Multi-objective Tabu Search Algorithm Research Articles

Multi-objective two-level medical facility location problem and tabu search algorithm

The medical facility location problem has attracted increasing attention in recent years because the rational layout of medical facilities plays an important role in implementing the hierarchical diagnosis and treatment system in many countries. To promote the implementation of a hierarchical diagnosis and treatment system, a two-level medical facility location problem with multiple patient flows between demand points and medical facilities is studied in this paper. We use a direct interpretation of the two-level medical facility location problem as a multi-objective problem to effectively balance different conflicting objectives. Based on the multi-objective tabu search algorithm and the fast construction method of the Pareto non-dominated solution, we also propose a solution approach to yield a set of solutions that can represent the trade-offs among conflicting objectives. The applicability and validation of the presented model and performance of the proposed optimization approach are evaluated using a real case. The experimental results not only indicate that the proposed solution approach can effectively solve the two-level medical facility location problem, but also suggest that the presented model can provide significant results in determining locations for medical facilities.

A heuristic optimization approach for multi-vehicle and one-cargo green transportation scheduling in shipbuilding

To actively respond to the call for green shipbuilding, block cooperative transportation has been particularly concerned in reducing carbon emission in the shipyard, and hence a “multi-vehicle and one-cargo” (MVOC) green transportation scheduling problem emerges. Aiming to solve this problem effectively and improve transportation efficiency and reduce energy consumption, a bi-objective mathematical model combined routing model with synchronization constraints is proposed to simultaneously minimize non-value-added transportation time cost and total CO2 emission. A Pareto-based multi-objective Tabu Search (MOTS) algorithm is then designed to solve the model, in which local improvements are developed to generate promising neighboring individuals. Experimental results show that the proposed MOTS algorithm can effectively solve the problem even on a large scale and outperform the classic algorithm of nondominated sorting genetic algorithm-II (NSGA-Ⅱ). It is hoped that this work enables an operation mode with high efficiency and low energy consumption and provides useful insights for flatcar transportation scheduling operators in the shipyard.

Generating bicriteria schedules for correlated parallel machines involving tardy jobs and weighted completion time

This research focuses on studying the correlated parallel machine scheduling problem with release dates to minimize the number of tardy jobs and the total weighted completion time to find Pareto optima of all non-dominated solutions for both criteria. First, a mixed integer programming (MIP) model to find the entire efficient frontier for the studied problem has been proposed. Next, a bicriteria heuristic, named UTWC, and three artificial bee colony (ABC) variant algorithms have been proposed to tackle the studied problem. The three ABC variant algorithms are ABC, ABC with variable neighborhood search scheme (ABC_VNS), and ABC with simulated annealing scheme (ABC_SA). For small problem instances, we compare the proposed heuristic UTWC and three ABC variant algorithms with the efficient frontier generated by solving the MIP model. For large problem instances, we compare the UTWC and three ABC variant algorithms with an existing multi-objective tabu search algorithm (TSA). We create a reference set by combining the solutions from the three ABC variant algorithms and the TSA. The computational results indicate that the UTWC heuristic can find a set of non-dominated solutions that are uniformly distributed above the efficient frontier. The proposed ABC_VNS algorithm outperforms all the compared algorithms in both small and large problem instances.

A multi objective approach for DRT service using tabu search

Urban population is increasing fast. This is creating new challenges to public transport systems since some groups of citizens as elderly people may have sensory, cognitive or motor impairments that need to be addressed. This work explores the potential of a Demand Responsive Transport (DRT) system for people with reduced mobility in an urban environment. For this purpose, the Dial-A-Ride Problem (DARP) was implemented using a multivariable minimisation approach. In this approach, an Assigning Request to Vehicles (ARV) algorithm is used to obtain an initial solution. Then a Multi-Objective Tabu Search Algorithm (MOTSA) is applied to the initial solution to search for the non-dominated solution (optimisation phase). In this optimisation phase, the total travelled distance, the deadheading distance and the number of vehicles were minimised. The performance of the model was computed combining different parameters’ values of the number of requests, boarding time for each user, the number of seats in each vehicle, vehicle’s speed, the total number of iterations, and candidate threshold number (the algorithm’s parameter). The computational results found a strong positive correlation between the number of requests and the: total travelled distance (rs = 0.977, p-value<0.001) and the number of vehicles (rs =0.883, p-value<0.001); and a low positive correlation between the number of requests and the optimised total travelled distance (rs =0.331, p-value<0.001) and the optimised number of vehicles (rs =0.340, p-value<0.001).

