A nonlinear approach to the multiorigin,multidestination fleet deployment problem

The problem of minimal-cost operation of a fleet of ships carrying a specific amount of bulk cargo from several origin ports to several destination ports during a specified time interval is examined. The fuel oil cost, a major component of the total operating cost, is realistically modeled as a nonlinear function of the vessels' operating speeds. Introduction of both full load and ballast speeds as independent variables results in a nonlinear optimization problem in which the vessels' allocation to the available routes and the optimal speed selection problem are coupled. Within the framework of our model, each vessel of the fleet may load at any origin, unload at a destination and return to the same origin. The solution method developed utilizes specific features of the above fleet deployment model, and may reduce substantially the dimensionality of the problem. Under certain conditions, decoupling of the speed selection from the vessel allocation problem can be achieved, and linear programming can be used to obtain an optimal solution. In the general case, a projected Lagrangian method appears to be more appropriate for the problem under consideration.     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

The two-machine permutation flow shop with state-dependent processing times

If the processing time of each job in a flow shop also depends on the time spent prior to processing, then the choice of a sequence influences processing times. This nonstandard scheduling problem is studied here for the minimum makespan schedule in a flow shop with two machines. The problem is NP-hard in the strong sense and already contains the main features of the general case [10]. Restricting to the case of permutation schedules, we first determine the optimal release times of the jobs for a given sequence. Permutation schedules are evaluated for this optimal policy, and the scheduling problem is solved using branch-and-bound techniques. We also show the surprising result that the optimal schedule may not be a permutation schedule. Numerical results on randomly generated data are provided for permutation schedules. Our numerical results confirm our preliminary study [10] that fairly good approximate solutions can efficiently be obtained in the case of limited computing time using the heuristics due to Gilmore and Gomory [7]. © 1993 John Wiley & Sons, Inc.     

Primal dual algorithms for the vehicle refueling problem

Mehrez, Stern, and Ronen have defined a vehicle refueling problem in which a fleet of vehicles travels on a round-trip, self-contained mission from a common origin, with the objective of maximizing the operational range of the fleet. They have defined a “pure refueling chain” strategy for transferring fuel between vehicles in the fleet, and have solved the problem in the special cases when all vehicles have the same fuel capacity or consumption rate. In this article we present algorithms for the general case, where vehicles have different capacities and consumption rates. Our approach is based on a new primal dual formulation of the problem. The exact algorithm was effective to find the optimal solution for a fleet size n ⩽13. For larger fleets, we present an approximation version of it, which very quickly found a solution within 1% of the maximum possible range for arbitrarily large (up to n = 200) fleets. We also show that a small number of the best vehicles can always reach almost the same range as a large fleet. © 1992 John Wiley & Sons, Inc.     

直接藕合多种语言编程模块的MTS的设计与实现

以通用菜单工具作为应用软件系统的用户界面、多种语言编程模块的藕合接口已成为一种趋势。本文提出一种可在操作系统和foxBASE环境下组合(或嵌入)运行的、支持DBMS授权扩充机制、实现多种语言混合编程模块直接藕合的通用菜单工具(MTS)。同时,又对MTS中的菜单对象、授权,菜单文件的数据结构、菜单驱动(维护)模块设计和基于批处理文件的模块藕合方法进行了讨论。     

Interval estimation of a global optimum for large combinatorial problems

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.     

面向武器装备体系组合规划的集成决策优化框架

针对当前武器装备体系组合规划存在选择空间规模大、决策目标数量多等问题,提出一种集成决策优化框架,用于组合选择和规划武器装备的发展型号、时间和数量。首先对武器装备体系组合规划问题的NP-Hard和高维多目标性质进行定量化分析和公式化描述;然后采用目标规划方法将该问题构建为双目标优化模型;再基于NSGA-II多目标演化计算方法,开发面向本问题的优化算法,求得该模型的Pareto解集合;最后通过TOPSIS方法,从Pareto解集合中求取符合决策者偏好的满意解。通过某侦察预警监视体系发展规划示例,验证了当给定经验数据和决策者偏好信息后,该框架可获得符合要求的武器装备体系组合规划方案,能够支撑武器装备体系发展论证和规划。     

