Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem

This paper presents a new hybrid algorithm that executes large neighbourhood search algorithm in combination with the solution construction mechanism of the ant colony optimization algorithm (LNS–ACO) for the capacitated vehicle routing problem (CVRP). The proposed hybrid LNS–ACO algorithm aims at enhancing the performance of the large neighbourhood search algorithm by providing a satisfactory level of diversification via the solution construction mechanism of the ant colony optimization algorithm. Therefore, LNS–ACO algorithm combines its solution improvement mechanism with a solution construction mechanism. The performance of the proposed algorithm is tested on a set of CVRP instances. The hybrid LNS–ACO algorithm is compared against two other LNS variants and some of the formerly developed methods in terms of solution quality. Computational results indicate that the proposed hybrid LNS–ACO algorithm has a satisfactory performance in solving CVRP instances.     

A biased‐randomized algorithm for the two‐dimensional vehicle routing problem with and without item rotations

This paper proposes an efficient algorithm, with a reduced number of parameters, for solving the two‐dimensional loading‐capacitated vehicle routing problem (2L‐CVRP). This problem combines two of the most important issues in logistics, that is, vehicle routing and packing problems. Our approach contemplates unrestricted loading including the possibility of applying 90° rotations to each rectangular‐shaped item while loading it into the vehicle, which is a realistic assumption seldom considered in the existing literature. The algorithm uses a multistart approach that is designed to avoid local minima and also to make the algorithm an easily parallelizable one. At each restart, a biased randomization of a savings‐based routing algorithm is combined with an enhanced version of a classical packing heuristic to produce feasible good solutions for the 2L‐CVRP. The proposed algorithm has been compared with the classical benchmarks for two different 2L‐CVRP variants, that is, with and without item rotations. Experimental results show that our approach outperforms several best‐known solutions from previous work, both in terms of quality and the computational time needed to obtain them.     

The SR-GCWS hybrid algorithm for solving the capacitated vehicle routing problem

The capacitated vehicle routing problem (CVRP) is a well known problem which has long been tackled by researchers for several decades now, not only because of its potential applications but also due to the fact that CVRP can be used to test the efficiency of new algorithms and optimization methods. The objective of our work is to present SR-GCWS, a hybrid algorithm that combines a CVRP classical heuristic with Monte Carlo simulation using state-of-the-art random number generators. The resulting algorithm is tested against some well-known benchmarks. In most cases, our approach is able to compete or even outperform much more complex algorithms, which is especially interesting if we consider that our algorithm does not require any previous parameter fine-tuning or set-up process. Moreover, our algorithm has been able to produce high-quality solutions almost in real-time for most tested instances. Another important feature of the algorithm worth mentioning is that it uses a randomized constructive heuristic, capable of generating hundreds or even thousands of alternative solutions with different properties. These alternative solutions, in turn, can be really useful for decision-makers in order to satisfy their utility functions, which are usually unknown by the modeler. The presented methodology may be a fine framework for the development of similar algorithms for other complex combinatorial problems in the routing arena as well as in some other research fields.     

Discussion related to “Wang,C.-H., & Lu,J.-Z. (2009). A hybrid genetic algorithm that optimizes capacitated vehicle routing problem. Expert Systems with Applications, 36(2), 2921–2936”

This paper presents a discussion arisen after reading “A hybrid genetic algorithm that optimizes capacitated vehicle routing problem”, by Wang & Lu, (Wang, C.-H., & Lu, J.-Z. (2009). A hybrid genetic algorithm that optimizes capacitated vehicle routing problems. Expert System with Applications, 35, 2921–2936.). The discussed paper presents a hybrid genetic algorithm applied to the Capacitated Vehicle Routing Problem (CVRP). When the authors present the results obtained by the technique, they claim to have overcome the best-known solution in two instances of Christofides and Eilon CVRP Benchmark. This statement can create confusion and controversy, for several reasons that we will explain and clarify in this short communication.     

