Constructive heuristic algorithms for the open shop problem

In this paper we consider constructive heuristic algorithms for the open shop problem with minimization of the schedule length. By means of investigations of the structure of a feasible solution two types of heuristic algorithms are developed: construction of a rank-minimal schedule by solving successively weighted maximum cardinality matching problems and construction of an approximate schedule by applying insertion techniques combined with beam search. All presented algorithms are tested on benchmark problems from the literature. Our computational results demonstrate the excellent solution quality of our insertion algorithm, especially for greater job and machine numbers. For 29 of 30 benchmark problems with at least 10 jobs and 10 machines we improve the best known values obtained by tabu search.     

Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillard’s instances for the blocking flow shop scheduling problem with the total flow time criterion.     

New heuristic algorithms for the windy rural postman problem

In this paper we deal with the windy rural postman problem. This problem generalizes several important arc routing problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a scatter search algorithm for the windy rural postman problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.     

New heuristic algorithms for solving the planar p-median problem

In this paper we propose effective heuristics for the solution of the planar p-median problem. We develop a new distribution based variable neighborhood search and a new genetic algorithm, and also test a hybrid algorithm that combines these two approaches. The best results were obtained by the hybrid approach. The best known solution was found in 466 out of 470 runs, and the average solution was only 0.000016% above the best known solution on 47 well explored test instances of 654 and 1060 demand points and up to 150 facilities.     

An improved hybrid algorithm for the set covering problem

The state-of-the-art ant colony optimization (ACO) algorithm to solve large scale set covering problems (SCP) starts by solving the Lagrangian dual (LD) problem of the SCP to obtain quasi-optimal dual values. These values are then exploited by the ACO algorithm in the form of heuristic estimates. This article starts by discussing the complexity of this approach where a number of new parameters are introduced to escape local optimums and normalize the heuristic values. To avoid these complexities, we propose a new hybrid algorithm that starts by solving the linear programming (LP) relaxation of the SCP. This solution is used to eliminate unnecessary columns, and to estimate the heuristic information. To generate solutions, we use a Max–Min Ant System (MMAS) algorithm that employs a novel mechanism to update the pheromone trail limits to maintain a predetermined exploration rate. Computational experiments on different sets of benchmark instances prove that our proposed algorithm can be considered the new state-of-the-art meta-heuristic to solve the SCP.     

Distributed algorithms for covering, packing and maximum weighted matching

This paper gives poly-logarithmic-round, distributed δ-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio δ is the maximum number of variables in any constraint. Special cases include Covering Mixed Integer Linear Programs (CMIP), and Weighted Vertex Cover (with δ = 2). Via duality, the paper also gives poly-logarithmic-round, distributed δ-approximation algorithms for Fractional Packing linear programs (where δ is the maximum number of constraints in which any variable occurs), and for Max Weighted c-Matching in hypergraphs (where δ is the maximum size of any of the hyperedges; for graphs δ = 2). The paper also gives parallel (RNC) 2-approximation algorithms for CMIP with two variables per constraint and Weighted Vertex Cover. The algorithms are randomized. All of the approximation ratios exactly match those of comparable centralized algorithms.     

Solving the maximal covering location problem with heuristic concentration

The metaheuristic heuristic concentration (HC) is applied here to the solution of large instances of the maximal covering location problem with high percentage coverage. In these instances, exact methods may be too cumbersome for practical use, and heuristics can allow faster solution times with near-optimal results. We examined the performance of HC based on its ability to approach the optimal solutions to these problems and the run times of the algorithm compared to LP-IP runtimes. Exact solutions, generated by linear programming and branch and bound, provided a benchmark for comparison when the LP-IP problems could be run to completion. In all cases, HC found solutions with objective values no worse than 0.543% below the best known LP-IP objective value. In several instances, LP-IP runtime ballooned to as much as 38.5 h, while HC took no longer than 1.6 h in any instance. In one particular instance, LP-IP took 38.5 h to terminate, while HC found a near-optimal solution (within 0.306% of optimality) in only 25 min. Furthermore, in 62.5% of the runs, the second stage of HC improved on the first stage 1-opt algorithm.     

求解加权圆集布局问题的快速启发式搜索算法

加权圆集布局问题是基于性能驱动的一类布局问题,由于其NP-hard属性,难以在多项式时间内求解,提出一种快速启发式搜索算法。权矩阵的行向量1范数作为首次赌轮选择圆的启发信息,依次以权矩阵的当前行（其行号等于当前选择圆的序号）元素作为下次赌轮选择的启发信息,利用图形学理论给出低计算复杂度的定位规则,进而基于该定序定位规则提出一种启发式搜索算法,以求得该问题的最优解。数值实验表明,该算法的性能优于已有算法。     

Efficient heuristic algorithms for maximum utility product pricing problems

We propose improvements to some of the best heuristic algorithms for optimal product pricing problem originally designed by Dobson and Kalish in the late 1980s and in the early 1990s. Our improvements are based on a detailed study of a fundamental decoupling structure of the underlying mixed integer programming (MIP) problem and on incorporating more recent ideas, some from the theoretical computer science literature, for closely related problems. We provide very efficient implementations of the algorithms of Dobson and Kalish as well as our new algorithms. We show that our improvements lead to algorithms which generate solutions with better objective values and that are more robust in overall performance. Our computational experiments indicate that our implementation of Dobson–Kalish heuristics and our new algorithms can provide good solutions for the underlying MIP problems where the typical LP relaxations would have more than a trillion variables and more than three trillion constraints.     

Two methods of ordering the covering elements for the solution of the set covering problem

Two set-covering algorithms are proposed and proved, one selecting and ordering the covering candidates by degrees and the other using lexicographic ordering.Translated from Kibernetika, No. 4, pp. 70–74, July–August, 1989.     

