Tabu List Size Research Articles

A Probabilistic Tabu Search State Assignment Algorithm for Area and Power Optimization of Sequential Circuits

State assignment is the most critical step in the synthesis and optimization of sequential circuits as it significantly impacts sequential circuits area and power. Due to the high complexity of the state assignment problem and the ineffectiveness of existing deterministic algorithms in generating good solutions, evolutionary algorithms can be employed to obtain more effective state assignment solutions. In this paper, we propose a probabilistic tabu search (PTS) state assignment algorithm that is employed for the optimization of area and power of sequential circuits. The proposed algorithm is based on tabu search with the addition of exploiting code swap probabilities to prune the search space more effectively. Code swap probabilities are updated dynamically during the execution of the algorithm in such a way that code swaps that result in relatively inferior solutions will be assigned lower probabilities while those that result in good solutions will be assigned higher probabilities. In addition, tabu list size is changed dynamically during execution to help the algorithm get out of local minima. Based on experimental results, we show that the proposed PTS state assignment algorithm is more effective than all existing state assignment algorithms as it generates state assignment solutions with significantly lower area and power.

Production scheduling problem in a factory of automobile component primer painting

In a factory of automobile component primer painting, various automobile parts are attached to overhead hangers in a conveyor line and undergo a series of coating processes. Thereafter, the components are wrapped at a packaging station. The packaging process should be fully balanced by an appropriate sequence of components to prevent the bottleneck effect because each component requires different packaging times and materials. An overhead hanger has a capacity limit and can hold varying numbers of components depending on the component type. Capacity loss can occur if the hanger capacity is not fully utilized. To increase hanger utilization, companies sometimes mix two or more component types on the same hangers, and these hangers are called mixed hangers. However, mixed hangers generally cause heavy workload because different items require additional setup times during hanging and packing processes. Hence, having many mixed hangers is not recommended. A good production schedule requires a small number of mixed hangers and maximizes hanger utilization and packaging workload balance. We show that the scheduling problem is NP-hard and develop a mathematical programming model and efficient solution approaches for the problem. When applying the methods to solve real problems, we also use an initial solution-generating method that minimizes the mixing cost, set a rule for hanging the items on hangers considering eligibility constraint, and decrease the size of tabu list in proportion to the remaining computational time for assuring intensification in the final iterations of the search. Experimental results demonstrate the effectiveness of the proposed approaches.

Analysis of Tabu List Length on Job Shop Scheduling Problem

Tabu search is one of the meta-heuristics methods that can solve job shop scheduling problem because it has the ability to direct other methods to exit or avoid from local optimal solutions by utilizing the memory structure that records the trace of the search process that has been done that called tabu list. The size of tabu list is too small causes the local optimum and the size is too large causes the algorithm does not work effectively and will be slower for finding the best solution. In this research, the authors analyse the influence of the length of tabu list on the performance of tabu search algorithm on job shop scheduling problem. The size of tabu list is obtained by finding the median value of the minimum tabu list and the size of tabu list that obtained from the method of tabu search. The result of experiment shows that the length of tabu list that obtained by finding the median value is ideal for the small and large size job.

DEFINING TABU TENURE FOR THE QUADRATIC ASSIGNMENT PROBLEM

Tabu search (TS) algorithms are among the most efficient heuristic techniques in combinatorial optimization. Within these algorithms, it is important that the proper policies for maintaining the tabu tenure (tabu list size) are applied. In this paper, we discuss the mechanisms of defining the tabu tenure for the famous combinatorial optimization problem − the quadratic assignment problem (QAP). Several variants of maintaining the tabu tenure are implemented. They are examined on the instances taken from the QAP instances library − QAPLIB. The results from the experiments demonstrate that the deterministic strategies of defining the tabu tenure are preferable to the corresponding random strategies.