Savings based ant colony optimization for the capacitated minimum spanning tree problem

The problem of connecting a set of client nodes with known demands to a root node through a minimum cost tree network, subject to capacity constraints on all links is known as the capacitated minimum spanning tree (CMST) problem. As the problem is NP-hard, we propose a hybrid ant colony optimization (ACO) algorithm to tackle it heuristically. The algorithm exploits two important problem characteristics: (i) the CMST problem is closely related to the capacitated vehicle routing problem (CVRP), and (ii) given a clustering of client nodes that satisfies capacity constraints, the solution is to find a MST for each cluster, which can be done exactly in polynomial time. Our ACO exploits these two characteristics of the CMST by a solution construction originally developed for the CVRP. Given the CVRP solution, we then apply an implementation of Prim's algorithm to each cluster to obtain a feasible CMST solution. Results from a comprehensive computational study indicate the efficiency and effectiveness of the proposed approach.     

求解带容量约束车辆路径问题的混合变邻域生物共栖搜索算法

针对带容量约束的车辆路径问题,提出一种混合变邻域生物共栖搜索算法.设计基于客户点优先序列及车辆参考点模拟信息的有序编码,该编码方案使生物共栖搜索算法可以参与CVRP的离散优化;为了提高算法的全局搜索能力,根据有序编码特点构造3种共栖搜索算子,扩大搜索空间;同时,结合变邻域搜索算法设计客户点重置、交换和2-OPT三种局部搜索策略,以提高解方案质量.算例验证分析表明,所提算法能够有效地解决容量约束车辆路径问题,求解质量优于所对比算法,具有可靠的全局稳定性.     

求解多维背包问题的蚁群-拉格朗日松弛混合优化算法

针对多维背包问题(MKP) NP-hard、约束强的特点, 提出一种高效的蚁群-拉格朗日松弛(LR) 混合优化算法. 该算法以蚁群优化(ACO) 为基本框架, 并基于LR 对偶信息定义了一种MKP效用指标. ACO使得整体算法具有全局搜索能力, 所设计的效用指标将MKP的优化目标与约束条件有机地融合在一起. 该指标一方面可以用来定 义MKP核问题, 降低问题规模; 另一方面, 可以用作ACO的启发因子, 引导算法在有希望的解区域中强化搜索. 在大量标准算例上的测试结果表明, 所提出算法的鲁棒性较好; 与其他已有算法相比, 在求解质量和求解效率方面均具有很强的竞争力.

     

帝国竞争算法求解CVRP

针对带容量约束的车辆路径问题(CVRP),提出了一种带分裂机制的帝国竞争算法进行求解。首先,结合CVRP的特性,采用基于贪婪准则的编解码策略实现算法空间到解空间的转换。其次,提出帝国分裂策略来增强算法的全局搜索能力,并结合2-Opt提高算法的局部搜索能力。最后,通过25个基准算例的仿真实验表明:所提算法能有效求解CVRP,所有算例的优化误差不超过1.0%;与已有的帝国竞争算法、粒子群算法、遗传算法、布谷鸟搜索算法相比,所提算法的求解效率更高。     

Scheduling projects with multi-skilled personnel by a hybrid MILP/CP benders decomposition algorithm

We study an assignment type resource-con- strained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective cut-generating scheme based on temporal analysis in project scheduling is devised for resolving resource conflicts. The computational study shows that our hybrid MILP/CP algorithm is both effective and efficient compared to the pure MILP or CP method alone.     

Improvements of constraint programming and hybrid methods for scheduling of tests on vehicle prototypes

In the automotive industry, a manufacturer must perform several hundreds of tests on prototypes of a vehicle before starting its mass production. Tests must be allocated to suitable prototypes and ordered to satisfy temporal constraints and various kinds of test dependencies. The manufacturer aims to minimize the number of prototypes required. We present improvements of constraint programming (CP) and hybrid approaches to effectively solve random instances from an existing benchmark. CP mostly achieves better solutions than the previous heuristic technique and genetic algorithm. We also provide customized search schemes to enhance the performance of general search algorithms. The hybrid approach applies mixed integer linear programming (MILP) to solve the planning part and CP to find the complete schedule. We consider several logical principles such that the MILP model can accurately estimate the prototype demand, while its size particularly for large instances does not exceed memory capacity. Moreover, the robustness is alleviated when we allow CP to partially change the allocation obtained from the MILP model. The hybrid method can contribute to optimal solutions in some instances.     

