A variable neighborhood search for the network design problem with relays

Given a set of commodities to be routed over a network, the network design problem with relays involves selecting a route for each commodity and determining the location of relays where the commodities must be reprocessed at certain distance intervals. We propose a hybrid approach based on variable neighborhood search. The variable neighborhood algorithm searches for the route for each commodity and the optimal relay locations for a given set of routes are determined by an implicit enumeration algorithm. We show that dynamic programming can be used to determine the optimal relay locations for a single commodity. Dynamic programming is embedded into the implicit enumeration algorithm to solve the relay location problem optimally for multiple commodities. The special structure of the problem is leveraged for computational efficiency. In the variable neighborhood search algorithm, the routes of the current solution are perturbed and reconstructed to generate neighbor solutions using random and greedy construction heuristics. Computational experiments on three sets of problems (80 instances) show that the variable neighborhood search algorithm with optimal relay allocations outperforms all existing algorithms in the literature.     

Metaheuristic hybridizations for the regenerator placement and dimensioning problem in sub-wavelength switching optical networks

Physical layer impairments severely limit the reach and capacity of optical systems, thereby hampering the deployment of transparent optical networks (i.e., no electrical signal regenerators are required). Besides, the high cost and power-consumption of regeneration devices makes it unaffordable for network operators to consider the opaque architecture (i.e., regeneration is available at every network node). In this context, translucent architectures (i.e., regeneration is only available at selected nodes) have emerged as the most promising short term solution to decrease costs and energy consumption in optical backbone networks. Concurrently, the coarse granularity and inflexibility of legacy optical technologies have re-fostered great interest in sub-wavelength switching optical networks, which introduce optical switching in the time domain so as to further improve resources utilization. In these networks, the complex regenerator placement and dimensioning problem emerges. In short, this problem aims at minimizing the number of electrical regenerators deployed in the network. To tackle it, in this paper both a greedy randomized adaptive search procedure and a biased random-key genetic algorithm are developed. Further, we enhance their performance by introducing both path-relinking and variable neighborhood descent as effective intensification procedures. The resulting hybridizations are compared among each other as well as against results from optimal and heuristic mixed integer linear programming formulations. Illustrative results over a broad range of network scenarios show that the biased random-key genetic algorithm working in conjunction with these two intensification mechanisms represents a compelling network planning algorithm for the design of future sub-wavelength optical networks.     

Optimal coordination of directional over-current relays using informative differential evolution algorithm

Growing interconnection in distribution system creates new problem for protection engineers. Particularly the design of overcurrent relay coordination in such system is an independent area of research. With the availability of new artificial based optimization algorithm relay coordination research gain a new momentum. Well established artificial based optimization algorithm such as genetic and particle swam optimization are successfully applied for such applications. This paper discusses the application of informative differential evolution algorithm with self adaptive re-clustering technique for selection of TDS and PSM for optimal coordination of directional overcurrent relays. Both continuous as well as discrete version of informative differential evolution algorithm are used for optimization of relay setting. Proper combination of backup relays for each primary relay are identified by using LINKNET graph theory approach. Coordination of directional overcurrent is developed for 9 bus and IEEE 30 bus distribution systems. The aim of problem is to minimize the total operating time of primary relays and eliminate the miscoordination among the primary and backup relay pairs. Discrete types of settings for electromechanical types of relay are also discussed in this paper. Moreover, the relay coordination problem is modified for providing optimal coordination time interval between 0.2 and 0.8 s among all primary and backup relays pairs. The results are compared with hybrid of genetic algorithm – nonlinear programming and sequential quadratic programming. Digsilient power factory software is used for verification of result.     

Solving the Passive Optical Network with Fiber Duct Sharing Planning Problem Using Discrete Techniques

Similar to the constrained facility location problem, the passive optical network (PON) planning problem necessitates the search for a subset of deployed facilities (splitters) and their allocated demand points (optical network units) to minimize the overall deployment cost. In this paper we use a mixed integer linear programming formulation stemming from network flow optimization to construct a heuristic based on limiting the total number of interconnecting paths when implementing fiber duct sharing. Then, a disintegration heuristic involving the construction of valid clusters from the output of a k means algorithm, reduce the time complexity while ensuring close to optimal results. The proposed heuristics are then evaluated using a real-world dataset, showing favourable performance.     

Candidate groups search for K-harmonic means data clustering

Clustering is a very popular data analysis and data mining technique. K-means is one of the most popular methods for clustering. Although K-mean is easy to implement and works fast in most situations, it suffers from two major drawbacks, sensitivity to initialization and convergence to local optimum. K-harmonic means clustering has been proposed to overcome the first drawback, sensitivity to initialization. In this paper we propose a new algorithm, candidate groups search (CGS), combining with K-harmonic mean to solve clustering problem. Computational results showed CGS does get better performance with less computational time in clustering, especially for large datasets or the number of centers is big.     

