Local Neighborhood Search Research Articles

A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows

This paper considers the vehicle routing problem with soft time windows, a challenging routing problem where customers' time windows may be violated at a certain cost. The vehicle routing problem with soft time windows has a lexicographic objective function, aimed at minimizing first the number of routes, then the number of violated time windows, and finally the total routing distance. We present a multistage very large-scale neighborhood search for this problem. Each stage corresponds to a variable neighborhood descent over a parameterizable very large-scale neighborhood. These neighborhoods contain an exponential number of neighbors, as opposed to classical local search neighborhoods. Often, searching very large-scale neighborhoods can produce local optima of a higher quality than polynomial-sized neighborhoods can. Furthermore, we use a sophisticated heuristic to determine service start times allowing us to minimize the number of violated time windows. We test our approach on a number of different problem types, and compare the results to the relevant state of the art. The experimental results show that our algorithm improves best known solutions on 53% of the most studied instances. Many of these improvements stem from a reduction of the number of vehicles, a critical objective in vehicle routing problems.

A hybridization of clonal selection algorithm with iterated local search and variable neighborhood search for the feature selection problem

Nature inspired methods are approaches that are used in various fields and for the solution of a number of problems. This study uses a hybridized version of the clonal selection algorithm, the clonal selection algorithm–iterated local search–variable neighborhood search (CSA–ILS–VNS), for the solution of the feature selection problem (FSP). The clonal selection algorithm is inspired by the clonal selection and affinity maturation process of B cells of the natural immune system once the immune system has detected a pathogen. The proposed clonal selection algorithm is combined with a number of nearest neighbour based classifiers and it is tested using various benchmark data sets from the UCI machine learning repository. The algorithm is compared with variants of the clonal selection algorithm [the classic clonal selection algorithm (CSA), the clonal selection algorithm–iterated local search (CSA–ILS) and the clonal selection algorithm–variable neighborhood search (CSA–VNS)], a particle swarm optimization algorithm, an ant colony optimization algorithm and a genetic algorithm.

Parallel Local Search to schedule communicating tasks on identical processors

Abstract This paper reports on the analysis of parallelization strategies for Local Search (LS) when the neighborhood size varies throughout the search. The Multiprocessor Scheduling Problem with Communication Delays (MSPCD) is used as benchmark for illustrating the methodology and results. The dynamic load distribution strategy implemented within a supervisor–worker framework is shown to offer the best performance. Experimental results on several sets of instances with up to 500 tasks show excellent speedups (super-linear in most cases) while preserving the quality of the final solution. The proposed parallel LS is incorporated into Multistart Local Search and Variable Neighborhood Search meta-heuristic frameworks to analyze its efficiency in a more complex environment. The comparison between the sequential and parallel versions of each meta-heuristic, using various numbers of processors, shows improvement in the solution quality within proportionally smaller CPU time.

Demand-responsive transit circulator service network design

Commuter rail systems are being introduced into many urban areas as an alternative mode to automobiles for commuting trips. It is anticipated that the shift from the auto mode to rail mode can greatly help alleviate traffic congestion in urban road networks. However, the right-of-way of many existing commuter rail systems is usually not ideally located. Since the locations of rail systems were typically chosen long ago to serve the needs of freight customers, the majority of current commuter rail passengers have to take a non-walkable connecting trip to reach their final destinations after departing the most conveniently located rail stations. To make rail a more viable commuting option and thus more competitive to the auto mode, a bus feeder or circulator system is proposed for transporting passengers from their departing rail stations to final work destinations in a seamless transfer manner. The key research question with operating such a bus circulator system is how to optimally determine a bus route and stopping sequence for each circulating tour by using the real-time demand information. In this paper, we name this joint routing and stopping optimization problem the circulator service network design problem, the objective of which is to minimize the total tour cost incurred to bus passengers and operators with respect to minimizing the walk time of each individual bus passenger. A bi-level nonlinear mixed integer programming model is constructed and a tabu search method with different local search strategies and neighborhood evaluation methods is then developed for tackling the circulator service network design problem.

Polynomial-time local-improvement algorithm for Consecutive Block Minimization

A block of consecutive ones (bco for short) in a binary m×n-matrix is any maximal sequence of consecutive ones occurring in the same row. We consider the Consecutive Block Minimization (CBM) problem in which the aim is to minimize the number of bco's by permuting the matrix's columns. The paper introduces a pair of O(n2)-sized local search neighborhoods in which the number of bco's of a neighbor is computed in O(m) time. The performance of a local-search algorithm is then evaluated on some real-world and some randomly-generated instances of the problem.