Detecting infeasibility and generating cuts for mixed integer programming using constraint programming

We study a hybrid MIP/CP solution approach in which CP is used for detecting infeasibilities and generating cuts within a branch-and-cut algorithm for MIP. Our framework applies to MIP problems augmented by monotone constraints that can be handled by CP. We illustrate our approach on a generic multiple machine scheduling problem, and present a number of computational experiments.     

A hybrid integer and constraint programming approach to solve nurse rostering problems

The Nurse Rostering Problem can be defined as assigning a series of shift sequences (schedules) to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality schedules are a reduction in outsourcing costs and an increase in job satisfaction of employees. In this paper, we present a hybrid algorithm, which combines Integer Programming and Constraint Programming to efficiently solve the highly-constrained Nurse Rostering Problem. We exploit the strength of IP in obtaining lower-bounds and finding an optimal solution with the capability of CP in finding feasible solutions in a co-operative manner. To improve the performance of the algorithm, and therefore, to obtain high-quality solutions as well as strong lower-bounds for a relatively short time, we apply some innovative ways to extract useful information such as the computational difficulty of instances and constraints to adaptively set the search parameters. We test our algorithm using two different datasets consisting of various problem instances, and report competitive results benchmarked with the state-of-the-art algorithms from the recent literature as well as standard IP and CP solvers, showing that the proposed algorithm is able to solve a wide variety of instances effectively.     

Locally affine patch mapping and global refinement for image super-resolution

This paper deals with the super-resolution (SR) problem based on a single low-resolution (LR) image. Inspired by the local tangent space alignment algorithm in [16] for nonlinear dimensionality reduction of manifolds, we propose a novel patch-learning method using locally affine patch mapping (LAPM) to solve the SR problem. This approach maps the patch manifold of low-resolution image to the patch manifold of the corresponding high-resolution (HR) image. This patch mapping is learned by a training set of pairs of LR/HR images, utilizing the affine equivalence between the local low-dimensional coordinates of the two manifolds. The latent HR image of the input (an LR image) is estimated by the HR patches which are generated by the proposed patch mapping on the LR patches of the input. We also give a simple analysis of the reconstruction errors of the algorithm LAPM. Furthermore we propose a global refinement technique to improve the estimated HR image. Numerical results are given to show the efficiency of our proposed methods by comparing these methods with other existing algorithms.     

A probability matrix based particle swarm optimization for the capacitated vehicle routing problem

Particle swam optimization (PSO) is a relatively new metaheuristic that has recently drawn much attention from researchers in various optimization areas. However, application of PSO for the capacitated vehicle routing problem (CVRP) is very limited. This paper proposes a simple PSO approach for solving the CVRP. The proposed PSO approach uses a probability matrix as the main device for particle encoding and decoding. While existing research used the PSO solely for assignment of customers to routes and used other algorithms to sequence customers within the routes, the proposed approach applies the PSO approach to both simultaneously. The computational results show the effectiveness of the proposed PSO approach compared to the previous approaches.     

An efficient hybrid Taguchi-genetic algorithm for protein folding simulation

Given the amino-acid sequence of a protein, the prediction of a protein’s tertiary structure is known as the protein folding problem. The protein folding problem in the hydrophobic–hydrophilic lattice model is to find the lowest energy conformation. In order to enhance the performance of predicting protein structure, in this paper we propose an efficient hybrid Taguchi-genetic algorithm that combines genetic algorithm, Taguchi method, and particle swarm optimization (PSO). The GA has the capability of powerful global exploration, while the Taguchi method can exploit the optimum offspring. In addition, we present the PSO inspired by a mutation mechanism in a genetic algorithm. We demonstrate that our algorithm can be applied successfully to the protein folding problem based on the hydrophobic-hydrophilic lattice model. Simulation results indicate that our approach performs very well against existing evolutionary algorithm.     