The one-machine just-in-time scheduling problem with preemption

This paper investigates the notion of preemption in scheduling, with earliness and tardiness penalties. Starting from the observation that the classical cost model where penalties only depend on completion times does not capture the just-in-time philosophy, we introduce a new model where the earliness costs depend on the start times of the jobs. To solve this problem, we propose an efficient representation of dominant schedules, and a polynomial algorithm to compute the best schedule for a given representation. Both a local search algorithm and a branch-and-bound procedure are then derived. Experiments finally show that the gap between our upper bound and the optimum is very small.     

闪电分叉过程算法优化的K-means聚类

K-means聚类算法是在数据挖掘和数据分析中一种常用算法,但是其存在依赖初始值和易陷入局部最优值的缺陷,针对这些不足,本文提出一种闪电分叉过程算法优化的K-means聚类,克服聚类算法在初始值选择困难的问题,提高K-means聚类算法的求解精度,降低陷入局部最优的可能性。从UCI数据集中选取6个真实的数据集进行仿真实验,结果表明本文改进后的聚类算法有更好的求解精度和鲁棒性。     

Incorporating the threat of terrorist attacks in the design of public service facility networks

In this paper, we consider the design problem of a public service facility network with existing facilities when there is a threat of possible terrorist attacks. The aim of the system planner, who is responsible for the operation of the network, is to open new facilities, relocate existing ones if necessary, and protect some of the facilities to ensure a maximum coverage of the demand that is assumed to be aggregated at customer zones. By doing so, the system planner anticipates that a number of unprotected facilities will be rendered out-of-service by terrorist attacks. It is assumed that the sum of the fixed cost of opening new facilities, the relocation costs, and the protection costs cannot exceed a predetermined budget level. Adopting the approach of gradual (or partial) coverage, we formulate a bilevel programming model where the system planner is the leader and the attacker is the follower. The objective of the former is the maximization of the total service coverage, whereas the latter wants to minimize it. We propose a heuristic solution procedure based on tabu search where the search space consists of the decisions of the system planner, and the corresponding objective value is computed by optimally solving the attacker??s problem using CPLEX. To assess the quality of the solutions produced by the tabu search (TS) heuristic, we also develop an exhaustive enumeration method, which explores all the possible combinations of opening new facilities, relocating existing ones, and protecting them. Since its time complexity is exponential, it can only be used for relatively small instances. Therefore, to be used as a benchmark method, we also implement a hill climbing procedure employed with the same type of moves as the TS heuristic. Besides, we carry out a sensitivity analysis on some of the problem parameters to investigate their effect on the solution characteristics.     

Updating credal networks is approximable in polynomial time

Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks.     

Variable Selection in Linear Regression With Many Predictors

With advanced capability in data collection, applications of linear regression analysis now often involve a large number of predictors. Variable selection thus has become an increasingly important issue in building a linear regression model. For a given selection criterion, variable selection is essentially an optimization problem that seeks the optimal solution over 2^m possible linear regression models, where m is the total number of candidate predictors. When m is large, exhaustive search becomes practically impossible. Simple suboptimal procedures such as forward addition, backward elimination, and backward-forward stepwise procedure are fast but can easily be trapped in a local solution. In this article we propose a relatively simple algorithm for selecting explanatory variables in a linear regression for a given variable selection criterion. Although the algorithm is still a suboptimal algorithm, it has been shown to perform well in extensive empirical study. The main idea of the procedure is to partition the candidate predictors into a small number of groups. Working with various combinations of the groups and iterating the search through random regrouping, the search space is substantially reduced, hence increasing the probability of finding the global optimum. By identifying and collecting “important” variables throughout the iterations, the algorithm finds increasingly better models until convergence. The proposed algorithm performs well in simulation studies with 60 to 300 predictors. As a by-product of the proposed procedure, we are able to study the behavior of variable selection criteria when the number of predictors is large. Such a study has not been possible with traditional search algorithms.

This article has supplementary material online.     

A hybrid scatter search heuristic for personalized crew rostering in the airline industry

The crew scheduling problem in the airline industry is extensively investigated in the operations research literature since efficient crew employment can drastically reduce operational costs of airline companies. Given the flight schedule of an airline company, crew scheduling is the process of assigning all necessary crew members in such a way that the airline is able to operate all its flights and constructing a roster line for each employee minimizing the corresponding overall cost for personnel. In this paper, we present a scatter search algorithm for the airline crew rostering problem. The objective is to assign a personalized roster to each crew member minimizing the overall operational costs while ensuring the social quality of the schedule. We combine different complementary meta-heuristic crew scheduling combination and improvement principles. Detailed computational experiments in a real-life problem environment are presented investigating all characteristics of the procedure. Moreover, we compare the proposed scatter search algorithm with optimal solutions obtained by an exact branch-and-price procedure and a steepest descent variable neighbourhood search.     

基于商品关联度的智能仓库储位分配问题研究

储位分配方案是直接影响智能仓库工作效率和拣选成本的关键因素.根据历史订单信息定义了商品之间的关联度,以同一货架上的商品之间的关联度之和极大化为目标建立了智能仓库储位分配问题的数学模型,并设计了求解模型的算法.首先根据历史订单信息计算商品之间的关联度,然后结合商品的周转率、商品之间的关联度等信息,设计了启发式算法求解智能仓库储位分配问题,并且分析了启发式算法的时间复杂度.通过大量的模拟计算验证了本文建立的数学模型和设计的启发式算法的有效性,证明了以同一货架上商品之间关联度极大化为目标和以订单拣选过程中搬运货架总次数极小化为目标的一致性.通过对比分析本文算法得到的储位分配结果与随机储位分配结果可以看出,利用基于商品关联度的启发式算法得到的储位分配方案比随机储位分配方案对应的货架搬运次数平均减少了30.08%.     

