A TABOO SEARCH BASED APPROACH TO FIND THE PARETO OPTIMAL SET IN MULTIPLE OBJECTIVE OPTIMIZATION

Taboo search is a heuristic optimization technique which works with a neighbourhood of solutions to optimize a given objective function. It is generally applied to single objective optimization problems. Taboo search has the potential for solving multiple objective optimization (MOO) problems, because it works with more than one solution at a time, and this gives it the opportunity to evaluate multiple objective functions simultaneously. In this paper, a taboo search based algorithm is developed to find Pareto optimal solutions in multiple objective optimization problems. The developed algorithm has been tested with a number of problems and compared with other techniques. Results obtained from this work have proved that a taboo search based algorithm can find Pareto optimal solutions in MOO effectively.     

A tabu search approach for buffer allocation in production lines with unreliable machines

The optimal allocation of buffers is an important research issue in designing production lines. In this study, a tabu search (TS) algorithm is proposed to find near-optimal buffer allocation plans for a serial production line with unreliable machines. The main objective is to maximize the production rate, i.e. throughput, of the line. The efficiency of the proposed method is also tested to solve buffer allocation problems with the objective of total buffer size minimization. To estimate the throughput of the line with a given specific buffer allocation, an analytical decomposition approximation method is used. The performance of the tabu search algorithm is demonstrated on existing benchmark problems. The results obtained by the TS algorithm are clearly encouraging, as the TS algorithm is much better than the other algorithms for all considered benchmark problems.     

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.     

FITTING OF TABU SEARCH TO OPTIMIZE FUNCTIONS OF CONTINUOUS VARIABLES

Tabu Search (TS) is a stochastic global optimization procedure which proved efficient to solve various combinatorial optimization problems. However, very few works deal with its application to global minimization of functions depending on continuous variables. The aim of this paper is to propose an adaptation of TS to the optimization of continuous functions, and to study the influence of the main algorithm parameters on the convergence towards the optimum. In particular, the application of TS to function optimization involves the definition of the current solution neighbourhood and the management of the tabu list. The efficiency of TS applied to continuous global optimization has been tested in detail by using classical multimodal functions for which minima are known. © 1997 by John Wiley & Sons, Ltd.     

An improved version of the multiple trajectory search for real value multi-objective optimization problems

Multi-objective optimization is widely used in science, engineering and business. In this article, an improved version of the multiple trajectory search (MTS) called MTS2 is presented and successfully applied to real-value multi-objective optimization problems. In the first step, MTS2 generates M initial solutions distributed over the solution space. These solutions are called seeds. Some seeds with good objective values are selected as foreground seeds. Then, MTS2 chooses a suitable region search method for each foreground seed according to the landscape of the neighbourhood of the seed. During the search, MTS2 focuses its search on some promising areas specified by the foreground seeds. The performance of MTS2 was examined by applying it to solve the benchmark problems provided by the Competition of Performance Assessment of Constrained/Bound Constrained Multi-Objective Optimization Algorithms held at the 2009 IEEE Congress on Evolutionary Computation.     

Studying the effect of different combinations of timetabling with sequencing algorithms to solve the no-wait job shop scheduling problem

This paper considers the no-wait job shop (NWJS) problem with makespan minimisation criteria. It is well known that this problem is strongly NP-hard. Most of the previous studies decompose the problem into a timetabling sub-problem and a sequencing sub-problem. Each study proposes a different sequencing and timetabling algorithm to solve the problem. In this research, this important question is aimed to be answered: is the timetabling or the sequencing algorithm more important to the effectiveness of the developed algorithm? In order to find the answer, three different sequencing algorithms are developed; a tabu search (TS), a hybrid of tabu search with variable neighbourhood search (TSVNS), and a hybrid of tabu search with particle swarm optimisation (TSPSO). Afterwards, the sequencing algorithms are combined with four different timetabling methods. All the approaches are applied to a large number of test problems available in the literature. Statistical analysis reveals that although some of the sequencing and timetabling algorithms are more complicated than the others, they are not necessarily superior to simpler algorithms. In fact, some of the simpler algorithms prove to be more effective than complicated and time-consuming methods.     

