A GRASP for the biquadratic assignment problem

The biquadratic assignment problem (BiQAP) is a generalization of the quadratic assignment problem (QAP). It is a nonlinear integer programming problem where the objective function is a fourth degree multivariable polynomial and the feasible domain is the assignment polytope. BiQAP problems appear in VLSI synthesis. Due to the difficulty of this problem, only heuristic solution approaches have been proposed. In this paper, we propose a new heuristic for the BiQAP, a greedy randomized adaptive search procedure (GRASP). Computational results on instances described in the literature indicate that this procedure consistently finds better solutions than previously described algorithms.     

一种求解物流设施二次分配问题的混合分布估计算法

为了求解物流设施二次分配问题,提出了一种混合分布估计算法(HEDA)。首先,根据QAP的距离和物流量矩阵信息,提出了一种基于假设物流中心启发式规则的种群初始化方法,用于提高初始种群的质量和算法的搜索效率;其次,针对HEDA的概率模型,提出了一种概率矩阵初始构型生成机制和扰动操作,用于提高算法的全局探索能力;最后,在分析QAP的结构性质的基础上,设计了一种基于快速评价的局部搜索策略,用于提高算法的局部开发能力。仿真计算实验和算法比较验证了HEDA的优化性能。     

Massively parallel tabu search for the quadratic assignment problem

A new heuristic algorithm to perform tabu search on the Quadratic Assignment Problem (QAP) is developed. A massively parallel implementation of the algorithm on the Connection Machine CM-2 is provided. The implementation usesn ² processors, wheren is the size of the problem. The elements of the algorithm, calledPar_tabu, include dynamically changing tabu list sizes, aspiration criterion and long term memory. A new intensification strategy based on intermediate term memory is proposed and shown to be promising especially while solving large QAPs. The combination of all these elements gives a very efficient heuristic for the QAP: the best known or improved solutions are obtained in a significantly smaller number of iterations than in other comparative studies. Combined with the implementation on CM-2, this approach provides suboptimal solutions to QAPs of bigger dimensions in reasonable time.     

NeuroGenetic approach for combinatorial optimization: an exploratory analysis

Given the NP-Hard nature of many optimization problems, it is often impractical to obtain optimal solutions to large-scale problems in reasonable computing time. For this reason, heuristic and metaheuristic search approaches are used to obtain good solutions fast. However, these techniques often struggle to develop a good balance between local and global search. In this paper we propose a hybrid metaheuristic approach which we call the NeuroGenetic approach to search for good solutions for these large scale optimization problems by at least partially overcoming this challenge. The proposed NeuroGenetic approach combines the Augmented Neural Network (AugNN) and the Genetic Algorithm (GA) search approaches by interleaving the two. We chose these two approaches to hybridize, as they offer complementary advantages and disadvantages; GAs are very good at searching globally, while AugNNs are more proficient at searching locally. The proposed hybrid strategy capitalizes on the strong points of each approach while avoiding their shortcomings. In the paper we discuss the issues associated with the feasibility of hybridizing these two approaches and propose an interleaving algorithm. We also provide empirical evidence demonstrating the effectiveness of the proposed approach.     

A Memory Adaptive Reasoning Technique for Solving the Capacitated Minimum Spanning Tree Problem

In this paper we propose a hybrid memory adaptive heuristic for solving the Capacitated Minimum Spanning Tree (CMST) problem. We augment the problem formulation with additional non-redundant constraints via use of adaptive memory, to improve upon the performance of an elementary heuristic (the Esau-Williams heuristic). Our methodology is tested against many of the previously reported heuristics for the CMST. We conclude that our generalized procedure performs on par with the best of these approaches in terms of solution quality, while expending a very modest amount of computational effort.     

A Tabu Search Algorithm for the Quadratic Assignment Problem

Tabu search approach based algorithms are among the widest applied to various combinatorial optimization problems. In this paper, we propose a new version of the tabu search algorithm for the well-known problem, the quadratic assignment problem (QAP). One of the most important features of our tabu search implementation is an efficient use of mutations applied to the best solutions found so far. We tested this approach on a number of instances from the library of the QAP instances—QAPLIB. The results obtained from the experiments show that the proposed algorithm belongs to the most efficient heuristics for the QAP. The high efficiency of this algorithm is also demonstrated by the fact that the new best known solutions were found for several QAP instances.     

General variable neighborhood search for the uncapacitated single allocation <Emphasis Type="Italic">p</Emphasis>-hub center problem

In this paper we propose a general variable neighborhood search heuristic for solving the uncapacitated single allocation p-hub center problem (USApHCP). For the local search step we develop a nested variable neighborhood descent strategy. The proposed approach is tested on benchmark instances from the literature and found to outperform the state-of-the-art heuristic based on ant colony optimization. We also test our heuristic on large scale instances that were not previously considered as test instances for the USApHCP. Moreover, exact solutions were reached by our GVNS for all instances where optimal solutions are known.     

