A heuristic algorithm for the m-machine,n-job flow-shop sequencing problem

In a general flow-shop situation, where all the jobs must pass through all the machines in the same order, certain heuristic algorithms propose that the jobs with higher total process time should be given higher priority than the jobs with less total process time. Based on this premise, a simple algorithm is presented in this paper, which produces very good sequences in comparison with existing heuristics. The results of the proposed algorithm have been compared with the results from 15 other algorithms in an independent study by Park [13], who shows that the proposed algorithm performs especially well on large flow-shop problems in both the static and dynamic sequencing environments.     

A heuristic algorithm for the period vehicle routing problem

In this paper we consider the period vehicle routing problem, which is the problem of designing routes for delivery vehicles to meet customer service level requirements (not all customers require delivery on every day in the period). A heuristic algorithm, based upon the daily vehicle routing algorithm of Fisher and Jaikumar, is presented and computational results are given for test problems drawn from the literature.     

A heuristic model for the sequence-dependent lot scheduling problem

This paper presents a heuristic algorithm for finding a good solution for the sequence-dependent lot scheduling problem. Unlike available methods, the algorithm eliminates the need for creating new artificial problems and implementing feasibility tests. It also eliminates the tedious task of translating setup relationships into a mathematical programming formulation. The result is a conceptually simple solution technique that is practically motivated and easily implemented for use on the shop floor. Comparison of algorithm performance with published results demonstrates the efficacy of the approach.     

考虑风险规避的秘书问题求解的一个启发式方法

秘书问题是一类序贯观察与选择问题,描述了动态的信息搜索与决策过程.针对现有的以寻找满意解为目标的启发式方法存在诸多局限,提出了新的启发式方法,该方法基于当前观测中侯选项在已观察侯选项中的相对排名、待观测侯选项数量以及决策者的抱负水平,决策者可以通过设定抱负水平灵活决定该启发式方法的结果导向.推导了该启发式方法的性能指标,并通过仿真的方法与已有启发式方法的性能进行了比较.结果发现,该启发式方法在最终选择的侯选项的期望排名和稳定性,以及风险解的避免上均优于已有的启发式方法.     

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

A hybrid heuristic for the uncapacitated single allocation hub location problem

The uncapacitated single allocation hub location problem (USAHLP), with the hub-and-spoke network structure, is a decision problem in regard to the number of hubs and location–allocation. In a pure hub-and-spoke network, all hubs, which act as switching points for internodal flows, are interconnected and none of the non-hubs (i.e., spokes) are directly connected. The key factors for designing a successful hub-and-spoke network are to determine the optimal number of hubs, to properly locate hubs, and to allocate the non-hubs to the hubs. In this paper two approaches to determine the upper bound for the number of hubs along with a hybrid heuristic based on the simulated annealing method, tabu list, and improvement procedures are proposed to resolve the USAHLP. Computational experiences indicate that by applying the derived upper bound for the number of hubs the proposed heuristic is capable of obtaining optimal solutions for all small-scaled problems very efficiently. Computational results also demonstrate that the proposed hybrid heuristic outperforms a genetic algorithm and a simulated annealing method in solving USAHLP.     

A spanning heuristic for the unordered and ordered matching identification problem

The matching identification problem (MIP) is a combinatoric search problem related to the fields of learning from examples, boolean functions, and knowledge acquisition. The MIP involves identifying a single “goal” item from a large set of items. Because there is commonly a cost associated with evaluating each guess, the goal item should be identified in as few guesses as possible. As in most search problems, the items have a similar structure, which allows an evaluation of each guessed item. In other words, each guessed item elicits partial information about the goal item, i.e. how similar the guess is to the goal. With this information the goal is more quickly identified.The unordered MIP has been studied by Mehrez and Steinberg (ORSA J. Comput. 7 (1995) 211) in which they proposed two different types of algorithms. The purpose of the present paper is to suggest an improved Spanning Heuristic algorithm. Its improvement increases as the problem size increases. Further results and comparisons are derived for the unordered and ordered cases.This research shows that when the search space is very large, it is better to inquire from items that are known not to be the goal (they have been ruled out by previous guesses), for the purpose of acquiring more information about the goal. As the search space is narrowed, it is better to guess items that have not been ruled out.     

A heuristic for the time constrained asymmetric linear sum assignment problem

The linear sum assignment problem is a fundamental combinatorial optimisation problem and can be broadly defined as: given an \(n \times m, m \ge n\) benefit matrix \(B = (b_{ij})\), matching each row to a different column so that the sum of entries at the row-column intersections is maximised. This paper describes the application of a new fast heuristic algorithm, Asymmetric Greedy Search, to the asymmetric version (\(n \ne m\)) of the linear sum assignment problem. Extensive computational experiments, using a range of model graphs demonstrate the effectiveness of the algorithm. The heuristic was also incorporated within an algorithm for the non-sequential protein structure matching problem where non-sequential alignment between two proteins, normally of different numbers of amino acids, needs to be maximised.     

The freight allocation problem with all-units quantity-based discount: A heuristic algorithm

This paper studies a problem encountered by a buying office for one of the largest retail distributors in the world. An important task for the buying office is to plan the distribution of goods from Asia to various destinations across Europe. The goods are transported along shipping lanes by shipping companies, which offer different discount rates depending on the freight quantity. To increase the reliability of transportation, the shipper imposes a quantity limit on each shipping company on each shipping lane. To guarantee a minimum business volume, each shipping company requests a minimum total freight quantity over all lanes if it is contracted. The task involves allocating projected demand of each shipping lane to shipping companies subject to the above conditions such that the total cost is minimized.Existing work on this and related problems employs commercial linear programming software to solve their models. However, since the problem is NP−hard in the strong sense, it is unlikely to be solvable optimally in reasonable time for large cases. Hence, we propose the first heuristic-based algorithm for the problem, which combines a filter-and-fan search scheme with a tabu search mechanism. Experiments on randomly generated test instances show that as the size of the problem increases, our algorithm produces superior solutions in less time compared to a leading mixed-integer programming solver.     