Vehicle fleet refueling strategies to maximize operational range

The focus of this research is on self-contained missions requiring round-trip vehicle travel from a common origin. For a single vehicle the maximal distance that can be reached without refueling is defined as its operational range. Operational range is a function of a vehicle's fuel capacity and fuel consumption characteristics. In order to increase a vehicle's range beyond its operational range replenishment from a secondary fuel source is necessary. In this article, the problem of maximizing the range of any single vehicle from a fleet of n vehicles is investigated. This is done for four types of fleet configurations: (1) identical vehicles, (2) vehicles with identical fuel consumption rates but different fuel capacities, (3) vehicles which have the same fuel capacity but different fuel consumption rates, and (4) vehicles with both different fuel capacities and different consumption rates. For each of the first three configurations the optimal refueling policy that provides the maximal range is determined for a sequential refueling chain strategy. In such a strategy the last vehicle to be refueled is the next vehicle to transfer its fuel. Several mathematical programming formulations are given and their solutions determined in closed form. One of the major conclusions is that for an identical fleet the range of the farthest vehicle can be increased by at most 50% more than the operational range of a single vehicle. Moreover, this limit is reached very quickly with small values of n. The performance of the identical fleet configuration is further investigated for a refueling strategy involving a multiple-transfer refueling chain, stochastic vehicle failures, finite refueling times, and prepositioned fleets. No simple refueling ordering rules were found for the most general case (configuration 4). In addition, the case of vehicles with different fuel capacities is investigated under a budget constraint. The analysis provides several benchmarks or bounds for which more realistic structures may be compared. Some of the more complex structures left for future study are described.     

求解不确定型车辆路径问题的弱鲁棒优化方法

为降低鲁棒优化模型最优解的保守性,以最小化违约车辆数和总惩罚成本为目标,建立针对旅行时间不确定的开放式车辆路径问题的弱鲁棒优化模型。对于不确定数据集的每个取值,该模型的最优解可以使其目标函数值始终不超过某数值,进而改善最优解的保守性。为提高启发式算法发现最优解的概率,提出一种自设计遗传算法对模型进行求解,其主要思想是利用粒子群算法搜索出可使遗传算法预期产生最好解的算法要素,并将其进行组合,从而产生新的遗传算法。采用新产生的遗传算法对模型继续求解,输出最好解。计算结果表明:与以往的鲁棒优化方法相比,弱鲁棒优化方法的最优解的保守性显著降低。     

On the treatment of force-level constraints in times-equential combat problems

The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.     

An analytical evaluation of optimal solution value estimation procedures

The estimation of optimal solution values for large-scale optimization problems is studied. Optimal solution value estimators provide information about the deviation between the optimal solution and the heuristic solution. Some estimation techniques combine heuristic solutions with randomly generated solutions. In particular, we examine a class of jacknife-based estimators which incorporate any heuristic solution value with the two best randomly generated solution values. The primary contribution of this article is that we provide a framework to analytically evaluate a class of optimal solution value estimators. We present closed-form results on the relationship of heuristic performance, sample size, and the estimation errors for the case where the feasible solutions are uniformly distributed. In addition, we show how to compute the estimation errors for distributions other than uniform given a specific sample size. We use a triangular and an exponential distribution as examples of other distributions. A second major contribution of this article is that, to a large extent, our analytical results confirm previous computational results. In particular, the best estimator depends on how good the heuristic is, but seems to be independent of the underlying distribution of solution values. Furthermore, there is essentially an inverse relationship between the heuristic performance and the performance of any estimator. © 1994 John Wiley & Sons, Inc.     

Optimal design of accelerated life testing plans for periodical replacement with penalty

Accelerated life testing (ALT), enhanced by optimal test plans, has been widely accepted in practice as a quick approach for estimating the reliability of a product. From the estimation result, preventive maintenance schedules can be determined to ensure the performance of the product under its normal operating conditions. By default, maintenance decision‐making is regarded as the last and least rewarding step. However, sometimes the maintenance schedules, such as preventive maintenance intervals, are predetermined due to customer concerns and/or by various mandatory regulations and rules. Under such circumstances, how to accurately estimate the expenditure (e.g., on maintenance or spare parts management) associated with these maintenance requirements becomes an important issue. A viable solution is to incorporate the maintenance requirements into ALT plans. This paper provides an approach for the optimal design of ALT plans oriented by a mandatory periodical replacement schedule subject to a discounted penalty. The objective is to improve the estimation accuracy of the economic impact of this maintenance requirement. A numerical experiment is provided to demonstrate the approach in practical use. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

蒙特卡洛优化法在机组组合问题中的应用

机组组合(UC)是电力系统经济运行的重要内容之一。根据UC约束特点将机组组合问题分解为单机多时段和多机单时段问题。基于蒙特卡洛(MC)优化法原理,解决单机多时段的启停问题及最后过滤比较找出最优可行解;利用运行费用可导性,解决了爬坡约束并得出多机单时段下的最优解。最后在Madab 6.1下通过算例验证了该方法的可行性。     