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.     

OPTIMAL STRUCTURAL DESIGN BY ANT COLONY OPTIMIZATION

Ant colony optimization (ACO) is a relatively new heuristic combinatorial optimization algorithm in which the search process is a stochastic procedure that incorporates positive feedback of accumulated information. The positive feedback (;i.e., autocatalysis) facility is a feature of ACO which gives an emergent search procedure such that the (common) problem of algorithm termination at local optima may be avoided and search for a global optimum is possible.

The ACO algorithm is motivated by analogy with natural phenomena, in particular, the ability of a colony of ants to ‘optimize’ their collective endeavours. In this paper the biological background for ACO is explained and its computational implementation is presented in a structural design context. The particular implementation of ACO makes use of a tabu search (TS) local improvement phase to give a computationally enhanced algorithm (ACOTS).

In this paper ACOTS is applied to the optimal structural design, in terms of weight minimization, of a 25-bar space truss. The design variables are the cross-sectional areas of the bars, which take discrete values. Numerical investigation of the 25-bar space truss gave the best (i.e., lowest to-date) minimum weight value. This example provides evidence that ACOTS is a useful and technically viable optimization technique for discrete-variable optimal structural design.     

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.     

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

With the expansion of the application scope of social computing problems, many path problems in real life have evolved from pure path optimization problems to social computing problems that take into account various social attributes, cultures, and the emotional needs of customers. The actual soft time window vehicle routing problem, speeding up the response of customer needs, improving distribution efficiency, and reducing operating costs is the focus of current social computing problems. Therefore, designing fast and effective algorithms to solve this problem has certain theoretical and practical significance. In this paper, considering the time delay problem of customer demand, the compensation problem is given, and the mathematical model of vehicle path problem with soft time window is given. This paper proposes a hybrid tabu search (TS) & scatter search (SS) algorithm for vehicle routing problem with soft time windows (VRPSTW), which mainly embeds the TS dynamic tabu mechanism into the SS algorithm framework. TS uses the scattering of SS to avoid the dependence on the quality of the initial solution, and SS uses the climbing ability of TS improves the ability of optimizing, so that the quality of search for the optimal solution can be significantly improved. The hybrid algorithm is still based on the basic framework of SS. In particular, TS is mainly used for solution improvement and combination to generate new solutions. In the solution process, both the quality and the dispersion of the solution are considered. A simulation experiments verify the influence of the number of vehicles and maximum value of tabu length on solution, parameters’ control over the degree of convergence, and the influence of the number of diverse solutions on algorithm performance. Based on the determined parameters, simulation experiment is carried out in this paper to further prove the algorithm feasibility and effectiveness. The results of this paper provide further ideas for solving vehicle routing problems with time windows and improving the efficiency of vehicle routing problems and have strong applicability.     

包装物回收物流中的车辆路径优化问题

目的提高遗传算法(GA)求解包装物回收车辆路径优化问题的性能。方法通过对传统GA算法的改进,提出混合蜂群遗传算法(HBGA)。首先改进传统GA算法的初始种群生成方式,设计初始种群混合生成算子;其次,提出最大保留交叉算子,对优秀子路径进行保护;然后,在上述改进的基础上引入蜜蜂进化机制,用以保证种群多样性和优秀个体特征信息的利用程度;最后,对标准算例集进行仿真测试。结果与传统GA算法相比,HBGA算法在全局寻优能力、算法稳定性和运行速度方面均有所改善。HBGA算法的全局寻优能力和算法稳定性均优于粒子群算法(PSO)、蚁群算法(ACO)和禁忌搜索算法(TS),但运行速度稍慢于TS算法。结论对传统GA算法的改进是合理的,且HBGA算法整体求解性能优于PSO算法、ACO算法和TS算法。     

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).     