Iterated local search for the quadratic assignment problem

Iterated local search (ILS) is a simple and powerful stochastic local search method. This article presents and analyzes the application of ILS to the quadratic assignment problem (QAP). We justify the potential usefulness of an ILS approach to this problem by an analysis of the QAP search space. However, an analysis of the run-time behavior of a basic ILS algorithm reveals a stagnation behavior which strongly compromises its performance. To avoid this stagnation behavior, we enhance the ILS algorithm using acceptance criteria that allow moves to worse local optima and we propose population-based ILS extensions. An experimental evaluation of the enhanced ILS algorithms shows their excellent performance when compared to other state-of-the-art algorithms for the QAP.     

Reactive tabu adaptive memory programming search for the vehicle routing problem with backhauls

A heuristic approach based on a hybrid operation of reactive tabu search (RTS) and adaptive memory programming (AMP) is proposed to solve the vehicle routing problem with backhauls (VRPB). The RTS is used with an escape mechanism which manipulates different neighbourhood schemes in a sophisticated way in order to get a continuously balanced intensification and diversification during the search process. The adaptive memory strategy takes the search back to the unexplored regions of the search space by maintaining a set of elite solutions and using them strategically with the RTS. The AMP feature brings an extra robustness to the search process that resulted in early convergence when tested on most of the VRPB instances. We compare our algorithm against the best methods in the literature and report new best solutions for several benchmark problems.     

Combining very large scale and ILP based neighborhoods for a two-level location problem

In this paper we tackle a generalization of the Single Source Capacitated Facility Location Problem in which two sets of facilities, called intermediate level and upper level facilities, have to be located; the dimensioning of the intermediate set, the assignment of clients to intermediate level facilities, and of intermediate level facilities to upper level facilities, must be optimized, as well. Such problem arises, for instance, in telecommunication network design: in fact, in hierarchical networks the traffic arising at client nodes often have to be routed through different kinds of facility nodes, which provide different services. We propose a heuristic approach, based on very large scale neighborhood search to tackle the problem, in which both ad hoc algorithms and general purpose solvers are applied to explore the search space. We report on experimental results using datasets from the capacitated location literature. Such results show that the approach is promising and that Integer Linear Programming based neighborhoods are significantly effective.     

GRASP with path-relinking for the generalized quadratic assignment problem

The generalized quadratic assignment problem (GQAP) is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. The GQAP has numerous applications, including facility design, scheduling, and network design. In this paper, we propose several GRASP with path-relinking heuristics for the GQAP using different construction, local search, and path-relinking procedures. We introduce a novel approximate local search scheme, as well as a new variant of path-relinking that deals with infeasibilities. Extensive experiments on a large set of test instances show that the best of the proposed variants is both effective and efficient.     

Adaptive memory programming for matrix bandwidth minimization

In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This is a classic problem, introduced in the late sixties, that also has a well-known formulation in terms of graphs. Different exact and heuristic approaches have been proposed for the bandwidth problem. Our contribution consists of two new algorithms, one based on the tabu search methodology and the other based on the scatter search framework. We also present a hybrid method combining both for improved outcomes. Extensive computational testing shows the influence of the different elements in heuristic search, such as neighborhood definition, local search, combination methods and the use of memory. We compare our proposals with the most recent and advanced methods for this problem, concluding that our new methods can compete with them in speed and running time.     

A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times

This paper presents a hybrid of a general heuristic framework and a general purpose mixed-integer programming (MIP) solver. The framework is based on local search and an adaptive procedure which chooses between a set of large neighborhoods to be searched. A mixed integer programming solver and its built-in feasibility heuristics is used to search a neighborhood for improving solutions. The general reoptimization approach used for repairing solutions is specifically suited for combinatorial problems where it may be hard to otherwise design suitable repair neighborhoods. The hybrid heuristic framework is applied to the multi-item capacitated lot sizing problem with setup times, where experiments have been conducted on a series of instances from the literature and a newly generated extension of these. On average the presented heuristic outperforms the best heuristics from the literature, and the upper bounds found by the commercial MIP solver ILOG CPLEX using state-of-the-art MIP formulations. Furthermore, we improve the best known solutions on 60 out of 100 and improve the lower bound on all 100 instances from the literature.     

