Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019     

Column generation for stochastic green telecommunication network planning with switchable base stations

We present the green telecommunication network planning problem with switchable base stations, where the location and configuration of the base stations are optimized, while taking into account uncertainty and variability of demand. The problem is formulated as a two‐stage stochastic program under demand uncertainty with integers in both stages. Since solving the presented problem is computationally challenging, we develop the corresponding Dantzig‐Wolfe reformulation and propose a solution approach based on column generation. Comprehensive computational results are provided for instances of varying characteristics. The results show that the joint location and dynamic switching of base stations leads to significant savings in terms of energy cost. Up to 30% reduction in power consumption cost is achieved while still serving all users. In certain cases, allowing dynamic configurations leads to more installed base stations and higher user coverage, while having lower total energy consumption. The Dantzig‐Wolfe reformulation provides solutions with a tight LP‐gap eliminating the need for a full branch‐and‐price scheme. Furthermore, the proposed column generation solution approach is computationally efficient and outperforms CPLEX on the majority of the tested instances. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 351–366, 2016     

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Algorithms for solving the conditional covering problem on paths

Consider the conditional covering problem on an undirected graph, where each node represents a site that must be covered by a facility, and facilities may only be established at these nodes. Each facility can cover all sites that lie within some common covering radius, except the site at which it is located. Although this problem is difficult to solve on general graphs, there exist special structures on which the problem is easily solvable. In this paper, we consider the special case in which the graph is a simple path. For the case in which facility location costs do not vary based on the site, we derive characteristics of the problem that lead to a linear‐time shortest path algorithm for solving the problem. When the facility location costs vary according to the site, we provide a more complex, but still polynomial‐time, dynamic programming algorithm to find the optimal solution. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

The parallel machine replacement problem consists of finding a minimum cost replacement policy for a finite population of economically interdependent machines. In this paper, we formulate a stochastic version of the problem and analyze the structure of optimal policies under general classes of replacement cost functions. We prove that for problems with arbitrary cost functions, there can be optimal policies where a machine is replaced only if all machines in worse states are replaced (Worse Cluster Replacement Rule). We then show that, for problems with replacement cost functions exhibiting nonincreasing marginal costs, there are optimal policies such that, in any stage, machines in the same state are either all kept or all replaced (No‐Splitting Rule). We also present an example that shows that economies of scale in replacement costs do not guarantee optimal policies that satisfy the No‐Splitting Rule. These results lead to the fundamental insight that replacement decisions are driven by marginal costs, and not by economies of scale as suggested in the literature. Finally, we describe how the optimal policy structure, i.e., the No‐Splitting and Worse Cluster Replacement Rules, can be used to reduce the computational effort required to obtain optimal replacement policies. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

信息不完备群组决策问题的ANP方法

群组决策是一类重要的决策问题,信息不完备的群组决策问题,因为判断矩阵有缺损,传统的AHP不能求解.文中将评价图引入信息不完备的群组决策问题,在此基础上提出用二次规划问题解决在这种情况下的权重确定问题,最后通过ANP的超矩阵得到总排序结果.经过实例检验,证明了ANP方法的正确性与可行性.     

基于DEA系统下的武器装备采办理论及运用

数据包络分析DEA(data envelopment analysis)系统主要是针对武器装备性能的论证和武器装备采办提供相应的分析工具。介绍了该系统组成及DEA模型算法的基本思路,分析了武器装备采购费用的相对有效性,并简要阐述了该系统在军事领域的应用前景。     

42－160柴油机离合器换向拨叉叉头优化设计的光弹验证

本文用光弹性实验方法验证了有限元法对４２—１６０柴油机离合器换向拨叉优化设计的结果。实验证明,有限元优化设计是正确、可靠的,效果是非常好的。