The use of hybrid manifold learning and support vector machines in the prediction of business failure

The prediction of business failure is an important and challenging issue that has served as the impetus for many academic studies over the past three decades. This paper proposes a hybrid manifold learning approach model which combines both isometric feature mapping (ISOMAP) algorithm and support vector machines (SVM) to predict the failure of firms based on past financial performance data. By making use of the ISOMAP algorithm to perform dimension reduction, is then utilized as a preprocessor to improve business failure prediction capability by SVM. To create a benchmark, we further compare principal component analysis (PCA) and SVM with our proposed hybrid approach. Analytic results demonstrate that our hybrid approach not only has the best classification rate, but also produces the lowest incidence of Type II errors, and is capable of achieving an improved predictive accuracy and of providing guidance for decision makers to detect and prevent potential financial crises in the early stages.     

Development of a fuel consumption optimization model for the capacitated vehicle routing problem

Fuel consumption accounts for a large and increasing part of transportation costs. In this paper, the Fuel Consumption Rate (FCR), a factor considered as a load dependant function, is added to the classical capacitated vehicle routing problem (CVRP) to extend traditional studies on CVRP with the objective of minimizing fuel consumption. We present a mathematical optimization model to formally characterize the FCR considered CVRP (FCVRP) as well as a string based version for calculation. A simulated annealing algorithm with a hybrid exchange rule is developed to solve FCVRP and shows good performance on both the traditional CVRP and the FCVRP in substantial computation experiments. The results of the experiments show that the FCVRP model can reduce fuel consumption by 5% on average compared to the CVRP model. Factors causing the variation in fuel consumption are also identified and discussed in this study.     

求解车辆路径安排问题的混合遗传算法

讨论了具有容量限制的车辆路径安排问题,设计了一个高效混合遗传算法。针对简单遗传算法易收敛于局部最优解的缺点,算法设计了交叉规则和选择策略。只有当两个个体的评价函数值满足一定条件时,才能进行交叉操作。采用优良个体保留策略执行选择操作,设计了保留函数。算法依据顶点间的位置关系,设计了优化策略,在每代进化中按概率选择一定数量的个体执行优化操作。数据实验表明,该算法是一个有效的求解车辆路径安排问题的混合遗传算法。     

A novel hybrid DE–random search approach for unit commitment problem

Differential evolution (DE) is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it very attractive for numerical optimization. DE uses a rather greedy and less stochastic approach to problem-solving than other evolutionary algorithms. DE combines simple arithmetic operators with the classical operators of recombination, mutation and selection to evolve from a randomly generated starting population to a final solution. Although global exploration ability of DE algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low and it suffers from the problem of untime convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of DE algorithm is presented in the proposed research. This research paper presents a hybrid version of DE algorithm combined with random search for the solution of single-area unit commitment problem. The hybrid DE–random search algorithm is tested with IEEE benchmark systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms, and by experimental analysis, it has been found that proposed algorithm yields global results for the solution of unit commitment problem.

     

A genetic algorithm for MRF-based segmentation of multi-spectral textured images

A segmentation approach based on a Markov random field (MRF) model is an iterative algorithm; it needs many iteration steps to approximate a near optimal solution or gets a non-suitable solution with a few iteration steps. In this paper, we use a genetic algorithm (GA) to improve an unsupervised MRF-based segmentation approach for multi-spectral textured images. The proposed hybrid approach has the advantage that combines the fast convergence of the MRF-based iterative algorithm and the powerful global exploration of the GA. In experiments, synthesized color textured images and multi-spectral remote-sensing images were processed by the proposed approach to evaluate the segmentation performance. The experimental results reveal that the proposed approach really improves the MRF-based segmentation for the multi-spectral textured images.