Solving a bi-objective mixed-model assembly-line sequencing using metaheuristic algorithms considering ergonomic factors, customer behavior, and periodic maintenance

In today’s competitive world, companies must maintain their customers and attract new ones. Hence, they paid a great attention paid to mixed model assembly lines (MMAL). In this study, a two-step framework was developed to investigate and optimize customer relationships and the sequence of orders in an MMAL. First, based on customers past behavior, they were grouped into three clusters with high, normal, and low priority. Then, an optimal sequence was defined using a mathematical model. The objectives of the sequence were maximizing, first, the satisfaction of customers with high priority and, second, profits. Moreover, orders for low priority customers could be rejected. A multi-objective tabu search algorithm was proposed to solve the sequencing problem and then compared with non-dominated sorting genetic algorithm II and multi objective simulated annealing. The results indicated that this new algorithm is superior to others. We also developed an algorithm for the integration of periodic maintenance with sequencing of orders. The results suggested that the lack of this integration causes non-optimal sequences.

Multi-Objective Tabu Search Algorithm to Minimize Weight and Improve Formability of Al3105-St14 Bi-Layer Sheet

Nowadays, with extending applications of bi-layer metallic sheets in different industrial sectors, accurate specification of each layer is very prominent to achieve desired properties. In order to predict behavior of sheets under different forming modes and determining rupture limit and necking, the concept of Forming Limit Diagram (FLD) is used. Optimization problem with objective functions and important parameters aims to find optimal thickness for each of Al3105-St14 bi-layer metallic sheet contributors. Optimized point is achieved where formability of the sheet approaches to maximum extent and its weight to minimum extent. In this paper, multi-objective Tabu search algorithm is employed to optimize the considered problem. Finally, derived Pareto front using Tabu search algorithm is presented and results are compared with the solutions obtained from genetic algorithm. Comparison revealed that Tabu search algorithm provides better results than genetic algorithm in terms of Mean Ideal Distance, Spacing, non-uniformity of Pareto front and CPU time.

A multi-objective tabu search algorithm for product portfolio selection: A case study in the automotive industry

In the automotive industry, the high customizability of the final products leads to the need for managing large portfolios of variants of the same product, given the different combination of optional components that characterizes each variant. Due to the large number of components and to the variability of the final product demand brought about by such high customizability, planning how many units per variant should be produced in a given period is a critical task. This is especially true in the medium term, when few available components are left. In this paper, a proactive approach that can help find the best set of variants, to which available capacity should be allocated, is proposed. The problem of finding the best set of product variants is rephrased as a product portfolio selection problem and modeled as a multiple-objective multi-dimensional knapsack. A tabu search algorithm has been developed to provide a solution to the problem. The proposed approach has been tested in a real case study from the automotive industry; the results show its effectiveness in terms of providing a good set of trade-off product portfolios among which the product manager can choose.