Exploiting Variable Associations to Configure Efficient Local Search in Large-Scale Set Partitioning Problems

We present a data mining approach for reducing the search space of local search algorithms in large-scale set partitioning problems (SPPs). We construct a k-nearest neighbor graph by extracting variable associations from the instance to be solved, in order to identify promising pairs of flipping variables in the large neighborhood search. We incorporate the search space reduction technique into a 2-flip neighborhood local search algorithm with an efficient incremental evaluation of solutions and an adaptive control of penalty weights. We also develop a 4-flip neighborhood local search algorithm that flips four variables alternately along 4-paths or 4-cycles in the k-nearest neighbor graph. According to computational comparison with the latest solvers, our algorithm performs effectively for large-scale SPP instances with up to 2.57 million variables.

Variable neighborhood search heuristics for a test assembly design problem

Test assembly design problems appear in the areas of psychology and education, among others. The goal of these problems is to construct one or multiple tests to evaluate the test subject. This paper studies a recent formulation of the problem known as the one-dimensional minimax bin-packing problem with bin size constraints (MINIMAX_BSC). In the MINIMAX_BSC, items are initially divided into groups and multiple tests need to be constructed using a single item from each group, while minimizing differences among the tests. We first show that the problem is NP-Hard, which remained an open question. Second, we propose three different local search neighborhoods derived from the exact resolution of special cases of the problem, and combine them into a variable neighborhood search (VNS) metaheuristic. Finally, we test the proposed algorithm using real-life-based instances. The results show that the algorithm is able to obtain optimal or near-optimal solutions for instances with up to 60000-item pools. Consequently, the algorithm is a viable option to design large-scale tests, as well as to provide tests for online small-sized situations such as those found in e-learning platforms.

Teacher training enhances the teaching-learning-based optimisation metaheuristic when used to solve multiple-choice multidimensional knapsack problems

A new metaheuristic, the teaching-learning-based optimisation TLBO metaheuristic, based on the relationship between teachers and learners has recently been proposed by Rao, Savsani and Vakharia 2011 for solving continuous nonlinear optimisation problems. It is of particular interest because it is a population-based metaheuristic that can be easily adapted to solve combinatorial optimisation problems and requires no parameter fine-tuning other than determining the size of the population and convergence criteria. In this paper, we enhance the performance of the TLBO method by introducing 'teacher training' before the teaching phase of TLBO. That is, before the teaching phase of TLBO, we perform a local neighbourhood search on the best solution the teacher in the current population. The effectiveness of teacher training TT in terms of both solution quality and convergence rate will be demonstrated by using this approach TT-TLBO to solve a large 393 number of problem instances from the literature for the important NP-Hard multiple-choice multidimensional knapsack problem MMKP. Furthermore, we will demonstrate that TLBO outperforms the best published solution approaches for the MMKP.

Local search heuristics for the mobile facility location problem

In the mobile facility location problem (MFLP), one seeks to relocate (or move) a set of existing facilities and assign clients to these facilities so that the sum of facility movement costs and the client travel costs (each to its assigned facility) is minimized. This paper studies formulations and develops local search heuristics for the MFLP. First, we develop an integer programming (IP) formulation for the MFLP by observing that for a given set of facility destinations the problem may be decomposed into two polynomially solvable subproblems. This IP formulation is quite compact in terms of the number of nonzero coefficients in the constraint matrix and the number of integer variables; and allows for the solution of large-scale MFLP instances. Using the decomposition observation, we propose two local search neighborhoods for the MFLP. We report on extensive computational tests of the new IP formulation and local search heuristics on a large range of instances. These tests demonstrate that the proposed formulation and local search heuristics significantly outperform the existing formulation and a previously developed local search heuristic for the problem.

Novel dynamic diversity controlling EAs for coevolving optimal negotiation strategies

Finding optimal strategies for negotiation with incomplete information is a challenging issue in agent-based automated negotiation research. Although there are some previous works on finding the strategies through coevolutionary learning using evolutionary algorithms (EAs), their coevolving strategies tend to converge to non-global optima (which bring about ineffective negotiation outcomes for participating agents) due to biased coevolution and failures in coevolution. To cope with these drawbacks, this work introduces and compares novel genetic algorithms (GAs) and estimation of distribution algorithms (EDAs) that have additional capability of dynamic diversity control: (1) the dynamic diversity controlling GA (D2C-GA), (2) the dynamic diversity controlling EDA (D2C-EDA), (3) the improved D2C-GA (ID2C-GA) and (4) the improved D2C-EDA (ID2C-EDA). While D2C-GA and D2C-EDA adopt the novel diversification and refinement (DR) procedure, ID2C-GA and ID2C-EDA adopt the modified and enhanced DR (mDR) procedure with two additional local heuristics population repair and local neighborhood search. An extensive series of experiments were carried out to compare and evaluate the performance of the simple GA (S-GA), the simple EDA (S-EDA), and the novel GAs and EDAs in coevolving effective negotiation strategies of two self-interested negotiation agents for their various deadline combinations. Favorable empirical results showed that (i) ID2C-EDA could coevolve (near-)optimal negotiation strategies for all the considered cases due to its good generalization performance and (ii) it also generally outperformed S-GA, S-EDA, D2C-GA, D2C-EDA and ID2C-GA in terms of solution accuracy, coevolutionary search capability and average coevolution restart ratio. Interestingly, it was also found that the coevolution performance of ID2C-GA and ID2C-EDA is complementary in that ID2C-GA and ID2C-EDA generally achieved better results in the cases of equal and different deadlines, respectively.

