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.     

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.     

A heuristic for facilities layout planning

A new matrix representation of a planar graph and its dual is presented. This is then used to implement a heuristic for facilities layout planning.     

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.     

An efficient spread-based evolutionary algorithm for solving dynamic multi-objective optimization problems

Dynamic multi-objective optimization algorithms are used as powerful methods for solving many problems worldwide. Diversity, convergence, and adaptation to environment changes are three of the most important factors that dynamic multi-objective optimization algorithms try to improve. These factors are functions of exploration, exploitation, selection and adaptation operators. Thus, effective operators should be employed to achieve a robust dynamic optimization algorithm. The algorithm presented in this study is known as spread-based dynamic multi-objective algorithm (SBDMOA) that uses bi-directional mutation and convex crossover operators to exploit and explore the search space. The selection operator of the proposed algorithm is inspired by the spread metric to maximize diversity. When the environment changed, the proposed algorithm removes the dominated solutions and mutated all the non-dominated solutions for adaptation to the new environment. Then the selection operator is used to select desirable solutions from the population of non-dominated and mutated solutions. Generational distance, spread, and hypervolume metrics are employed to evaluate the convergence and diversity of solutions. The overall performance of the proposed algorithm is evaluated and investigated on FDA, DMOP, JY, and the heating optimization problem, by comparing it with the DNSGAII, MOEA/D-SV, DBOEA, KPEA, D-MOPSO, KT-DMOEA, Tr-DMOEA and PBDMO algorithms. Empirical results demonstrate the superiority of the proposed algorithm in comparison to other state-of-the-art algorithms.

     

An ant colony algorithm for solving budget constrained and unconstrained dynamic facility layout problems

The main characteristic of today's manufacturing environments is volatility. Under a volatile environment, demand is not stable. It changes from one production period to another. To operate efficiently under such environments, the facilities must be adaptive to changing production requirements. From a layout point of view, this situation requires the solution of the dynamic layout problem (DLP). DLP is a computationally complex combinatorial optimization problem for which optimal solutions can only be found for small size problems. It is known that classical optimization procedures are not adequate for this problem. Therefore, several heuristics including taboo search, simulated annealing and genetic algorithm are applied to this problem to find a good solution. This work makes use of the ant colony optimization (ACO) algorithm to solve the DLP by considering the budget constraints. The paper makes the first attempt to show how the ACO can be applied to DLP with the budget constraints. In the paper, example applications are presented and computational experiments are performed to present suitability of the ACO to solve the DLP problems. Promising results are obtained from the solution of several test problems.     

An effective discrete dynamic convexized method for solving the winner determination problem

The winner determination problem (WDP) arises in combinatorial auctions. It is known to be NP-hard. In this paper, we propose a discrete dynamic convexized method for solving this problem. We first propose an adaptive penalty function to convert the WDP into an equivalent unconstrained integer programming problem. Based on the structure of the WDP, we construct an unconstrained auxiliary function, which is maximized iteratively using a local search and is updated whenever a better maximizer is found. By increasing the value of a parameter in the auxiliary function, the maximization of the auxiliary function can escape from previously converged local maximizers. To evaluate the performance of the dynamic convexized method, extensive experiments were carried out on realistic test sets from the literature. Computational results and comparisons show that the proposed algorithm improved the best known solutions on a number of benchmark instances.     

An approachto the machine layout problem in a cellular manufacturing environment

The model of the machine layout problem MLP in a cellular manufacturing environment attains additional dimensions as it should satisfy the qualitative interconnections between the machines and the location restrictions of an existing factory environment. A new MLP model based on merging pre-emptive goal programming and simulated annealing has been developed for machine layout in cells. This model seeks to find feasible solutions by addressing practical issues of implementation as well as reducing the total travel distances for parts between machines. The new model can also be applied to facility layout problems FLP . The computational work is demonstrated by applying the model to problems of both quantitative and qualitative types, and has produced encouraging results. This model is particularly attractive for layout problems with realistic goals and constraints. To show the performance of the model in handling real-world problems, a practical example has been introduced and solved using the proposed model.     

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.     

An efficient tabu search algorithm for the single- machine mean tardiness problem

In this paper, an efficient tabu search algorithm is prepared for solving the single-machine mean tardiness problem. The proposed implementation of the tabu search approach suggests simple techniques for generating neighbourhoods of a given sequence and a combined scheme for intensification and diversification. The tabu search method is shown to produce results very close to the optimal solution using randomly generated problems with varying degrees of difficulty.     

Exact and approximate algorithms for the loop layout problem

Control parameters, such as order frequency, safety stock and safety time, are important tools to improve the logistic performance in material planning. In practice, the adjustment of control parameters appears to be very difficult. One of the reasons is the lack of relevant tactical control information: a simple, periodical and per-commodity integrated feedback of performance and process information often is not available to the logistic operator. Therefore, the material planner is offered a fairly limited overview and insight of the processes to be controlled. This problem has been investigated in several plants in the Netherlands. A solution to this problem is first to measure the performance, the frequency of process disturbances and the effect of the parameters on performance for all commodities involved. And second, to integrate this information and provide feedback to the responsible material planner. In this article a design for decision support is presented to integrate and give feedback of relevant tactical control information. Prototype information systems are now being tested in practice and in the laboratory. The expectation is that this type of decision support will help the operator to make more systematic and effective diagnoses.     

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.     

Flexible multi-manned assembly line balancing problem: Model,heuristic procedure,and lower bounds for line length minimization

Assembly lines dedicated to the production of large products often allow multiple workers to perform tasks simultaneously on the product. Previous works on such multi-manned lines define workstations with fixed, discrete, and restrictive frontiers, despite commonly considering continuous paced line control. This paper proposes flexible station frontiers for multi-manned lines and shows that such innovation allows significantly shorter line lengths. A new Mixed Integer Linear Programming model and a novel model-based heuristic procedure are presented to describe and optimize lines. Algorithmic lower bounds are also introduced for the problem. The formulation was compared to a literature benchmark of regular multi-manned solutions. These experiments showed that flexible multi-manned formulations can lead to line length reductions of up to 42%. Such reductions were obtained for most instances (81 out of 88), with an average value of 18%. The relationship between cycle time and minimal line length is also analyzed, demonstrating that efficient solution sets can be continuous or discrete, depending on the instance.     

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.     

Hybrid heuristic for design of cellular manufacturing systems

Cell design in Cellular Manufacturing Systems (CMS) assumes significance due to the incremental nature of implementation. In this study a hybrid heuristic has been developed considering incremental aspect of implementation. The heuristic identifies complete cells (if they exist), otherwise forms a CMS with combination of regular cells and a remainder cell which caters to the needs of exceptional parts/operations. The heuristic has been tested with the standard problems in the literature. It is found that the proposed heuristic produces superior solutions in 62.22% cases and the same solutions in the remaining cases. Further, statistical testing has been conducted and found that the performance of the proposed heuristic is significantly better than the existing methods.