Tabu search heuristic for efficiency of dynamic facility layout problem

The facility layout problem (FLP) is a well-researched problem of finding positions of departments on a plant floor such that departments do not overlap and some specific critical criteria involved in FLP are optimized. In addition, the facility layout dramatically influences the efficiency of material handling within a manufacturing system. In order to ensure optimal performance within a manufacturing system, the facility layout should reflect changes throughout time. However, the static facility layout problem with constant material flows between departments may not be a realistic scenario because a manufacturing facility is a dynamic system that constantly evolves. On the other hand, layout problem has multi-objective nature, and it is necessary to apply various criteria and goals for determining a good facility layout. As a result, this research is about determining a solution for dynamic facility layout problem (DFLP) with equal departments by applying data envelopment analysis (DEA) with consideration of some specific criteria which are cost, adjacency, and distance requested. Cost as a negative criterion is minimized and used as an input, whereas adjacency and distance requested are considered positive criteria and used as output of DEA model. In the proposed algorithm, at first, the initial layout is generated, and then its neighborhood is created by the pair exchange and reverse strategy. By applying tabu search heuristic using diversification strategy which includes “frequency-based memory,” “penalty function,” and “dynamic tabu list size” to the DEA model, the most desired efficient layout is obtained. Two data sets taken from the relevant literature are used to test and evaluate the performance of the proposed heuristic. Computational experiments show that the proposed heuristic outperforms other heuristics presented in relevant literature, and the most efficient layout is achieved.

CONSTRUCTION OF MIXED COVERING ARRAYS OF STRENGTHS 2 THROUGH 6 USING A TABU SEARCH APPROACH

The development of a new software system involves extensive tests of the software functionality in order to identify possible failures. Also, a software system already built requires a fine tuning of its configurable options to give the best performance in the environment where it is going to work. Both cases require a finite set of tests that avoids testing all the possible combinations (which is time consuming); to this situation mixed covering arrays (MCAs) are a feasible alternative. MCAs are combinatorial structures having a case per row. MCAs are small, in comparison with exhaustive search, and guarantee a level of interaction among the involved parameters (a difference with random testing). We present a tabu search algorithm (TSA) for the construction of MCAs. Also, we report the fine tuning process used to identify the best parameter values for TSA. The analyzed TSA parameters were three different initialization functions, five different tabu list sizes and the mixture of four neighborhood functions. The performance of TSA was evaluated with two benchmarks previously reported. The results showed that TSA improved the algorithms IPOG-F, ITCH, Jenny, TConfig, and TVG in relation with the size of the constructed matrices. Particularly, TSA found the optimal size in 20 of the 23 cases tested.

Non-adaptive and adaptive hybrid approaches for enhancing water quality management

Using optimization to help solve groundwater management problems cost-effectively is becoming increasingly important. Hybrid optimization approaches, that combine two or more optimization algorithms, will become valuable and common tools for addressing complex nonlinear hydrologic problems. Hybrid heuristic optimizers have capabilities far beyond those of a simple genetic algorithm (SGA), and are continuously improving. SGAs having only parent selection, crossover, and mutation are inefficient and rarely used for optimizing contaminant transport management. Even an advanced genetic algorithm (AGA) that includes elitism (to emphasize using the best strategies as parents) and healing (to help assure optimal strategy feasibility) is undesirably inefficient. Much more efficient than an AGA is the presented hybrid (AGCT), which adds comprehensive tabu search (TS) features to an AGA. TS mechanisms (TS probability, tabu list size, search coarseness and solution space size, and a TS threshold value) force the optimizer to search portions of the solution space that yield superior pumping strategies, and to avoid reproducing similar or inferior strategies. An AGCT characteristic is that TS control parameters are unchanging during optimization. However, TS parameter values that are ideal for optimization commencement can be undesirable when nearing assumed global optimality. The second presented hybrid, termed global converger (GC), is significantly better than the AGCT. GC includes AGCT plus feedback-driven auto-adaptive control that dynamically changes TS parameters during run-time. Before comparing AGCT and GC, we empirically derived scaled dimensionless TS control parameter guidelines by evaluating 50 sets of parameter values for a hypothetical optimization problem. For the hypothetical area, AGCT optimized both well locations and pumping rates. The parameters are useful starting values because using trial-and-error to identify an ideal combination of control parameter values for a new optimization problem can be time consuming. For comparison, AGA, AGCT, and GC are applied to optimize pumping rates for assumed well locations of a complex large-scale contaminant transport and remediation optimization problem at Blaine Naval Ammunition Depot (NAD). Both hybrid approaches converged more closely to the optimal solution than the non-hybrid AGA. GC averaged 18.79% better convergence than AGCT, and 31.9% than AGA, within the same computation time (12.5 days). AGCT averaged 13.1% better convergence than AGA. The GC can significantly reduce the burden of employing computationally intensive hydrologic simulation models within a limited time period and for real-world optimization problems. Although demonstrated for a groundwater quality problem, it is also applicable to other arenas, such as managing salt water intrusion and surface water contaminant loading.