Multiobjective tabu search algorithm for the optimal design of a thermo-acoustic magneto-hydro-dynamic electric generator

The aim of the proposed work is to study the optimal design of an innovative Thermo-Acoustic-Magneto-Hydro-Dynamic electric generator, with particular reference to the Magneto-Hydro-Dynamic section. A multi-objective optimization algorithm, which makes use of a Tabu Search meta-heuristic, has been developed to this purpose. Thermo-Acoustic and Magneto-Hydro-Dynamic energy conversion processes give a great advantage by converting energy without solid moving components. This makes the cited technologies very interesting for the low weight, the low maintenance costs, and the high conversion efficiency. The design of the generator has to be optimized by considering conflicting objectives, i.e., maximizing the output power, minimizing the applied electrical voltage, and minimizing mass and size of the device. Therefore, a multi-objective vectorial optimization approach is mandatory. A fully vector scheme has been implemented that takes under control both the Pareto optimality of the solutions, and the uniformity in the Pareto front sampling.

A multi-objective tabu search algorithm based on decomposition for multi-objective unconstrained binary quadratic programming problem

Unconstrained binary quadratic programming problem (UBQP) is a well-known NP-hard problem. In this problem, a quadratic 0–1 function is maximized. Numerous single-objective combinatorial optimization problems can be expressed as UBQP. To enhance the expressive ability of UBQP, a multi-objective extension of UBQP and a set of benchmark instances have been introduced recently. A decomposition-based multi-objective tabu search algorithm for multi-objective UBQP is proposed in this paper. In order to obtain a good Pareto set approximation, a novel weight vector generation method is first introduced. Then, the problem is decomposed into a number of subproblems by means of scalarizing approaches. The choice of different types of scalarizing approaches can greatly affect the performance of an algorithm. Therefore, to take advantages of different scalarizing approaches, both the weighted sum approach and the Tchebycheff approach are utilized adaptively in the proposed algorithm. Finally, in order to better utilize the problem-specific knowledge, a tabu search procedure is designed to further optimize these subproblems simultaneously. Experimental results on 50 benchmark instances indicate that the proposed algorithm performs better than current state-of-the-art algorithms.

Multi-objective integrated acyclic crew rostering and vehicle assignment problem in public bus transportation

In this study, we try to solve a real planning problem faced in public bus transportation. It is a multi-objective integrated crew rostering and vehicle assignment problem. We model this problem as a multi-objective set partitioning problem. Most of the time, crew rostering problem with a single-objective function is considered, and the output may not satisfy some transport companies. To minimize the cost and maximize the fairness of the workload among the drivers, we define many criteria. Although crew rostering problem and its integrated versions appear in the literature, it is the first time these two problems are integrated. We propose a new multi-objective tabu search algorithm to obtain near Pareto-optimal solutions. The algorithm works with a set of solutions using parallel search. We test our algorithm for the case with ten objectives and define a method to choose solutions from the approximated efficient frontier to present to the user. We discuss the performance of our meta-heuristic approach.

Multiobjective multistage distribution system planning using tabu search

This study presents a multiobjective tabu search algorithm to solve the multistage planning problem of a distribution system formulated as a multiobjective dynamic mixed integer non-linear programming problem. Multiobjective problems do not have a specific solution, but a set of solutions that allows us to observe the trade-off among the analysed objectives. Taking into account this concept, the objective functions of the model proposed in this study are: costs (investment and operational) and reliability. The actions deemed in this model for each period of the planning horizon are: increase in the capacity of existing substations (or construction of new ones), exchange of cables in existing lines (and construction of new feeders), reconfiguration of the network, allocation of sectionalising switches and construction of tie lines. The system's reliability is evaluated by means of the non-supplied energy under contingencies using the n − 1 criterion. By line switching and the use of tie lines, part of the loads affected by a contingency can be restored, thus, the non-supplied energy can be evaluated by solving a distribution network restoration problem. Numerical results are presented for a 54-bus system.

