimisation for scheduling. Although it is a fundamental form of the problem, the single machine scheduling problem with two or more objectives is known to be NP-hard. For this reason we consider the single machine problem a good test bed for solution algorithms. While there is a plethora of research into various aspects of scheduling problems, little has been done in evaluating the performance of the Simulated Annealing algorithm for the fundamental problem, or using it in combination with other techniques. Speci cally, this has not been done for minimising total weighted earliness and tardiness, which is the optimisation objective of this work. If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible solution schedules. It is thus of de nite practical necessity to reduce the search space in order to nd an optimal or acceptable suboptimal solution in a shorter time, especially when scaling up the problem size. This is of particular importance in the application area of packet scheduling in wireless communications networks where the tolerance for computational delays is very low. The main contribution of this work is to investigate the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo methods before running the Simulated Annealing algorithm on the pruned search space can result in overall reduced running times. The search space is divided into a number of sections and Metropolis-Hastings Markov Chain Monte Carlo is performed over the sections in order to reduce the search space for Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time and number of sections of the pre-sampling algorithm, and the run time of Simulated Annealing for minimising the percentage deviation of the nal result from the optimal solution cost. Algorithm performance is determined both by computational complexity and the quality of the solution (i.e. the percentage deviation from the optimal). We nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation from the optimal, as compared to the basic Simulated Annealing algorithm on the full search space. More importantly, we are able to reduce the complexity of nding the optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis- Hastings iterations, r inner samples and m sections.MT 201

Iterated search methods for earliness and tardiness minimization in hybrid flowshops with due windows

[EN] In practice due dates usually behave more like intervals rather than specific points in time. This paper studies hybrid flowshops where jobs, if completed inside a due window, are considered on time. The objective is therefore the minimization of the weighted earliness and tardiness from the due window. This objective has seldom been studied and there are almost no previous works for hybrid flowshops. We present methods based on the simple concepts of iterated greedy and iterated local search. We introduce some novel operators and characteristics, like an optimal idle time insertion procedure and a two stage local search where, in the second stage, a limited local search on a exact representation is carried out. We also present a comprehensive computational campaign, including the reimplementation and comparison of 9 competing procedures. A thorough evaluation of all methods with more than 3000 instances shows that our presented approaches yield superior results which are also demonstrated to be statistically significant. Experiments also show the contribution of the new operators in the presented methods. (C) 2016 Elsevier Ltd. All rights reserved.The authors would like to thank Professors Lofti Hidri and Mohamed Haouari for sharing with us the source codes and explanations of the lower bounds. Quan-Ke Pan is supported by the National Natural Science Foundation of China (Grant No. 51575212), Program for New Century Excellent Talents in University (Grant No. NCET-13-0106), Science Foundation of Hubei Province in China (Grant No. 2015CFB560), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130042110035), Key Laboratory Basic Research Foundation of Education Department of Liaoning Province (LZ2014014), Open Research Fund Program of the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, China. Ruben Ruiz and Pedro Alfaro-Fernandez are supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) financed by FEDER funds.Pan, Q.; Ruiz García, R.; Alfaro-Fernandez, P. (2017). Iterated search methods for earliness and tardiness minimization in hybrid flowshops with due windows. Computers & Operations Research. 80:50-60. https://doi.org/10.1016/j.cor.2016.11.022S50608

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

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

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines

This paper deals with a realistic cyclic scheduling problem in the food industry environment in which parallel machines are considered to process perishable jobs with given release dates, due dates and deadlines. Jobs are subject to post-production shelf life limitation and must be delivered to retailers during the corresponding time window bounded by due dates and deadlines. Both early and tardy jobs are penalized by partial weighted earliness/tardiness functions and the overall problem is to provide a cyclic schedule of minimum cost. A mixed integer programming model is proposed and a heuristic solution beside an iterated greedy algorithm is developed to generate good and feasible solutions for the problem. The proposed MIP, heuristic and iterated greedy produce a series of solutions covering a wide range of cases from slow optimal solutions to quick and approximated schedules.Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202.Shirvani, N.; Ruiz García, R.; Shadrokh, S. (2014). Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines. International Journal of Production Economics. 156:1-12. https://doi.org/10.1016/j.ijpe.2014.04.013S11215

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 both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve 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. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs

Common due date early

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 91-96.This study considers a scheduling problem with position-dependent deteriorating jobs and a maintenance activity in a single machine. Even in the absence of maintenance activity and deterioration problem is NP-hard. A solution comprises the following: (i) positions of jobs, (ii) the position of the maintenance activity, (iii) starting time of the first job in the schedule. After the maintenance activity, machine will revert to its initial condition and deterioration will start anew. The objective is to minimize the total weighted earliness and tardiness costs. Jobs scheduled before (after) the due-date are penalized according to their earliness (tardiness) value. Polynomial (O(n log n)) time solutions are provided for some special cases. No polynomial solution exists for instances with tight due-dates. We propose a mixed integer programming model and efficient algorithms for the cases where mathematical formulation is not efficient in terms of computational time requirements. Computational results show that the proposed algorithms perform well in terms of both solution quality and computation time.Şirvan, FatmaM.S

Exact and Heuristic Algorithms for the Job Shop Scheduling Problem with Earliness and Tardiness Over a Common Due Date

Scheduling has turned out to be a fundamental activity for both production and service organizations. As competitive markets emerge, Just-In-Time (JIT) production has obtained more importance as a way of rapidly responding to continuously changing market forces. Due to their realistic assumptions, job shop production environments have gained much research effort among scheduling researchers. This research develops exact and heuristic methods and algorithms to solve the job shop scheduling problem when the objective is to minimize both earliness and tardiness costs over a common due date. The objective function of minimizing earliness and tardiness costs captures the essence of the JIT approach in job shops. A dynamic programming procedure is developed to solve smaller instances of the problem, and a Multi-Agent Systems approach is developed and implemented to solve the problem for larger instances since this problem is known to be NP-Hard in a strong sense. A combinational auction-based approach using a Mixed-Integer Linear Programming (MILP) model to construct and evaluate the bids is proposed. The results showed that the proposed combinational auction-based algorithm is able to find optimal solutions for problems that are balanced in processing times across machines. A price discrimination process is successfully implemented to deal with unbalanced problems. The exact and heuristic procedures developed in this research are the first steps to create a structured approach to handle this problem and as a result, a set of benchmark problems will be available to the scheduling research community

Scheduling for non regular performance measure under the due window approach

Cataloged from PDF version of article.In the last two decades, Just-In-Time (JIT) production has proved to be an essential requirement of world class manufacturing. This has made schedulers most concerned about the realization of a JIT environment. The JIT concept requires not only a penalty for backorder and lateness but also for earliness. This can be translated into non-regular scheduling objectives. The most obvious objective can be to minimize the deviation of completion times. Concerning earliness/tardiness problems, researchers have usually considered systems where jobs incur no penalty for completion at a certain point of time (i.e. due date). In practice, however, job completions can also be accepted without penalty within an interval in time, which is known as the due window. This paper studies the scheduling problems in terms of the non-regular measure, mean absolute deviation (MAD), under the due window approach. The study is conducted in a dynamic job shop environment. Furthermore, we propose two new rules that perform quite e ectively for the MAD measure. 1999 Elsevier Science Ltd. All rights reserved