Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

Heuristic,meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation

The allocation of fresh produce to shelf space represents a new decision support research area which is motivated by the desire of many retailers to improve their service due to the increasing demand for fresh food. However, automated decision making for fresh produce allocation is challenging because of the very short lifetime of fresh products. This paper considers a recently proposed practical model for the problem which is motivated by our collaboration with Tesco. Moreover, the paper investigates heuristic and meta-heuristic approaches as alternatives for the generalized reduced gradient algorithm, which becomes inefficient when the problem size becomes larger. A simpler single-item inventory problem is firstly studied and solved by a polynomial time bounded procedure. Several dynamic greedy heuristics are then developed for the multi-item problem based on the procedure for the single-item inventory problem. Experimental results show that these greedy heuristics are much more efficient and provide competitive results when compared to those of a multi-start generalized reduced gradient algorithm. In order to further improve the solution, we investigated simulated annealing, a greedy randomized adaptive search procedure and three types of hyper-heuristics. Their performance is tested and compared on a set of problem instances which are made publicly available for the research community.     

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.     

Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid

This letter studies the problem of minimizing increasing set functions, equivalently, maximizing decreasing set functions, over the base matroid. This setting has received great interest, since it generalizes several applied problems including actuator and sensor placement problems in control, task allocation problems, video summarization, and many others. We study two greedy heuristics, namely, the forward and reverse greedy. We provide two novel performance guarantees for the approximate solutions obtained by them depending on both submodularity ratio and curvature.     

A theoretical justification of the set covering greedy heuristic of Caprara et al.

Large scale set covering problems have often been approached by constructive greedy heuristics, and much research has been devoted to the design and evaluation of various greedy criteria for such heuristics. A criterion proposed by Caprara et al. (1999) is based on reduced costs with respect to the yet unfulfilled constraints, and the resulting greedy heuristic is reported to be superior to those based on original costs or ordinary reduced costs.We give a theoretical justification of the greedy criterion proposed by Caprara et al. by deriving it from a global optimality condition for general non-convex optimisation problems. It is shown that this criterion is in fact greedy with respect to incremental contributions to a quantity which at termination coincides with the deviation between a Lagrangian dual bound and the objective value of the feasible solution found.     

A probabilistic model applied to emergency service vehicle location

This paper is concerned with the formulation and the solution of a probabilistic model for determining the optimal location of facilities in congested emergency systems. The inherent uncertainty which characterizes the decision process is handled by a new stochastic programming paradigm which embeds the probabilistic constraints within the traditional two-stage framework. The resulting model drops simplifying assumptions on servers independence allowing at the same time to handle the spatial dependence of demand calls. An exact solution method and different tailored heuristics are presented to efficiently solve the problem. Computational experience is reported with application to various networks.     

Heuristics for the flow line problem with setup costs

This paper presents two new heuristics for the flowshop scheduling problem with sequence-dependent setup times (SDSTs) and makespan minimization objective. The first is an extension of a procedure that has been very successful for the general flowshop scheduling problem. The other is a greedy randomized adaptive search procedure (GRASP) which is a technique that has achieved good results on a variety of combinatorial optimization problems. Both heuristics are compared to a previously proposed algorithm based on the traveling salesman problem (TSP). In addition, local search procedures are developed and adapted to each of the heuristics. A two-phase lower bounding scheme is presented as well. The first phase finds a lower bound based on the assignment relaxation for the asymmetric TSP. In phase two, attempts are made to improve the bound by inserting idle time. All procedures are compared for two different classes of randomly generated instances. In the first case where setup times are an order of magnitude smaller than the processing times, the new approaches prove superior to the TSP-based heuristic; for the case where both processing and setup times are identically distributed, the TSP-based heuristic outperforms the proposed procedures.     