Spatial planning via extremal optimization enhanced by cell-based local search

A new treatment is presented for land use planning problems by means of extremal optimization in conjunction to cell-based neighborhood local search. Extremal optimization, inspired by self-organized critical models of evolution has been applied mainly to the solution of classical combinatorial optimization problems. Cell-based local search has been employed by the author elsewhere in problems of spatial resource allocation in combination with genetic algorithms and simulated annealing. In this paper it complements extremal optimization in order to enhance its capacity for a spatial optimization problem. The hybrid method thus formed is compared to methods of the literature on a specific characteristic problem. It yields better results both in terms of objective function values and in terms of compactness. The latter is an important quantity for spatial planning. The present treatment yields significant compactness values as emergent results.

A hybrid framework for optimizing beam angles in radiation therapy planning

The purpose of this paper is twofold: (1) to examine strengths and weaknesses of recently developed optimization methods for selecting radiation treatment beam angles and (2) to propose a simple and easy-to-use hybrid framework that overcomes some of the weaknesses observed with these methods. Six optimization methods—branch and bound (BB), simulated annealing (SA), genetic algorithms (GA), nested partitions (NP), branch and prune (BP), and local neighborhood search (LNS)—were evaluated. Our preliminary test results revealed that (1) one of the major drawbacks of the reported algorithms was the limited ability to find a good solution within a reasonable amount of time in a clinical setting, (2) all heuristic methods require selecting appropriate parameter values, which is a difficult chore, and (3) the LNS algorithm has the ability to identify good solutions only if provided with a good starting point. On the basis of these findings, we propose a unified beam angle selection framework that, through two sequential phases, consistently finds clinically relevant locally optimal solutions. Considering that different users may use different optimization approaches among those mentioned above, the first phase aims to quickly find a good feasible solution using SA, GA, NP, or BP. This solution is then used as a starting point for LNS to find a locally optimal solution. Experimental results using this unified method on five clinical cases show that it not only produces consistently good-quality treatment solutions but also alleviates the effort of selecting an initial set of appropriate parameter values that is required by all of the existing optimization methods.

Artificial chromosomes with genetic algorithm 2 (ACGA2) for single machine scheduling problems with sequence-dependent setup times

Artificial chromosomes with genetic algorithm (ACGA) is one of the latest versions of the estimation of distribution algorithms (EDAs). This algorithm has already been applied successfully to solve different kinds of scheduling problems. However, due to the fact that its probabilistic model does not consider variable interactions, ACGA may not perform well in some scheduling problems, particularly if sequence-dependent setup times are considered. This is due to the fact that the previous job will influence the processing time of the next job. Simply capturing ordinal information from the parental distribution is not sufficient for a probabilistic model. As a result, this paper proposes a bi-variate probabilistic model to add into the ACGA. This new algorithm is called the ACGA2 and is used to solve single machine scheduling problems with sequence-dependent setup times in a common due-date environment. A theoretical analysis is given in this paper. Some heuristics and local search algorithm variable neighborhood search (VNS) are also employed in the ACGA2. The results indicate that the average error ratio of this ACGA2 is half the error ratio of the ACGA. In addition, when ACGA2 is applied in combination with other heuristic methods and VNS, the hybrid algorithm achieves optimal solution quality in comparison with other algorithms in the literature. Thus, the proposed algorithms are effective for solving the scheduling problems.

Flower Pollination Algorithm with Dimension by Dimension Improvement

Flower pollination algorithm (FPA) is a new nature-inspired intelligent algorithm which uses the whole update and evaluation strategy on solutions. For solving multidimension function optimization problems, this strategy may deteriorate the convergence speed and the quality of solution of algorithm due to interference phenomena among dimensions. To overcome this shortage, in this paper a dimension by dimension improvement based flower pollination algorithm is proposed. In the progress of iteration of improved algorithm, a dimension by dimension based update and evaluation strategy on solutions is used. And, in order to enhance the local searching ability, local neighborhood search strategy is also applied in this improved algorithm. The simulation experiments show that the proposed strategies can improve the convergence speed and the quality of solutions effectively.