An improved MIP heuristic for the intermodal hub location problem

Optimization methods have been commonly developed for the intermodal hub location problem because it has a broad range of practical applications. These methods include exact methods (limited on solving large-size problems) and heuristics (no guarantee on solution quality). In order to avoid their weakness but to leverage their strength, we develop an improved MIP heuristic combining branch-and-bound, Lagrangian relaxation, and linear programming relaxation. In the heuristic, we generate a population of initial feasible solutions using the branch-and-bound and Lagrangian relaxation methods and create a linear-relaxed solution using the linear programming relaxation method. We combine these feasible and linear-relaxed solutions to fix a portion of hub location variables so as to create a number of restricted hub location subproblems. We then combine the branch-and-bound method to solve these restricted subproblems for iteratively improving solution quality. We discuss in detail the application of the method to the intermodal hub location problem. The discussion is followed by extensive statistical analysis and computational tests, where the analysis shows statistical significance of solutions for guiding the heuristic search and comparisons with other methods indicate that the proposed approach is computationally tractable and is able to obtain competitive results.     

A mixed integer programming and heuristic algorithm for a warehouses location problem

A warehouses location problem is treated using a mixed integer programming and a heuristic algorithm. A simplification of freight rates schedules, based upon shipments consolidation and a linear regression of rates vs distances was made. Warehousing costs were divided according to fixed and variable and related to the throughput of the warehouses. Consideration was given in the analysis to the choice between owning and leasing each warehouse. In the case studied, the analysis demonstrated that a possible saving of approximately 22 per cent in annual distribution costs could be realized under the optimized warehouse location network.     

An efficient heuristic procedure for solving the layout design problem

The limited ability of schematic procedures, constraints of linear programming techniques, inflexibility of construction methods and inadequacy of dynamic programming approaches to provide acceptable solutions to realistic size layout design problems has led to an ever increasing interest in heuristic procedures. Comparative studies have shown that heuristic procedures can satisfy more desirable qualities in an ‘ideal algorithm’ to a greater extent than competitive techniques. Excessive computational effort, which has been one of the main criticisms levelled against heuristic approaches in the past, proves to be less of a problem in relation to layout design. By utilizing unique attributes associated with real-life problems and using small incisive modifications it is demonstrated how a heuristic procedure can be significantly improved.     

A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations

In this paper a fast greedy sequential heuristic for the vertex colouring problem is presented. The suggested algorithm builds the same colouring of the graph as the well-known greedy sequential heuristic in which on every step the current vertex is coloured in the minimum possible colour. Our main contributions include introduction of a special matrix of forbidden colours and application of efficient bitwise operations on bit representations of the adjacency and forbidden colours matrices. Computational experiments show that in comparison with the classical greedy heuristic the average speedup of the developed approach is 2.6 times on DIMACS instances.     

A hybrid approach to sequencing jobs using heuristic rules and neural networks

A hybrid approach to solve job sequencing problems using heuristic rules and artificial neural networks is proposed. The problem is to find a job sequence for a single machine that minimizes the total weighted tardiness of the jobs. Two different cases are considered: (1) when there are no setups, and (2) when there are sequence-dependent setup times. So far, successful heuristic rules for these cases are: apparent tardiness cost (ATC) rule proposed by Vepsalainen and Morton for the former case, and an extended version of the ATC rule (ATCS) proposed by Lee, Bhaskaran, and Pinedo for the latter. Both approaches utilize some look-ahead parameters for calculating the priority index of each job. As reported by Bhaskaran and Pinedo, the proper value of the look-ahead parameter depends upon certain problem characteristics, such as due-date tightness and due-date range. Thus, an obvious extension of the ATC or the ATCS rule is to adjust the parameter values depending upon the problem characteristics: this is known to be a difficult task. In this paper, we propose an application of a neural network as a tool to ‘predict’ proper values of the look-ahead parameters. Our computational tests show that the proposed hybrid approach outperforms both the ATC rule with a fixed parameter value and the ATCS using the heuristic curve-fitting method.     

A hybrid genetic algorithm for the batch sequencing problem on identical parallel machines

The batch sequencing problem (BSP) has been the focus of much research thanks to its practical applicability and NP-hard nature. This study aims to solve an extension of the problem from single machine case to parallel machine case. A dispatching rule called the EDD (Earliest Due Date)-Greedy heuristic and a pure genetic algorithm (GA) are proposed, and then combine them through an insertion method called the Gene Bank Strategy. Several test cases of up to 12 machines and 60 jobs are randomly generated and solved. Those experiments show that the introduced hybrid GA can provide far better results than its two component algorithms that can also independently solve the problem.     

Exact and heuristic algorithms for solving the generalized minimum filter placement problem

We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model. The authors gratefully acknowledge the comments of two anonymous referees, whose input led to an improved version of this paper. Dr. Smith gratefully acknowledges the support of the Office of Naval Research under Grant #N00014-03-1-0510 and the Defense Advanced Research Projects Agency under Grant #N66001-01-1-8925.