改进的蝗虫优化算法在双目标应急物资中心选址问题中的应用

近年来世界各地频发灾情疫情等紧急事件,严重影响人民的生活物资保障。在这种情况下,急需建立应急物资中心来缓解燃眉之急。该类问题通常面临资源稀缺并且时间相对紧迫的处境,因此需要在短时间内获得合理的应急设施选址方案来提升服务的质量和效率。本文对应急物资中心选址问题展开研究,提出一种考虑后续运输成本以及有概率发生紧急事件而导致无法正常运送物资的双目标离散选址模型,并为此设计一种二进制多目标蝗虫优化算法。该算法采用模糊关联熵系数来引导迭代更新,同时为其添加外部档案,最优解选择机制和竞争决策机制来提升算法性能。多次数值实验表明该算法的计算效率和求解质量较高,可作为应急物资中心选址问题的一种可行且有效的算法。     

Heuristics for the Maximum Outerplanar Subgraph Problem

Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem. In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem. In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs. We compare a greedy heuristic against a triangular cactus heuristic and its greedy variation. We also use the solutions from the greedy heuristics as initial solutions for a simulated annealing algorithm.The main experimental result is that simulated annealing with initial solution taken from the greedy triangular cactus heuristic yields the best known approximations for the maximum outerplanar subgraph problem.Work funded by the Tampere Graduate School in Information Science and Engineering (TISE) and supported by the Academy of Finland (Project 51528).     

Two-level evolutionary approach to the survivable mesh-based transport network topological design

The complete topology design problem of survivable mesh-based transport networks is to address simultaneously design of network topology, working path routing, and spare capacity allocation based on span-restoration. Each constituent problem in the complete design problem could be formulated as an Integer Programming (IP) and is proved to be NP\mathcal{NP} -hard. Due to a large amount of decision variables and constraints involved in the IP formulation, to solve the problem directly by exact algorithms (e.g. branch-and-bound) would be impractical if not impossible. In this paper, we present a two-level evolutionary approach to address the complete topology design problem. In the low-level, two parameterized greedy heuristics are developed to jointly construct feasible solutions (i.e., closed graph topologies satisfying all the mesh-based network survivable constraints) of the complete problem. Unlike existing “zoom-in”-based heuristics in which subsets of the constraints are considered, the proposed heuristics take all constraints into account. An estimation of distribution algorithm works on the top of the heuristics to tune the control parameters. As a result, optimal solution to the considered problem is more likely to be constructed from the heuristics with the optimal control parameters. The proposed algorithm is evaluated experimentally in comparison with the latest heuristics based on the IP software CPLEX, and the “zoom-in”-based approach on 28 test networks problems. The experimental results demonstrate that the proposed algorithm is more effective in finding high-quality topologies than the IP-based heuristic algorithm in 21 out of 28 test instances with much less computational costs, and performs significantly better than the “zoom-in”-based approach in 19 instances with the same computational costs.     

Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered. In CLRP-FD, facility location problem (FLP) and vehicle routing problem (VRP) are observed simultaneously. Indeed, the vehicles and the depots have a predefined capacity to serve the customers that have fuzzy demands. To model this problem, a fuzzy chance constrained programming model of that is designed based upon the fuzzy credibility theory. To solve this problem, a greedy clustering method (GCM) including the stochastic simulation is proposed. To obtain the best value of the dispatcher preference index of the model and to analyze its influence on the final solution, numerical experiments are carried out. Finally, to show the performance of the greedy clustering method, associated results are compared with the lower bound of the solutions.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

An exact algorithm for the capacitated facility location problems with single sourcing

Facility location problems are often encountered in many areas such as distribution, transportation and telecommunication. We describe a new solution approach for the capacitated facility location problem in which each customer is served by a single facility. An important class of heuristic solution methods for these problems are Lagrangian heuristics which have been shown to produce high quality solutions and at the same time be quite robust. A primal heuristic, based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied, is incorporated into the Lagrangian heuristic. Finally, a branch-and-bound method, based on the Lagrangian heuristic is developed, and compared computationally to the commercial code CPLEX. The computational results indicate that the proposed method is very efficient.     

A comparison of algorithm RS with algorithm OPTSOL70

In a very recent paper (Almiñana and Pastor (1997)) we proposed a new lagrangian surrogate heuristic, called RS, for solving the location (or unicost) set covering problem. In that paper we show that RS is more accurate than the pair of greedy type heuristics FMC/CMA and that RS outperforms the surrogate heuristic SH. Here we are going to compare algorithms RS with the best designed hybrid algorithm for the location set covering problem, known as OPTSOL70.     

On solving the discrete location problems when the facilities are prone to failure

The classical discrete location problem is extended here, where the candidate facilities are subject to failure. The unreliable location problem is defined by introducing the probability that a facility may become inactive. The formulation and the solution procedure have been motivated by an application to model and solve a large size problem for locating base stations in a cellular communication network. We formulate the unreliable discrete location problems as 0–1 integer programming models, and implement an enhanced dual-based solution method to determine locations of these facilities to minimize the sum of fixed cost and expected operating (transportation) cost. Computational tests of some well-known problems have shown that the heuristic is efficient and effective for solving these unreliable location problems.     