A New Local Search Algorithm for Binary Optimization

We develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w2/(2w-1) approximation guarantee for set packing problems with exactly w ones in each column of the constraint matrix A, when using Q = w2. Most importantly, we find that the method has practical promise on large, randomly generated instances of both set covering and set packing problems, as it delivers performance that is competitive with leading general-purpose optimization software (CPLEX 11.2).

Allocating job-shop manpower to minimize : Optimality criteria, search heuristics, and probabilistic quality metrics

We address questions raised by Lobo et al. in 2012 regarding the NP-hard problem of finding an optimal allocation of workers to machine groups in a job shop so as to minimize L max , the maximum job lateness. Lobo et al. formulated a lower bound on L max given a worker allocation, and an algorithm to find an allocation yielding the smallest such lower bound. In this article we establish optimality criteria to verify that a given allocation corresponds to a schedule that yields the minimum value of L max . For situations in which the optimality criteria are not satisfied, we present the Heuristic Search Procedure (HSP), which sequentially invokes three distinct search heuristics, the Local Neighborhood Search Strategy (LNSS), Queuing Time Search Strategy 1 (QSS1), and Queuing Time Search Strategy 2 (QSS2), before delivering the best allocation encountered by LNSS, QSS1, and QSS2. HSP is designed to find allocations allowing a heuristic scheduler to generate schedules with a smaller value of L max than that achieved via the allocation yielding the final lower bound of Lobo et al. Comprehensive experimentation indicated that HSP delivered significant reductions in L max . We also estimate a probability distribution for evaluating the quality (closeness to optimality) of an allocation delivered by a heuristic search procedure such as HSP. This distribution permits assessing the user's confidence that a given allocation will enable the heuristic scheduler to generate its best possible schedule—i.e., the schedule with the heuristic scheduler's smallest achievable L max value.

On-line range images registration with GPGPU

AbstractThis paper concerns implementation of algorithms in the two important aspects of modern 3D data processing: data registration and segmentation. Solution proposed for the first topic is based on the 3D space decomposition, while the latter on image processing and local neighbourhood search. Data processing is implemented by using NVIDIA compute unified device architecture (NIVIDIA CUDA) parallel computation. The result of the segmentation is a coloured map where different colours correspond to different objects, such as walls, floor and stairs. The research is related to the problem of collecting 3D data with a RGB-D camera mounted on a rotated head, to be used in mobile robot applications. Performance of the data registration algorithm is aimed for on-line processing. The iterative closest point (ICP) approach is chosen as a registration method. Computations are based on the parallel fast nearest neighbour search. This procedure decomposes 3D space into cubic buckets and, therefore, the time of the matching is deterministic. First technique of the data segmentation uses accele-rometers integrated with a RGB-D sensor to obtain rotation compensation and image processing method for defining pre-requisites of the known categories. The second technique uses the adapted nearest neighbour search procedure for obtaining normal vectors for each range point.

Metaheuristic algorithms for the simultaneous slot allocation problem

In this study, the authors propose the formalisation of the Simultaneous Slot Allocation Problem (SSAP), that extends, in two directions, the current way of allocating airport slots in Europe. The SSAP requires, first, to perform the slot allocation at all airports simultaneously and, second, to respect airspace sector capacities. The authors solve the SSAP with two algorithms based on metaheuristics, namely Iterated Local Search and Variable Neighborhood Search, and with an algorithm based on an integer linear programming model. They compare these algorithms on randomly generated instances and show that for small instances metaheuristics are competitive with the integer linear programming model. Nevertheless, the integer linear programming model is unable to solve medium or large instances because of memory and computation time requirements. Metaheuristics, instead, can deal with large instances, allocating slots to more than 99.8% of flights.

Variable neighborhood descent heuristic for covering design problem

Abstract In this paper we consider a variable neighborhood descent (VND) heuristic, a variant of variable neighborhood search, for the covering design problem. The neighborhood structures and local search are based on the systematic removing and adding blocks to the covering. We have tested VND search on the greedy coverings and established 13 new best known upper bounds. The proposed approach is also applicable to any covering design.

Variable Neighborhood Search for Google Machine Reassignment problem

Abstract We present a hybrid method to efficiently solve Google Machine Reassignment problem (MRP), the problem proposed at ROADEF/EURO Challenge 2012 competition. We study, implement, combine and empirically examine different local search neighborhoods to solve the set of available instances. Intensification and diversification of search is achieved through the suitable change of the objective function and sorting the processes. We present results obtained with the solver that respect the given computational time of 5 minutes. Some of the obtained results are proven to be optimal or near optimal. With the presented method we were ranked first at ROADEF/EURO Challenge 2012 competition.