Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.     

Effects and relationships of parameters in a rule–based fuzzy system

Hierarchies of criteria and fuzzy rule systems represent an approach which effectively portrays the problem of multiple objectives found in classic decision–making scenarios such as order sequencing or the evaluation of various corporate strategies. They further help the decision–maker to select a concrete course of action. The relevant decision criteria are formalized with the help of linguistic variables. A hierarchy of criteria is then used to relate them to one another and to combine them by rule–bases. Evaluation using fuzzy sets leads to an aggregated rating of the individual alternatives. A problem of such fuzzy systems is the large number of required parameters and their influence on the evaluation results. This article will use the example of a simple criteria hierarchy for a sequencing problem to analyze the effects of individual parameters and their relationships amongst one another in a fuzzy system.     

Fuzzy inference-based multiple criteria FMS scheduling

This paper proposes a fuzzy inference-based scheduling decision for flexible manufacturing systems (FMS) with multiple objectives. The objectives have different and dynamic preference levels. It is inferred that the changes in the production environment may be sensed by environmental variables. The detected changes are input in a fuzzy inference mechanism, which outputs the current preference levels of all objectives. A multiple criteria scheduling decision is then made, using the partitioned combination of the preference levels. An example of application is presented. Simulation results show very good performance for the proposed system.     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.     

A tabu search algorithm for solving a multicriteria flexible job shop scheduling problem

The problem that we consider in this article is a flexible job shop scheduling problem issued from the printing and boarding industry. Two criteria have to be minimised, the makespan and the maximum lateness. Two tabu search algorithms are proposed for finding a set of non-dominated solutions: the first is based on the minimisation of one criterion subject to a bound on the second criterion (ε-constraint approach) and the second is based on the minimisation of a linear combination of criteria. These algorithms are tested on benchmark instances from the literature and the results are discussed. The total tardiness is considered as a third criterion for the second tabu search and results are presented and discussed.     

Maintenance policy selection in manufacturing firms using the fuzzy MCDM approach

In manufacturing firms, there is a critical need for proper maintenance of manufacturing facilities. The maintenance process enhances customer satisfaction and reliability of the products, and increases the profit of the manufacturer. Therefore, a proper maintenance policy selection is a critical issue for manufacturers, as an inefficient maintenance policy affects not only the direct cost of the firm but also the other aspects. In the present study, maintenance policy selection at the level of the firm rather than the equipment level is shown, and for selection various criteria have been identified. The presented work not only provides the best alternatives but also provides an alternative ranking, which facilitates decision-makers in choosing alternatives according to their constraints. These selection criteria are different in nature, as some give a crisp value, whereas others are defined in linguistic terms. To select the appropriate maintenance policy, a distance-based fuzzy multicriteria decision-making (MCDM) approach has been employed. The proposed method provides the means for integrating the economic figure of merit with the strategic performance variables. The MCDM approach is efficient in incorporating data, in the form of linguistic variables, triangular fuzzy numbers, and crisp numbers, into the evaluation process of maintenance policy alternatives. A comprehensive example illustrates the application of the distance-based fuzzy MCDM approach.     

Multicriteria analysis based on constructing payoff matrices and applying methods of decision making in?fuzzy environment

There exist two classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion or several criteria, but their unique solutions are unachievable, due to decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of models (??X,M?? and ??X,R?? models) can be constructed. Analysis of ??X,M?? and ??X,R?? models (based on applying the Bellman-Zadeh approach to decision making in a fuzzy environment and using fuzzy preference modeling techniques, respectively) serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. The paper results are of a universal character and are illustrated by an example.     

Jointly solving the group scheduling and machining speed selection problems: A hybrid tabu search and simulated annealing approach

In a cellular manufacturing environment, once the machines and parts have been grouped the remaining tasks are sequencing part families and scheduling operations for the parts within each part family so that some planning goals such as minimization of tardiness can be achieved. This type of problem is called group scheduling and will be analysed in this paper. The solution of the group scheduling is affected by the machining speed specified for each operation since the completion time of each operation is a function of machining speed. As such, the group scheduling and machining speed selection problems should be simultaneously solved to provide meaningful solutions. This, however, further complicates the solution procedure. In view of this, a hybrid tabu-simulated annealing approach is proposed to solve the group scheduling problem. The main advantage of this approach is that a short term memory provided by the tabu list can be used to avoid solution re-visits while preserving the stochastic nature of the simulated annealing method. The performance of this new method has been tested and favourably compared with two other algorithms using tabu search and simulated annealing alone.     

Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives

Considering the high required capital outlay and moderate risk of a flexible manufacturing system (FMS) investment, economic justification techniques are insufficient by themselves since they cannot cope with the benefits such as flexibility and enhanced quality offered by advanced manufacturing technologies. A robust decision-making procedure for evaluating FMS requires the consideration of both economic and strategic investment measures. A distance-based fuzzy multicriteria decision-making (MCDM) framework based on the concepts of ideal and anti-ideal solutions is presented for the selection of an FMS from a set of mutually exclusive alternatives. The proposed method provides the means for integrating the economic figure of merit with the strategic performance variables. The multicriteria decision approach presented here enables us to incorporate data in the forms of linguistic variables, triangular fuzzy numbers and crisp numbers into the evaluation process of FMS alternatives. Linguistic variables are also used to indicate the criteria's importance weights assigned by the decisionmakers. A comprehensive example illustrates the application of the multicriteria decision analysis.     

Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness

This paper addresses the NP-hard problem of scheduling N independent jobs on a single machine with release dates, due dates, sequence dependent setup times, and no preemption where the objective is to minimize the weighted sum of squared tardiness. A Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangian relaxation. Sequence dependent setup times are formulated as capacity constraints, and then are relaxed using Lagrangian multipliers. The primal problem is decomposed into job-level subproblems which are solved optimally and an approximate dual problem is then solved using a sub-gradient technique. The result of the relaxation is a list of jobs sequenced by beginning times that is then improved via a three-way swap. Experimental results are compared with EDD (Earliest Due Date) and ATCS (Apparent Tardiness Cost with Setups) dispatching rules, a four-way swap local search, tabu search, and simulated annealing. The adopted approach results in superior solution quality with respect to EED, ATCS, four-way swap, and tabu search results. It has comparable solution quality to the simulated annealing results, but is substantially more computationally efficient. Overall, the approach is capable of dealing with realistically sized single machine scheduling problems with release dates, due dates, and sequence dependent setup times.     

A flow-based tabu search algorithm for the RCPSP with transfer times

In this paper, we propose a tabu search algorithm for the resource-constrained project scheduling problem with transfer times. Solutions are represented by resource flows extending the disjunctive graph model for shop scheduling problems. Neighborhoods are defined by parallel and serial modifications rerouting or reversing flow on certain arcs. This approach is evaluated from a theoretical and experimental point of view. Besides studying the connectivity of different neighborhoods, computational results are presented for benchmark instances with and without transfer times.     

Tabu search‐based approach to multi‐objective machine‐part cell formation

The machine‐part cell formation with respect to multiple objectives has been an attractive search topic since 1990 and many methodologies have been applied to consider simultaneously more than one objective. However, the majority of these works unify the various objectives into a single objective. The final result of such an approach is a compromise solution, whose non‐dominance is not guaranteed. A Pareto‐optimality‐based multi‐objective tabu search (MOTS) algorithm is presented for the machine‐part grouping problems with multiple objectives: it minimizes the total cost, which includes intra‐ and inter‐cell transportation cost and machine investment cost, minimizing the intra‐cell loading unbalance and minimizing the inter‐cell loading unbalance. A new approach is developed to maintain the archive storing non‐dominated solutions produced by the tabu search. The comparisons and analysis show that the proposed algorithm has considerable promise in multi‐objective cell design.     

An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimization

This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation‐based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd.     

A novel multiple attribute material selection approach with uncertain membership linguistic information

In engineering design, the decision to select an optimal material has become a challenging task for the designers, and the evaluation of alternative materials may be based on some multiple attribute decision making (MADM) methods. However, the current methods for material selection may induce the information losing and cannot represent the real preference of decision maker precisely. Therefore, in this paper, inspired by the idea of the intuitionistic linguistic variables, we define a new fuzzy variable called uncertain membership linguistic variable (UMLV) which composes two linguistic variables and membership degrees of elements to the linguistic variables. Meanwhile, the operational laws, score function, accuracy function and comparison rules of the UMLV are defined. Then, some aggregation operators are developed for aggregating the uncertain membership linguistic information such as the uncertain membership linguistic weighted average (UMLWA) operator, the uncertain membership linguistic weighted geometric (UMLWG) operator, the uncertain membership linguistic ordered weighted average (UMLOWA) operator and the uncertain membership linguistic ordered weighted geometric (UMLOWG) operator, and some desirable properties of these operators are discussed. Based on the proposed operators, an approach is proposed for material selection problems under uncertain membership linguistic environment. Finally, two numerical examples for material selection are given to illustrate the application of the proposed approach.     