Contributions to the quadratic assignment problem

Tree search procedures for solving the Koopmans Beckmann quadratic assignment problem (QAP) are unable to solve any reasonable size QAP's mainly because good quality lower bounds for this problem cannot be computed.The purpose of this paper is to propose a bounding technique based on the extraction from the QAP formulation, of a large linear assignment problem (which can then be solved optimally), leaving as a residual problem as ‘small’ a QAP as possible. The solution of this residual QAP can then be bounded by a separate procedure. This 2-step method produces improved bounds as compared with those produced by the direct application of the bounding algorithms to the original QAP. In addition, a procedure is described for the a priori fixing of variables in the QAP formulation, thus reducing the number of variables in the problem.     

A complementary tool to enhance the effectiveness of existing methods for heterogeneous fixed fleet vehicle routing problem

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of the standard vehicle routing problem (VRP), in which the vertices have to be served using a fixed number of vehicles that could be different in size and fixed or variable costs. In this article, we propose an integer linear programming-based heuristic approach in order to solve the HFFVRP that could be used as a complementary tool to improve the performance of the existing methods of solving this problem. Computational results show the effectiveness of the proposed method.     

A compromised large-scale neighborhood search heuristic for capacitated air cargo loading planning

Cost effectiveness is central to the air freight forwarders. In this work, we study how an air freight forwarder should plan its cargo loading in order to minimize the total freight cost given a limited number of rented containers. To solve the problem efficiently for practical implementation, we propose a new large-scale neighborhood search heuristic. The proposed large-scale neighborhood relaxes the subset-disjoint restriction made in the existing literature; the relaxation risks a possibility of infeasible exchanges while at the same time it avoids the potentially large amount of checking effort required to enforce the subset-disjoint restriction. An efficient procedure is then used to search for improvement in the neighborhood. We have also proposed a subproblem to address the difficulties caused by the fixed charges. The compromised large-scale neighborhood (CLSN) search heuristic has shown stably superior performance when compared with the traditional large-scale neighborhood search and the mixed integer programming model.     

On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem

This paper focuses on branching strategies that are involved in branch and bound algorithms when solving multi-objective optimization problems. The choice of the branching variable at each node of the search tree constitutes indeed an important component of these algorithms. In this work we focus on multi-objective knapsack problems. In the literature, branching heuristics used for these problems are static, i.e., the order on the variables is determined prior to the execution. This study investigates the benefit of defining more sophisticated branching strategies. We first analyze and compare a representative set of classic branching heuristics and conclude that none can be identified as the best overall heuristic. Using an oracle, we highlight that combining branching heuristics within the same branch and bound algorithm leads to considerably reduced search trees but induces high computational costs. Based on learning adaptive techniques, we propose then dynamic adaptive branching strategies that are able to select the suitable heuristic to apply at each node of the search tree. Experiments are conducted on the bi-objective 0/1 unidimensional knapsack problem.     

Decomposition methods for the lot-sizing and cutting-stock problems in paper industries

We investigate the one-dimensional cutting-stock problem integrated with the lot-sizing problem in the context of paper industries. The production process in paper mill industries consists of producing raw materials characterized by rolls of paper and cutting them into smaller rolls according to customer requirements. Typically, both problems are dealt with in sequence, but if the decisions concerning the cutting patterns and the production of rolls are made together, it can result in better resource management. We investigate Dantzig–Wolfe decompositions and develop column generation techniques to obtain upper and lower bounds for the integrated problem. First, we analyze the classical column generation method for the cutting-stock problem embedded in the integrated problem. Second, we propose the machine decomposition that is compared with the classical period decomposition for the lot-sizing problem. The machine decomposition model and the period decomposition model provide the same lower bound, which is recognized as being better than the linear relaxation of the classical lot-sizing model. To obtain feasible solutions, a rounding heuristic is applied after the column generation method. In addition, we propose a method that combines an adaptive large neighborhood search and column generation method, which is performed on the machine decomposition model. We carried out computational experiments on instances from the literature and on instances adapted from real-world data. The rounding heuristic applied to the first column generation method and the adaptive large neighborhood search combined with the column generation method are efficient and competitive.     

Heuristics for a project management problem with incompatibility and assignment costs

Consider a project which consists of a set of jobs to be performed, assuming each job has a duration of at most one time period. We assume that the project manager provides a set of possible durations (in time periods) for the whole project. When a job is assigned to a specific time period, an assignment cost is encountered. In addition, for some pairs of jobs, an incompatibility cost is encountered if they are performed at the same time period. Both types of cost depend on the duration of the whole project, which also has to be determined. The goal is to assign a time period to each job while minimizing the costs. We propose a tabu search heuristic, as well as an adaptive memory algorithm, and compare them with other heuristics on large instances, and with an exact method on small instances. Variations of the problems are also discussed     

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.