Tratamento de um problema de escalonamento considerando datas de entrega, turnos de produção e trocas de ferramentas via Busca Tabu

Neste trabalho é abordado o Problema de Escalonamento em um Job Shop aplicado a um Sistema de Manufatura Flexível (SMF), sendo consideradas restrições de datas de entrega, turnos de produção e trocas de ferramentas. O SMF considerado é composto de uma máquina versátil, um sistema de transporte e manuseio de materiais e um sistema computacional. O problema é representado por uma função objetivo f, na qual é possível definir três políticas de minimização: (i) tempo de atraso, (ii) tempo de parada para a troca de ferramentas e (iii) tempo de trocas de ferramentas. A aplicação das políticas é feita pela definição de pesos às variáveis de decisão de f. A busca pelo escalonamento que minimiza f é feita utilizando a técnica de Busca Tabu (BT). Foram realizados experimentos onde é observado o impacto de cinco regras de geração de soluções iniciais no desempenho da Busca Tabu. Também foram realizados experimentos nos quais se verifica o comportamento da busca frente à escolha das políticas de minimização. Nestes experimentos notou-se o conflito entre a política de minimização de atraso e as de minimização de trocas de ferramentas e de paradas para trocas de ferramentas. O aumento dos parâmetros da BT, nbmax (número máximo de iterações sem encontrar melhora no resultado global da busca) e tamanho da Lista Tabu, melhora o desempenho da busca para encontrar melhores resultados na minimização do atraso.

A methodology for solving the unequal area facility layout problem using distance and shape-based measures

This paper presents a methodology for solving the unequal area facility layout problem commonly encountered in industry practice. A mixed-binary nonlinear-programming model is formulated to capture the operational issues encountered on the shop floor. In particular, in addition to the distance measure that is typically used to quantify the material handling costs, the impact of geometry or the shape of the departments is quantified in the formulation of the model. A higher-level heuristic solution algorithm, based on a concept known as ‘tabu search’, is proposed to efficiently solve industry-relevant problems. The methodology not only considers the impact of both distance and shape-based measures simultaneously in the proposed initial solution finding mechanism, but also in the evaluation of the objective function during the entire search procedure, in the hope that it will lead to identifying a better final solution. Taking into consideration fixed and variable tabu list sizes, along with long-term memory with maximum and minimum frequencies, has led to developing six different heuristics for the solution algorithm. A single factor experiment based on randomized block design has been used to compare the performances of the six different heuristics on three different problem structures—small, medium, and large—using the total cost as the criterion. Based on this experiment, the characterizations of search procedures have been recommended to facilitate identifying the best solution for each problem structure. The proposed method is also compared with those in the published literature by solving fairly well known unequal area facility layout problems. When an improvement is observed, the comparison has led to identifying a percentage improvement in total cost of approximately 2.8% to 11.8%, thus demonstrating the effectiveness of the model and the algorithm.