Part type selection problem in flexible manufacturing systems: tabu search algorithms

Production planning in flexible manufacturing systems is concerned with the organization of production in order to satisfy a given master production schedule. The planning problem typically gives rise to several hierarchical subproblems which are then solved sequentially or simultaneously. In this paper, we address one of the subproblems: the part type selection problem. The problem is to determine a subset of part types having production requirements for immediate and simultaneous processing over the upcoming period of the planning horizon, subject to the tool magazine and processing time limitation. Several versions of tabu search (TS) algorithm are proposed for solving the problem. A systematic computational test is conducted to test the performance of the TS algorithms. The best TS algorithm developed is compared to a simulated annealing algorithm.     

A simulated annealing algorithm with the random compound move for the sequential partitioning problem of directed acyclic graphs

In this paper, we present an approach for finding a minimum cost partition of the nodes of a directed acyclic graph into subsets of a given size, subject to the constraint that the precedence relationships among the elements are satisfied, based on the concept of simulated annealing. Simulated annealing is generally applicable, and can be used to obtain solutions arbitrarily close to an optimum. However, the standard simulated annealing approach with a conventional neighbourhood structure does not yield good solutions for this problem, since this is a multiple partitioning problem and the number of subsets is not fixed. For this problem, we develop an effective neighbourhood structure and a new acceptance criterion. We also assess the effectiveness of the developed algorithm. The results show that this proposed algorithm outperforms, in terms of solution quality, any other algorithm using tabu search. The computational time of the procedure is proportional to the number of nodes in the graph.     

A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.     

3.1. OR in banking

In this paper, we describe a deterministic multiperiod capacity expansion model in which a single facility serves the demand for many products. Potential applications for the model can be found in the capacity expansion planning of communication systems as well as in the production planning of heavy process industries. The model assumes that each capacity unit simultaneously serves a prespecified (though not necessarily integer) number of demand units of each product. Costs considered include capacity expansion costs, idle capacity holding costs, and capacity shortage costs. All cost functions are assumed to be nondecreasing and concave. Given the demand for each product over the planning horizon, the objective is to find the capacity expansion policy that minimizes the total cost incurred. We develop a dynamic programming algorithm that finds optimal policies. The required computational effort is a polynomial function of the number of products and the number of time periods. When the number of products equals one, the algorithm reduces to the well-known algorithm for the classical dynamic lot size problem.     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.     

110警车配置及巡逻方案

针对110警车调度问题,引入了图论中的最短路算法以及计算几何的相关理论,建立了车辆调配模型、巡逻路线模型以及基于模糊数学的评价指标模型.另外,用C++编写了一个可视化的软件,不仅实现了手动描点,自动求出覆盖线段集合的功能,同时利用计算机模拟警车的巡逻路线,最后通过计算机检验得到结果,其合理性和实用性都令人满意.针对问题一,通过人机结合,配置17辆警车就能实现D1的目标,很好地兼顾了警车巡逻的运行成本,减少公安部门车辆和人员等的投入.针对问题二,采用模糊数学相关理论使评价指标实现了从定性到定量的转变.针对问题三和六,在D1的基础上,兼顾了巡逻效果的显著性,采用最少被巡逻道路优先的贪心算法建立了动态巡逻模型,得到了合理的巡逻方案.在此方案中,我们动用了30辆警车完成了问题一的目标.另外还额外考虑了案发事件概率不均匀分布的情况,建立了改进模型.针对问题四,在完成问题三指标的基础上,为了尽可能提高巡逻车辆的隐蔽性和增强巡逻效果,采用轮盘赌算法来引入随机性.针对问题五,采用最远距离道路优先贪心策略,使模型尽可能满足条件D1,D2.针对问题七,提出了一些额外因素及其解决方案,进一步完善了模型,使模型更贴近现实.     

One-Dimensional Cutting Stock Problem with a Given Number of Setups: A Hybrid Approach of Metaheuristics and Linear Programming

One-dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which arises in many industrial applications. Since the setup costs for switching different cutting patterns become more dominant in recent cutting industry, we consider a variant of 1D-CSP, called the pattern restricted problem (PRP), to minimize the number of stock rolls while constraining the number of different cutting patterns within a bound given by users. For this problem, we propose a local search algorithm that alternately uses two types of local search processes with the 1-add neighborhood and the shift neighborhood, respectively. To improve the performance of local search, we incorporate it with linear programming (LP) techniques, to reduce the number of solutions in each neighborhood. A sensitivity analysis technique is introduced to solve a large number of associated LP problems quickly. Through computational experiments, we observe that the new algorithm obtains solutions of better quality than those obtained by other existing approaches.     

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.