海上编队雷达网优化部署系统的设计与实现

建立海上编队雷达网优化部署系统模型,包括实体模型和认知模型。仿真海上编队雷达网在无威胁条件下的优化部署和面临干扰和超低空突防威胁时的对抗过程,经过海上编队雷达网优化部署认知模型的解算,指挥舰队编队成员进行机动部署,编队成员通过重新机动,使编队雷达网获得较好的探测性能。仿真结果表明所建立模型的可行性和正确性。对于在未来海战场复杂电磁环境下,更好地发挥编队雷达网探测、预警能力具有重要意义。     

Generating Pareto‐optimal boundary points in multiparty negotiations using constraint proposal method

In this paper a constraint proposal method is developed for computing Pareto‐optimal solutions in multiparty negotiations over continuous issues. Constraint proposal methods have been previously studied in a case where the decision set is unconstrained. Here we extend the method to situations with a constrained decision set. In the method the computation of the Pareto‐optimal solutions is decentralized so that the DMs do not have to know each others' value functions. During the procedure they have to indicate their optimal solutions on different sets of linear constraints. When the optimal solutions coincide, the common optimum is a candidate for a Pareto‐optimal point. The constraint proposal method can be used to generate either one Pareto‐optimal solution dominating the status quo solution or several Pareto‐optimal solutions. In latter case a distributive negotiation among the efficient points can be carried out afterwards. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 210–225, 2001     

邻域加强的并行子空间优化过程

针对基于响应面的并行子空间优化(CSSo-RS)过程的不足,提出了基于邻域加强的改进CSSO-RS优化过程.其主要思路是在子空间优化后,在得到的最优解附近进行全部变量的优化,以更好地协调系统级优化与子空间优化.用经典测试函数及通用航空飞机参数优化问题对该算法进行测试,测试结果表明该算法使CSSO-RS优化效率得到较大的...     

An optimal critical level policy for inventory systems with two demand classes

Traditional inventory systems treat all demands of a given item equally. This approach is optimal if the penalty costs of all customers are the same, but it is not optimal if the penalty costs are different for different customer classes. Then, demands of customers with high penalty costs must be filled before demands of customers with low penalty costs. A commonly used inventory policy for dealing with demands with different penalty costs is the critical level inventory policy. Under this policy demands with low penalty costs are filled as long as inventory is above a certain critical level. If the inventory reaches the critical level, only demands with high penalty costs are filled and demands with low penalty costs are backordered. In this article, we consider a critical level policy for a periodic review inventory system with two demand classes. Because traditional approaches cannot be used to find the optimal parameters of the policy, we use a multidimensional Markov chain to model the inventory system. We use a sample path approach to prove several properties of this inventory system. Although the cost function is not convex, we can build on these properties to develop an optimization approach that finds the optimal solution. We also present some numerical results. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Discrete stochastic optimization using variants of the stochastic ruler method

We present two random search methods for solving discrete stochastic optimization problems. Both of these methods are variants of the stochastic ruler algorithm. They differ from our earlier modification of the stochastic ruler algorithm in that they use different approaches for estimating the optimal solution. Our new methods are guaranteed to converge almost surely to the set of global optimal solutions under mild conditions. We discuss under what conditions these new methods are expected to converge faster than the modified stochastic ruler algorithm. We also discuss how these methods can be used for solving discrete optimization problems when the values of the objective function are estimated using either transient or steady‐state simulation. Finally, we present numerical results that compare the performance of our new methods with that of the modified stochastic ruler algorithm when applied to solve buffer allocation problems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure

Quantity discounts are considered in the context of the single-period inventory model known as “the newsboy problem.” It is argued that the behavioral implications of the all-units discount schedule are more complex and interesting than the literature has suggested. Consideration of this behavior and the use of marginal analysis lead to a new method for solving this problem that is both conceptually simpler and more efficient than the traditional approach. This marginal-cost solution procedure is described graphically, an algorithm is presented, and an example is used to demonstrate that this solution procedure can be extended easily to handle complex discount schedules, such as some combined (simultaneously applied) purchasing and transportation cost discount schedules.     

Multiobjective flow-shop scheduling

Previous research on the scheduling of multimachine systems has generally focused on the optimization of individual performance measures. This article considers the sequencing of jobs through a multimachine flow shop, where the quality of the resulting schedule is evaluated according to the associated levels of two scheduling criteria, schedule makespan (C_max) and maximum job tardiness (T_max). We present constructive procedures that quantify the trade-off between C_max and T_max. The significance of this trade-off is that the optimal solution for any preference function involving only C_max and T_max must be contained among the set of efficient schedules that comprise the trade-off curve. For the special case of two-machine flow shops, we present an algorithm that identifies the exact set of efficient schedules. Heruistic procedures for approximating the efficient set are also provided for problems involving many jobs or larger flow shops. Computational results are reported for the procedures which indicate that both the number of efficient schedules and the error incurred by heuristically approximating the efficient set are quite small.