The Design of Multi-Element Airfoils Through Multi-Objective Optimization Techniques

This paper presents the development and the application of a multi-objective optimization framework for the design of two-dimensional multi-element high-lift airfoils. An innovative and efficient optimization algorithm, namely Multi-Objective Tabu Search (MOTS), has been selected as core of the framework. The flow-field around the multi-element configuration is simulated using the commercial computational fluid dynamics (cfd) suite Ansys cfx. Elements shape and deployment settings have been considered as design variables in the optimization of the Garteur A310 airfoil, as presented here. A validation and verification process of the cfd simulation for the Garteur airfoil is performed using available wind tunnel data. Two design examples are presented in this study: a single-point optimization aiming at concurrently increasing the lift and drag performance of the test case at a fixed angle of attack and a multi-point optimization. The latter aims at introducing operational robustness and off-design performance into the design process. Finally, the performance of the MOTS algorithm is assessed by comparison with the leading NSGA-II (Non-dominated Sorting Genetic Algorithm) optimization strategy. An equivalent framework developed by the authors within the industrial sponsor environment is used for the comparison. To eliminate cfd solver dependencies three optimum solutions from the Pareto optimal set have been cross-validated. As a result of this study MOTS has been demonstrated to be an efficient and effective algorithm for aerodynamic optimizations. Copyright © 2012 Tech Science Press.

A novel risk assessment and optimisation model for a multi-objective network security countermeasure selection problem

Budget cuts and the high demand in strengthening the security of computer systems and services constitute a challenge. Poor system knowledge and inappropriate selection of security measures may lead to unexpected financial and data losses. This paper proposes a novel Risk Assessment and Optimisation Model (RAOM) to solve a security countermeasure selection problem, where variables such as financial cost and risk may affect a final decision. A Multi-Objective Tabu Search (MOTS) algorithm has been developed to construct an efficient frontier of non-dominated solutions, which can satisfy organisational security needs in a cost-effective manner.

Capability-based virtual cellular manufacturing systems formation in dual-resource constrained settings using Tabu Search

Formation of Virtual Cellular Manufacturing Systems (VCMSs), as one of the main applications of Group Technology (GT), by presentation of unique and shared capability boundaries of machine tools through defining Resource Elements (REs) creates a good solution for Capability-Based VCMSs (CBVCMSs), which increases opportunities to create systems with more efficient utilizations. Considering workers as the second important resources in Dual-Resource Constraint (DRC) settings makes this problem more serious and critical to research because, in reality, jobs cannot be processed if workers, machines, or both are not available. This paper attempts to form CBVCMSs with DRC settings using a multi-objective mathematical model with a Goal Programming (GP) approach. Using the developed model, parts, machines, and workers are grouped and assigned to the generated virtual cells at the same time. The proposed model is solved through a multi-objective Tabu Search (TS) algorithm to find optimum or near-to-optimum solutions. The validity of the developed model is illustrated by two numerical examples taken from the literature and evaluated through comparing the performance of the CBVCMSs and the original classical CMSs in the System Capacity Utilization (SCU) point of view.

Efficient multi-objective tabu search for emergency equipment maintenance scheduling in disaster rescue

The paper describes a mathematical model of the emergency equipment maintenance scheduling problem particularly in disaster rescue operations, which aims to achieve a good balance between operational capability achieved by maintenance, cost-effectiveness, maintenance risks, and reserved maintenance capability for sustainable operations. We design a compact solution encoding that greatly facilitates the search process, and develop an efficient multi-objective tabu search algorithm that evolves a set of solutions towards the Pareto optimal frontier, using a weighted function based on the decision-maker’s preference to guide the search procedures. Simulation experiments and real-world application results demonstrate the effectiveness of our approach.

Parametric Optimization Design of Aircraft Based on Hybrid Parallel Multi-objective Tabu Search Algorithm

For dealing with the multi-objective optimization problems of parametric design for aircraft, a novel hybrid parallel multi-objective tabu search (HPMOTS) algorithm is used. First, a new multi-objective tabu search (MOTS) algorithm is proposed. Comparing with the traditional MOTS algorithm, this proposed algorithm adds some new methods such as the combination of MOTS algorithm and “Pareto solution”, the strategy of “searching from many directions” and the reservation of good solutions. Second, this article also proposes the improved parallel multi-objective tabu search (PMOTS) algorithm. Finally, a new hybrid algorithm—HPMOTS algorithm which combines the PMOTS algorithm with the non-dominated sorting-based multi-objective genetic algorithm (NSGA) is presented. The computing results of these algorithms are compared with each other and it is shown that the optimal result can be obtained by the HPMOTS algorithm and the computing result of the PMOTS algorithm is better than that of MOTS algorithm.