A multiple surrogate assisted evolutionary algorithm for optimization involving iterative solvers

In many real-world optimization problems, the underlying objective and constraint function(s) are evaluated using computationally expensive iterative simulations such as the solvers for computational electro-magnetics, computational fluid dynamics, the finite element method, etc. The default practice is to run such simulations until convergence using termination criteria, such as maximum number of iterations, residual error thresholds or limits on computational time, to estimate the performance of a given design. This information is used to build computationally cheap approximations/surrogates which are subsequently used during the course of optimization in lieu of the actual simulations. However, it is possible to exploit information on pre-converged solutions if one has the control to abort simulations at various stages of convergence. This would mean access to various performance estimates in lower fidelities. Surrogate assisted optimization methods have rarely been used to deal with such classes of problem, where estimates at various levels of fidelity are available. In this article, a multiple surrogate assisted optimization approach is presented, where solutions are evaluated at various levels of fidelity during the course of the search. For any solution under consideration, the choice to evaluate it at an appropriate fidelity level is derived from neighbourhood information, i.e. rank correlations between performance at different fidelity levels and the highest fidelity level of the neighbouring solutions. Moreover, multiple types of surrogates are used to gain a competitive edge. The performance of the approach is illustrated using a simple 1D unconstrained analytical test function. Thereafter, the performance is further assessed using three 10D and three 20D test problems, and finally a practical design problem involving drag minimization of an unmanned underwater vehicle. The numerical experiments clearly demonstrate the benefits of the proposed approach for such classes of problem.     

Applying tabu search and simulated annealing to the optimal design of sewer networks

Optimizations of sewer network designs create complicated and highly nonlinear problems wherein conventional optimization techniques often get easily bogged down in local optima and cannot successfully address such problems. In the past decades, heuristic algorithms possessing robust and efficient global search capabilities have helped to solve continuous and discrete optimization problems and have demonstrated considerable promise. This study applied tabu search (TS) and simulated annealing (SA) to the optimization of sewer network designs. For a case study, this article used the sewer network design of a central Taiwan township, which contains significantly varied elevations, and the optimal designs from TS and SA were compared with the original official design. The results show that, in contrast with the original design's failure to satisfy the minimum flow-velocity requirements, both TS and SA achieved least-cost solutions that also fulfilled all the constraints of the design criteria. According to the average performance of 200 trials, SA outperformed TS in both robustness and efficiency for solving sewer network optimization problems.     

A hybrid multi-objective particle swarm algorithm for a mixed-model assembly line sequencing problem

Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management where diversified customers' demands exist. In this article, three major goals are considered: (i) total utility work, (ii) total production rate variation and (iii) total setup cost. Due to the complexity of the problem, a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) is devised to obtain the locally Pareto-optimal frontier where simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed algorithm in terms of solution quality and diversity level, the algorithm is applied to various test problems and its reliability, based on different comparison metrics, is compared with three prominent multi-objective genetic algorithms, PS-NC GA, NSGA-II and SPEA-II. The computational results show that the proposed hybrid algorithm significantly outperforms existing genetic algorithms in large-sized problems.     

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.     

Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

禁忌鱼群算法及其在边坡稳定分析中的应用

构造了一种两点禁忌寻优算子以避免寻优过程中的迂回搜索,并用它模拟鱼群中单条鱼的追寻历史最优鱼、追尾、群聚三种行为,采用遗传算法中非均匀变异算子模拟单条鱼的觅食行为,鱼群中各个体通过这四种行为进行交流、合作从而形成了一种禁忌鱼群算法。将该算法应用于两个复杂土坡的最小安全系数搜索中,并同基本鱼群算法的计算结果进行了比较,结果证明禁忌鱼群算法具有搜索高效、适于约束优化问题求解等特点。     

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.