An effective krill herd algorithm with migration operator in biogeography-based optimization

Krill herd (KH) is a novel search heuristic method. To improve its performance, a biogeography-based krill herd (BBKH) algorithm is presented for solving complex optimization tasks. The improvement involves introducing a new krill migration (KM) operator when the krill updating to deal with optimization problems more efficiently. The KM operator emphasizes the exploitation and lets the krill cluster around the best solutions at the later run phase of the search. The effects of these enhancements are tested by various well-defined benchmark functions. Based on the experimental results, this novel BBKH approach performs better than the basic KH and other optimization algorithms.     

A tabu search approach for solving a difficult forest harvesting machine location problem

This paper deals with two main problems in forest harvesting. The first is that of selecting the locations for the machinery to haul logs from the points where they are felled to the roadside. The second consists in designing the access road network connecting the existing road network with the points where machinery is installed. Their combination induces a very important and difficult problem to solve in forest harvesting. It can be formulated as a combination of two difficult optimization problems: a plant location problem and a fixed charge network flow problem. In this paper, we propose a solution approach based on tabu search. The proposed heuristic includes several enhancements of the basic tabu search framework. The main difficulty lies in evaluating neighboring solutions, which involves decisions related to location of machinery and to road network arcs. Hence, the neighborhood is more complex than in typical applications of metaheuristics. Minimum spanning tree algorithms and Steiner tree heuristics are used to deal with this problem. Numerical results indicate that the heuristic approach is very attractive and leads to better solutions than those provided by state-of-the-art integer programming codes in limited computation times, with solution times significantly smaller. The numerical results do not vary too much when typical parameters such as the tabu tenure are modified, except for the dimension of neighborhood.     

Confident Search

Abstract

The task of searching for the best element or a good element in a large set P is central to many problems in artificial intelligence and related fields. Often, heuristic information is used to reduce the scope of the search; however, in many instances, this information carries no guarantee of good performance. This article begins with an arbitrary heuristic search procedure and supplies it with a confidence statement of the following form: With specified high probability β, the output of the confidence procedure will be among the best 100α% of the elements of P. The confidence procedure will report either the outcome of the heuristic search or a better alternative with the required properties; that is, it will either certify that the heuristic answer has the desired confidence property or it will produce a better answer having the property. The approach involves combining heuristic search with a form of heuristic sampling that tends to sample the better elements of P. The sample is designed in such a way that the best element in the sample has the desired confidence property—if the answer produced by the heuristic search is better still, it inherits the confidence property. Various devices permit the sampling procedure to retain its confidence property while (1) moving the sample in the direction suggested by the heuristic, (2) adjusting the heuristic preference in response to what is learned during sampling, and (3) reorganizing the sampling whenever promising discoveries are made by chance.     

A morph-based simulated annealing heuristic for a modified bin-packing problem

This paper presents a local-search heuristic, based on the simulated annealing (SA) algorithm for a modified bin-packing problem (MBPP). The objective of the MBPP is to assign items of various sizes to a fixed number of bins, such that the sum-of-squared deviation (across all bins) from the target bin workload is minimized. This problem has a number of practical applications which include the assignment of computer jobs to processors, the assignment of projects to work teams, and infinite-loading machine scheduling problems. The SA-based heuristic we developed uses a morph-based search procedure when looking for better allocations. In a large computational study we evaluated 12 versions of this new heuristic, as well as two versions of a previously published SA-based heuristic that used a completely random search. The primary performance measure for this evaluation was the mean percent above the best known objective value (MPABKOV). Since the MPABKOV associated with the best version of the random-search SA heuristic was more than 290 times larger than that of the best version of the morph-based SA heuristic, we conclude that the morphing process is a significant enhancement to SA algorithms for these problems.     

Routing and wavelength assignment by partition colouring

The problem of routing and wavelength assignment in all-optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths, followed by the solution of a partition colouring problem in a conflict graph. A new tabu search heuristic is also proposed for the partition colouring problem, which may be viewed as an extension of the graph colouring problem. Computational experiments are reported, showing that the tabu search heuristic outperforms the best heuristic for partition colouring by approximately 20% in the average and illustrating that the new approach for the problem of routing and wavelength assignment is more robust than a well established heuristic for this problem.     

Parametric enhancements of the Esau–Williams heuristic for the capacitated minimum spanning tree problem

The Capacitated Minimum Spanning Tree Problem is NP-hard and several heuristic solution methods have been proposed. They can be classified as classical ones and metaheuristics. Recent developments have shown that metaheuristics outperform classical heuristics. However, they require long computation times and there are difficulties in their parameter calibration and coding phases. This explains the popularity of the Esau–Williams (EW) heuristic in practice, and its use in many successful metaheuristics and second-order greedy methods. In this work, we are concerned with the EW heuristic and we propose simple new enhancements. Based on our computational experiments, we can say that they considerably improve its accuracy with minor increase in computation time, and without harming its simplicity.     

A breadth-first search applied to the minimization of the open stacks

This paper presents a heuristic for the minimization of the open stacks problem (MOSP). The proposed heuristic is based on a simple breadth-first search in MOSP graphs and two new greedy rules to overcome errors. The performance of the proposed heuristic is compared with the best exact and heuristic methods available in the literature. The results show that in addition to the suggested heuristic having much shorter running times than the exact algorithm, the error gap between them is small for a substantial proportion of almost 4500 benchmark instances taken from the literature. The proposed heuristic also has a more robust behaviour than the best heuristic for the MOSP, although less accurate. The proposed heuristic therefore constitutes a viable and cost-effective alternative for solving or obtaining good upper bounds for the MOSP.     