A Systematic Comparison and Multi-Objective Optimization of Humid Power Cycles—Part I: Thermodynamics

The steam injected gas turbine (STIG), humid air turbine (HAT), and TOP Humid Air Turbine (TOPHAT) cycles lie at the center of the debate on which humid power cycle will deliver optimal performance when applied to an aeroderivative gas turbine and, indeed, when such cycles will be implemented. Of these humid cycles, it has been claimed that the TOPHAT cycle has the highest efficiency and specific work, followed closely by the HAT, and then the STIG cycle. In this study, the systems have been simulated using consistent thermodynamic and economic models for the components and working fluid properties, allowing a consistent and nonbiased appraisal of these systems. Part I of these two papers focuses purely on the thermodynamic performance and the impact of the system parameters on the performance; Part II will study the economic performance. The three humid power systems and up to ten system parameters are optimized using a multi-objective Tabu Search algorithm, developed in the Cambridge Engineering Design Centre.

A Systematic Comparison and Multi-Objective Optimization of Humid Power Cycles—Part II: Economics

The steam injected gas turbine (STIG), humid air turbine (HAT), and TOP Humid Air Turbine (TOPHAT) cycles lie at the center of the debate on which humid power cycle will deliver optimal performance when applied to an aeroderivative gas turbine and, indeed, when such cycles will be implemented. Of these humid cycles, it has been claimed that the TOPHAT cycle has the highest efficiency and specific work, followed closely by the HAT and then the STIG cycle. In this study, the systems have been simulated using consistent thermodynamic and economic models for the components and working fluid properties, allowing a consistent and nonbiased appraisal of these systems. Part I of these two papers focused on the thermodynamic performance and the impact of the system parameters on the performance, Part II studies the economic performance of these cycles. The three humid power systems and up to ten system parameters are optimized using a multi-objective Tabu Search algorithm, developed in the Cambridge Engineering Design Centre.

The development of a multi-objective Tabu Search algorithm for continuous optimisation problems

While there have been many adaptations of some of the more popular meta-heuristics for continuous multi-objective optimisation problems, Tabu Search has received relatively little attention, despite its suitability and effectiveness on a number of real-world design optimisation problems. In this paper we present an adaptation of a single-objective Tabu Search algorithm for multiple objectives. Further, inspired by path relinking strategies common in discrete optimisation problems, we enhance our algorithm to allow it to handle problems with large numbers of design variables. This is achieved by a novel parameter selection strategy that, unlike a full parametric analysis, avoids the use of objective function evaluations, thus keeping the overall computational cost of the procedure to a minimum. We assess the performance of our two Tabu Search variants on a range of standard test functions and compare it to a leading multi-objective Genetic Algorithm, NSGA-II. The path relinking-inspired parameter selection scheme gives a clear performance improvement over the basic multi-objective Tabu Search adaptation and both variants perform comparably with the NSGA-II.

Tabu search for multiple-criteria manufacturing cell design

Cellular manufacturing (CM) is an important application of group technology (GT) in which families of parts are produced in manufacturing cells or in a group of various machines. Cell design/formation is the first step in the design of cellular manufacturing systems. Many efforts have been made towards cell design taking into consideration multiple criteria. This paper presents a Pareto-optimality-based multi-objective tabu search (MOTS) algorithm to the machine-part grouping problems with multiple objectives: minimizing the weighted sum of inter-cell and intra-cell moves and minimizing the total cell load variation A new approach is developed to evaluate the non-dominance of solutions produced by the tabu search. Comparisons between MOTS and the genetic algorithm (GA) are done and the results show that MOTS is quite promising in multi-objective cell design.