Scheduling unrelated parallel machines with sequence-dependent setups

A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented in this paper. To comply with industrial situations, the dynamic release of jobs and dynamic availability of machines are assumed. Recognizing the inherent difficulty in solving industrial-size problems efficiently, six different search algorithms based on tabu search are developed to identify the best schedule that gives the minimum weighted tardiness. To enhance both the efficiency and efficacy of the search algorithms, four different initial solution finding mechanisms, based on dispatching rules, are developed. While there is no evidence of identifying solutions of better quality by employing a specific initial solution finding mechanism, the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both. Based on the extensive statistical analysis performed, the search algorithm with short-term memory and fixed tabu list size is recommended for solving small size problems, while that with long-term memory and minimum frequency for solving medium and large size problems, combined with fixed tabu list size for the former and variable tabu list size for the latter.

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.

Design of manufacturing cells in the presence of alternative cell locations and material transporters

This paper addresses two significant issues in the design of cellular manufacturing (CM) systems: (i) the availability of alternative locations for a cell, and (ii) the use of alternative routes to move part loads between cells when the capacity of the material transporter (MT) employed is limited. In addition, several other important factors in the design of CM systems including machine capacity limitations, batches of part demands, non-consecutive operations of parts, and maximum number of machines assigned to a cell are considered. A nonlinear programming model, comprised of binary and general integer variables, is formulated for the research problem. A higher-level heuristic solution algorithm based upon a concept known as ‘tabu search’ is presented for solving industry-size problems. Six different versions of the heuristic are developed to investigate the impact of long-term memory and the use of fixed versus variable tabu-list sizes. Explicit method-based techniques are developed to convert the original nonlinear programming model into an equivalent mixed (binary)-integer linear programming model in order to test the efficacy of the proposed solution technique for solving small problem instances. The solutions obtained from the heuristics have average deviation of less than 3% of the optimal solutions, and require less than a minute in comparison with optimizing methods that needed 1–10 h of computation time. A carefully designed statistical experiment is used to compare the performance of the heuristics by solving three different problem structures, ranging from four to 30 parts, and three to nine locations. The experiment shows that as the problem size increases, the tabu-search-based heuristic using fixed tabu list size and long-term memory based on minimal frequency strategy is preferred over the other heuristics.

Defining tabu list size and aspiration criterion within tabu search methods

An investigation to explicitly define two key elements in tabu search methods is attempted. In this study a functional representation of the tabu list size is presented and a softer aspiration criterion is put forward. Experiments are conducted on a set of p-median problems. Scope and purpose Tabu search is a metaheuristic that proved successful in finding good solutions to difficult combinatorial problems that were hard to find otherwise. In this study, we attempt to help the user in the choice of some of the parameters used in this type of heuristics. We based our analysis on the tabu list size and on an implementation on how to define the aspiration criterion. This added information can be valuable to those users who apply these methods in a near systematic manner without relying heavily on experimentations. As an example we used a simple location problem to test the usefulness of these ideas.

Machine duplication and part subcontracting in the presence of alternative cell locations in manufacturing cell design

In this paper a model and a solution algorithm are reported to simultaneously deal with the processes of machine duplication and part subcontracting in the presence of two significant design issues in cellular manufacturing systems: (i) alternative cell locations; and (ii) the maximum number of machines assigned to a cell. As the problem, formulated as a polynomial programming model, is shown NP-hard in the strong sense, a higher-level heuristic algorithm based upon a concept known as ‘tabu search’ is presented. An example (small) problem is solved to demonstrate the functionality of the algorithm. Additionally, the small problem is solved for its optimal solution under different scenarios, both with linear single-row and linear double-row layout arrangements, and the solutions obtained are shown to match with those obtained with the heuristic algorithm. A comparison of six different versions of tabu search-based heuristics (TSH 1–TSH 6) is performed to investigate the impact of long-term memory and the use of fixed versus variable tabu-list sizes. A carefully constructed statistical experiment, based on randomised complete-block design, is used to test the performance on three different problem structures, classified as small, medium and large. The results show that TSH 6 with variable tabu-list size and long-term memory based on minimal frequencies is preferred for the single-row layout, while TSH 4 with variable tabu-list size and no long-term memory is preferred for the double-row layout. When subject to budgetary restrictions, the proposed approach can be used by parts manufacturing companies to determine which of the following three actions should be undertaken for each bottleneck part: bottleneck part left as in the initial solution, all the bottleneck machines connected to it are duplicated, or the part subcontracted.