The tree representation for the pickup and delivery traveling salesman problem with LIFO loading

The feasible solutions of the traveling salesman problem with pickup and delivery (TSPPD) are commonly represented by vertex lists. However, when the TSPPD is required to follow a policy that loading and unloading operations must be performed in a last-in-first-out (LIFO) manner, we show that its feasible solutions can be represented by trees. Consequently, we develop a novel variable neighborhood search (VNS) heuristic for the TSPPD with last-in-first-out loading (TSPPDL) involving several search operators based on the tree data structure. Extensive experiments suggest that our VNS heuristic is superior to the current best heuristics for the TSPPDL in terms of solution quality, while requiring no more computing time as the size of the problem increases.     

A tabu search heuristic for the generalized minimum spanning tree problem

This paper describes an attribute based tabu search heuristic for the generalized minimum spanning tree problem (GMSTP) known to be NP-hard. Given a graph whose vertex set is partitioned into clusters, the GMSTP consists of designing a minimum cost tree spanning all clusters. An attribute based tabu search heuristic employing new neighborhoods is proposed. An extended set of TSPLIB test instances for the GMSTP is generated and the heuristic is compared with recently proposed genetic algorithms. The proposed heuristic yields the best results for all instances. Moreover, an adaptation of the tabu search algorithm is proposed for a variation of the GMSTP in which each cluster must be spanned at least once.     

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.     

产品回收逆向物流网络设计问题的两阶段启发式算法

针对产品回收逆向物流网络设计问题,设计了一种嵌套了模拟退火算法的两阶段启发式算法。第一阶段确定回收点的选址-分配-存储的联合决策;第二阶段确定回收中心的选址-运输的联合决策,两个阶段相互迭代,从而实现最优解的搜索。通过与遗传算法比较,证明了两阶段启发式算法是一种有效的算法。     

A new enhancement of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem

In this work we are concerned with the Clarke–Wright savings method for the classical capacitated vehicle routing problem. This is an NP-hard problem and numerous heuristic solution methods have been proposed. They can be classified as the classical ones and metaheuristics. Recent developments have shown that classical heuristics do not compare with the best metaheuristic implementations. However, some of them are very fast and simple to implement. This explains the popularity of the Clarke–Wright savings method in practice and the motivation behind its enhancements. We follow this line of research and propose a new enhancement which differs from the previous ones in its saving criterion: Customer demands are considered in addition to distances. Based on the extensive computational experiments we can say that the new method is not only very fast but also very accurate.     

A beam search implementation for the irregular shape packing problem

This paper investigates the irregular shape packing problem. We represent the problem as an ordered list of pieces to be packed where the order is decoded by a placement heuristic. A placement heuristic from the literature is presented and modified with a more powerful nofit polygon generator and new evaluation criteria. We implement a beam search algorithm to search over the packing order. Using this approach many parallel partial solutions can be generated and compared. Computational results for benchmark problems show that the algorithm generates highly competitive solutions in significantly less time than the best results currently in the literature.     

A Constraint-Based Method for Project Scheduling with Time Windows

This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with higher-capacity requests is introduced, and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on a large set of previously studied RCPSP/max benchmark problems.     

Local search for a multi-drop multi-container loading problem

We consider a complex variant of the Container Loading Problem arising from a real-world industrial application. It includes several features such as multiple containers, box rotation, and bearable weight, which are of importance in many practical situations. In addition, it also considers the situation in which boxes have to be delivered to different destinations (multi-drop). Our solution technique is based on local search metaheuristics. Local search works on the space of sequences of boxes to be loaded, while the actual load is obtained by invoking, at each iteration, a specialized procedure called loader. The loader inserts the boxes in the container using a deterministic heuristic which produces a load that is feasible according to the constraints. We test our solver on real-world instances provided by our industrial partner, showing a clear improvement on the previous heuristic solution. In addition, we compare our solver on benchmarks from the literature on the basic container loading problems. The outcome is that the results are in some cases in-line with the best ones in the literature and for other cases they also improve upon the best known ones. All instances and solutions are made available on the web for future comparisons.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

Large Cliques Elude the Metropolis Process

In a random graph on n vertices, the maximum clique is likely to be of size very close to 2 lg n. However, the clique produced by applying the naive “greedy” heuristic to a random graph is unlikely to have size much exceeding lg n. The factor of two separating these estimates motivates the search for more effective heuristics. This article analyzes a heuristic search strategy, the Metropolis process, which is just one step above the greedy one in its level of sophistication. It is shown that the Metropolis process takes super-polynomial time to locate a clique that is only slightly bigger than that produced by the greedy heuristic.     

A hybrid iterated local search heuristic for the maximum weight independent set problem

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.     

Evaluating selection methods on hyper-heuristic multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a promising meta-heuristic to solve multi-objective problems (MOPs). Previous works have shown that selecting a proper combination of leader and archiving methods, which is a challenging task, improves the search ability of the algorithm. A previous study has employed a simple hyper-heuristic to select these components, obtaining good results. In this research, an analysis is made to verify if using more advanced heuristic selection methods improves the search ability of the algorithm. Empirical studies are conducted to investigate this hypothesis. In these studies, first, four heuristic selection methods are compared: a choice function, a multi-armed bandit, a random one, and the previously proposed roulette wheel. A second study is made to identify if it is best to adapt only the leader method, the archiving method, or both simultaneously. Moreover, the influence of the interval used to replace the low-level heuristic is analyzed. At last, a final study compares the best variant to a hyper-heuristic framework that combines a Multi-Armed Bandit algorithm into the multi-objective optimization based on decomposition with dynamical resource allocation (MOEA/D-DRA) and a state-of-the-art MOPSO. Our results indicate that the resulting algorithm outperforms the hyper-heuristic framework in most of the problems investigated. Moreover, it achieves competitive results compared to a state-of-the-art MOPSO.     

Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.