Efficient primal-dual heuristic for a dynamic location problem

In this paper the dynamic location problem with opening, closure and reopening of facilities is formulated and an efficient primal-dual heuristic that computes both upper and lower limits to its optimal solution is described. The problem here studied considers the possibility of reconfiguring any location more than once over the planning horizon. This problem is NP-hard (the simple plant location problem is a special case of the problem studied). A primal-dual heuristic based on the work of Erlenkotter [A dual-based procedure for uncapacitated facility location. Operations Research 1978;26:992–1009] and Van Roy and Erlenkotter [A dual-based procedure for dynamic facility location. Management Science 1982;28:1091–105] was developed and tested over a set of randomly generated test problems. The results obtained are quite good, both in terms of the quality of lower and upper bounds calculated as in terms of the computational time spent by the heuristic. A branch-and-bound procedure that enables to optimize the problem is also described and tested over the same set of randomly generated problems.     

一种有效的求解一维下料问题的启发式算法

使用了一种改进的顺序启发式算法,在排样方式的生成过程中不断修正当前排入毛坯的价值,使之趋于合理,依次选取求解背包函数获得的最大单位价值的排样方式组成当前排样方案,迭代调用该过程多次,最终选取最优的排样方案。在保证较高材料利用率的同时考虑减少排样方式,增加最后一根材料余料长度等多个优化目标。通过多组实验结果比较,证实了算法的有效性。     

MSC问题的一类表面DNA解法

利用基于表面的DNA粘贴模型求解最小集合覆盖问题。改进体现在计算模版表面穷举了所有可能的结果,同一时间验证结果是否满足条件,真正实现了DNA的强大并行性。同时在互补的寡聚核苷酸片段发生退火反应时,利用特殊的化学反应,通过催化剂来决定是否杂交,减少了人工参与,提高了计算效率。通过计算机仿真模拟验证了模型的可行性。     

Efficient model and heuristic for the intermodal terminal location problem

A multimodal transportation system transports freight using at least two transportation modes. Among available transportation modes, intermodal freight transportation transports freight in an intermodal container or conveyance without handling the freight itself when changing modes. The locations of intermodal terminals constitute the foundation of an intermodal transportation network. The intermodal terminal location problem therefore aims to determine terminal locations and routes within a transportation network in order to minimize the total transportation and operation costs through collaborations of unimodal road transport and intermodal transport chains. Relevant research includes that of Arnold et al., who first presented mathematical programming models for the problem. Sörensen et al. recently proposed a standard model for the same problem. However, these models are complex and time consuming. Some decision variables and constraints of Sörensen et al.׳s model are proven to be redundant. A modified mixed integer programming model is then developed to increase computation efficiency. The modified model finds more optimal solutions to the benchmark problems than current approaches do, within a reasonable time. Furthermore, two matheuristics are presented to solve the problem more efficiently while obtaining near optimal solutions.     

Exact and heuristic algorithms for the interval data robust assignment problem

We consider the Assignment Problem with interval data, where it is assumed that only upper and lower bounds are known for each cost coefficient. It is required to find a minmax regret assignment. The problem is known to be strongly NP-hard. We present and compare computationally several exact and heuristic methods, including Benders decomposition, using CPLEX, a variable depth neighborhood local search, and two hybrid population-based heuristics. We report results of extensive computational experiments.     

Implementation analysis of efficient heuristic algorithms for the traveling salesman problem

The state-of-the-art of local search heuristics for the traveling salesman problem (TSP) is chiefly based on algorithms using the classical Lin–Kernighan (LK) procedure and the stem-and-cycle (S&C) ejection chain method. Critical aspects of implementing these algorithms efficiently and effectively rely on taking advantage of special data structures and on maintaining appropriate candidate lists to store and update potentially available moves. We report the outcomes of an extensive series of tests on problems ranging from 1000 to 1,000,000 nodes, showing that by intelligently exploiting elements of data structures and candidate lists routinely included in state-of-the-art TSP solution software, the S&C algorithm clearly outperforms all implementations of the LK procedure. Moreover, these outcomes are achieved without the use of special tuning and implementation tricks that are incorporated into the leading versions of the LK procedure to enhance their computational efficiency.     

A tabu-search based heuristic for the hub covering problem over incomplete hub networks

Hub location problems deal with finding the location of hub facilities and with the allocation of demand nodes to these located hub facilities. In this paper, we study the single allocation hub covering problem over incomplete hub networks and propose an integer programming formulation to this end. The aim of our model is to find the location of hubs, the hub links to be established between the located hubs, and the allocation of non-hub nodes to the located hub nodes such that the travel time between any origin–destination pair is within a given time bound. We present an efficient heuristic based on tabu search and test the performance of our heuristic on the CAB data set and on the Turkish network.     

Experimental evaluation of approximation and heuristic algorithms for the dominating paths problem

Monitoring flows on networks is a research area for which a number of applications are waiting for models and algorithms to face new problems emerging with a very high pace. In this paper we analyze a particular optimization problem, namely the Dominating Paths Problem (DPP), that has application in this field especially for urban transportation networks. Given an undirected graph G=(V,E) and a subset B⊆V of bound vertices, we look for a set of vertices M of minimum size such that each element of M is the origin of one or more paths, and, the set of all these paths dominates B. For this NP-hard problem, we present an approximation algorithm and new heuristic procedures extensively evaluated on a set of test instances. We defined two different sets of benchmarks: grid graphs and random graphs. Moreover, we included two test cases taken from real traffic networks. Computational results, discussed in the paper, give insights both on problem and on algorithms’ performance.