A parallel adaptive tabu search approach

This paper presents a new approach for parallel tabu search based on adaptive parallelism. Adaptive parallelism was used to dynamically adjust the parallelism degree of the application with respect to the system load. Adaptive parallelism demonstrates that high-performance computing using a hundred of heterogeneous workstations combined with massively parallel machines is feasible to solve large optimization problems. The parallel tabu search algorithm includes different tabu list sizes and new intensification/diversification mechanisms. Encouraging results have been obtained in solving the quadratic assignment problem. We have improved the best known solutions for some large real-world problems.

Optimizing tabu list size for the traveling salesman problem

We study the problem of optimizing the size of the tabu list when applying tabu search with a short term memory function to the symmetric traveling salesman problem. Two types of local search heuristics are used: the 2-opt and 3-opt heuristics. Fifty test problems of 20, 50, and 100 nodes are generated randomly in the unit square. The sizes of the tabu list tested range from 1 to 150 depending on the problem size and the local search heuristic used. We identified the best tabu list size for each combination of problem size and heuristic within a given computational time limit. This study reveals that good tabu list sizes are smaller than generally believed and that smaller neighborhoods require larger tabu list sizes to be effective.

A Tabu search-based approach for scheduling job-shop type flexible manufacturing systems

The problem of scheduling parts in a job-shop type flexible manufacturing system (FMS) is investigated when each part can have alternative process plans and each operation required of a part can be performed on alternative machines. The mixed-(binary) integer programming model developed for the problem is proven strongly NP-hard. A higher-level heuristic solution algorithm based on a concept known as ‘tabu search’ is developed to determine the best (near-optimal) solution for problems of industrial merit. A comparison of six different versions of tabu search-based heuristics (TSH 1-TSH 6) is performed to investigate the impact of using long-term memory and the use of fixed versus variable tabu-list sizes. A carefully constructed statistical experiment, based on randomized complete-block design, is used to test the performance on four problem structures ranging from 4–14 parts. The results show that, as the problem size increases, TSH 3 with fixed tabu-list size and long-term memory is preferred over the other heuristics. Further, the branch-and-bound technique, by failing to identify as good a solution as that determined by the heuristics (TSH 1-TSH 6), let alone an optimal solution, for a small problem reinforces the need for developing efficient heuristics for solving real problems encountered in industry practice.

An efficient tabu search procedure for the p-Median Problem

In this paper we present a new solution heuristic for the p-Median Problem. The algorithm is based on tabu search principles, and uses short term and long term memory, as well as strategic oscillation and random tabu list sizes. Our proposed procedure is compared with two other move heuristics: a well-known interchange heuristic and a recent hybrid heuristic. In computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced.

An improved tabu search heuristic for solving facility layout design problems

The design of the facility layout of a manufacturing system, usually formulated and solved as a quadratic assignment problem (QAP), is of tremendous importance for its effective utilization. In this paper we discuss a new implementation of the tabu search metaheuristic to solve the QAP. Our tabu search implementation includes recency-based and long term memory structure, dynamic tabu list size strategies, and intensification and diversification strategies. The tabu search algorithm converges with a reasonable speed from any random initial solution to very good layouts. Our extensive computational experiments, including statistical analysis and library analysis, strongly support the superiority of our tabu search implementation (we refer to it as (CK)) over existing algorithms in the literature.

Tabu Search for the planar three-index assignment problem

Tabu Search is a very effective method for approximately solving hard combinatorial problems. In the current work we implement Tabu Search for solving the Planar Three-Index Assignment Problem. The problem deals with finding the minimum cost assignment between elements of three distinct sets demanding that every pair of elements, each representing a different set, appears in the same solution exactly once. The solutions of the problems correspond to Latin squares. These structures form the basis of the move generation mechanism employed by the Tabu Search procedures. Standard Tabu Search ideas such as candidate move list, variable tabu list size, and frequency-based memory are tested. Computational results for a range of problems of varying dimensions are presented.