A methodology to solve large-scale cooperative transportation planning problems

In this paper, we suggest a methodology to solve a cooperative transportation planning problem and to assess its performance. The problem is motivated by a real-world scenario found in the German food industry. Several manufacturers with same customers but complementary food products share their vehicle fleets to deliver their customers. After an appropriate decomposition of the entire problem into sub problems, we obtain a set of rich vehicle routing problems (VRPs) with time windows for the delivery of the orders, capacity constraints, maximum operating times for the vehicles, and outsourcing options. Each of the resulting sub problems is solved by a greedy heuristic that takes the distance of the locations of customers and the time window constraints into account. The greedy heuristic is improved by an appropriate Ant Colony System (ACS). The suggested heuristics to solve the problem are assessed within a dynamic and stochastic environment in a rolling horizon setting using discrete event simulation. We describe the used simulation infrastructure. The results of extensive simulation experiments based on randomly generated problem instances and scenarios are provided and discussed. We show that the cooperative setting outperforms the non-cooperative one.     

带时效性约束的配送中心多源选址问题研究

应用启发式算法求解带时效性约束的多源选址问题.分析物流配送的时效性问题,建立带时效性约束的配送中心多源选址模型.构造两步启发式算法:1)借助传统迭代算法,求解物流服务分配矩阵,把多源选址问题转化为单源选址问题;2)基于M ATLAB函数,设计优化程序,计算带时效性约束的单源选址模型.并给出算例,验证模型和算法的可行性.研究表明两步启发式算法是求解带时效性约束的物流配送中心多源连续选址问题的有效算法.     

A modified VNS metaheuristic for max-bisection problems

Variable neighborhood search (VNS) metaheuristic as presented in Festa et al. [Randomized heuristics for the MAX-CUT problem, Optim. Methods Software 17 (2002) 1033–1058] can obtain high quality solution for max-cut problems. Therefore, it is worthwhile that VNS metaheuristic is extended to solve max-bisection problems. Unfortunately, comparing with max-cut problems, max-bisection problems have more complicated feasible region via the linear constraint e^Tx=0. It is hard to directly apply the typical VNS metaheuristic to deal with max-bisection problems. In this paper, we skillfully combine the constraint e^Tx=0 with the objective function, obtain a new optimization problem which is equivalent to the max-bisection problem, and then adopt a distinct greedy local search technique to the resulted problem. A modified VNS metaheuristic based on the greedy local search technique is applied to solve max-bisection problems. Numerical results indicate that the proposed method is efficient and can obtain high equality solution for max-bisection problems.     

城市消防站点布局的改进启发式算法

面对数量较多需要及时处理的突发事故,为了满足最短应急时间限制,最低应急资源数和最少的出救点等目标,在城市规划决策中,考虑在一个确定应急限制期下的安全消防站选址问题,给出一个反映决策者对时间和费用偏好的折衷选址方案十分必要.从实际应用出发,运用改进启发式算法方法研究时间与资源限制条件下的多出救点组合模型求解问题.给出了应急限制期和安全消防设施点建立的费用模型,从理论上证明了模型求解方法的正确性.在给定限制期条件下,通过分析得出应急服务设施点选择方法.通过算例说明该计算方法的具体应用,为交通安全消防站点选择提供参考,该方法还适用于诸如医院急救站等类似公共设施的规划建设.     

The effect of material flow and workload on the performance of machine location heuristics

Depending on the problem structure and routing strategies a machine location problem plays an important role in controlling the material flow of work-in-process in discrete product manufacturing environment. In this paper we investigate the effect of material flow and workload on the performance of heuristics for solving an important design problem for job routing and material flow in a manufacturing system. In this research we first develop a model for workload or traffic intensity between machines in a shop floor and then identify different structures of the problems, especially the data. This measure is then used to evaluate the effect of workload on efficiency of the heuristics to solve machine location problems. Some concluding remarks are made on to the effect of the workload or the traffic intensity of materials within the machine cell on the performance of some known heuristics. Conclusions are also made on the performance measures such as makespan, transporter utilization and machine utilization, depending on the problem and data structures.