Evaluating artificial intelligence heuristics for a flexible Kanban system: simultaneous Kanban controlling and scheduling

This paper evaluates several artificial intelligence heuristics for a simultaneous Kanban controlling and scheduling on a flexible Kanban system. The objective of the problem is to minimise a total production cost that includes due date penalty, inventory, and machining costs. We show that the simultaneous Kanban controlling and scheduling is critical in minimising the total production cost (approximately 30% cost reduction over scheduling without a Kanban controlling). To identify the most effective search method for the simultaneous Kanban controlling and scheduling, we evaluated widely known artificial intelligence heuristics: genetic algorithm, simulated annealing, tabu search, and neighbourhood search. Computational results show that the tabu search performs the best in terms of solution quality. The tabu search also requires a much less computational time than the genetic algorithm and the simulated annealing. To further improve the solution quality and computational time for a simultaneous Kanban controlling and scheduling on a flexible Kanban system, we developed a two-stage tabu search. At the beginning of the tabu search process, an initial solution is constructed by utilising the customer due date information given by a decision support system. The two-stage tabu search performs better than the tabu search with a randomly generated initial solution in both the solution quality and computational time across all problem sizes. The difference in the solution quality is more pronounced at the early stages of the search.     

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.     

A tabu search heuristic for scheduling the production processes at an oil refinery

In this paper we present a tabu search heuristic which can be used for scheduling the production at an oil refinery. The scheduling problem is to decide which production modes to use at the different processing units at each point in time. The problem is a type of lot-sizing problem where costs of changeovers, inventories and production are considered. In the suggested tabu search heuristic we explore the use of variable neighbourhood, dynamic penalty and different tabu lists. Computational results are presented for different versions of the heuristic and the results are compared to the best-known lower bound for a set of scheduling scenarios.     

Job shop scheduling with a non-regular objective: A comparison of neighbourhood structures based on a sequencing/timing decomposition

Commercial software packages for production management are characterized by a gap between MRP logic, based on a backward scheduling approach, and finite capacity scheduling, usually based on forward scheduling. In order to partially bridge that gap, we need scheduling algorithms able to meet due dates while keeping WIP and inventory costs low. This leads us to consider job shop scheduling problems characterized by non-regular objective functions; such problems are even more difficult than classical job shop scheduling, and suitable heuristics are needed. One possibility is to consider local search strategies based on the decomposition of the overall problem into sequencing and timing sub-problems. For given job sequences, the optimal timing problem can be solved as a node potential problem on a graph. Since solving the timing problem is a relatively time-consuming task, we need to define a suitable neighbourhood structure to explore the space of job sequences; this can be done by generalizing well-known results for the minimum makespan problem. A related issue is if solving timing problems exactly is really necessary, or if an approximate solution is sufficient; hence, we also consider solving the timing problem approximately by a fast heuristic. We compare different neighbourhood structures, by embedding them within a pure local improvement strategy. Computational experiments show that the overall approach performs better than release/dispatch rules, although the performance improvement depends on the problem characteristics, and that the fast heuristic is quite competitive with the optimal timing approach. On the one hand, these results pave the way to the development of better local search algorithms (based e.g. on tabu search); on the other hand, it is worth noting that the heuristic timing approach, unlike the optimal one, can be extended to cope with the complicating features typical of practical scheduling problems.     

A coloured Petri net-based hybrid heuristic search approach to simultaneous scheduling of machines and automated guided vehicles

To achieve a significant improvement in the overall performance of a flexible manufacturing system, the scheduling process must consider the interdependencies that exist between the machining and transport systems. However, most works have addressed the scheduling problem as two independent decision making problems, assuming sufficient capacity in the transport system. In this paper, we study the simultaneous scheduling (SS) problem of machines and automated guided vehicles using a timed coloured Petri net (TCPN) approach under two performance objectives; makespan and exit time of the last job. The modelling approach allows the evaluation of all the feasible vehicle assignments as opposed to the traditional dispatching rules and demonstrates the benefits of vehicle-controlled assignments over machine-controlled for certain production scenarios. In contrast with the hierarchical decomposition technique of existing approaches, TCPN is capable of describing the dynamics and evaluating the performance of the SS problem in a single model. Based on TCPN modelling, SS is performed using a hybrid heuristic search algorithm to find optimal or near-optimal schedules by searching through the reachability graph of the TCPN with heuristic functions. Large-sized instances are solved in relatively short computation times, which were a priori unsolvable with conventional search algorithms. The algorithm’s performance is evaluated on a benchmark of 82 test problems. Experimental results indicate that the proposed algorithm performs better than the conventional ones and compares favourably with other approaches.     

Tabu search algorithm for flexible flow path design of unidirectional automated-guided vehicle systems

The unidirectional flow path design problem is one of the most important but difficult problems for the efficient design of automated-guided vehicle systems. As the problem was first formulated by Gaskins and Tanchoco, many researchers have studied the problem. However, the existing solution methods fail to provide an efficient solution approach. In this paper, a mathematical model for the unidirectional flow path design problem is developed. To obtain a near-to-optimal solution in reasonable computation time, a tabu search algorithm is presented. A fast construction algorithm first obtains a feasible initial solution, and a long-term memory structure and a neighbor solution generation approach are adapted to the problem characteristics and embedded in the proposed tabu search algorithm. Computational experiments show that the developed tabu search algorithm outperforms the Ko and Egbelu’s algorithm, Int J Prod Res, 41:2325–2343, (2003).