OPTIMAL LOGISTICS FOR MULTIPLE JEEPS

We consider variations of the classical jeep problems： the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.     

Optimal logistics for multiple jeeps

We consider variations of the classical jeep problems: the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.     

A turning restriction design problem in urban road networks

Turning restriction is one of the commonest traffic management techniques and an effective low cost traffic improvement strategy in urban road networks. However, the literature has not paid much attention to the turning restriction design problem (TRDP), which aims to determine a set of intersections where turning restrictions should be implemented. In this paper, a bi-level programming model is proposed to formulate the TRDP. The upper level problem is to minimize the total travel cost from the viewpoint of traffic managers, and the lower level problem is to depict travelers’ route choice behavior based on stochastic user equilibrium (SUE) theory. We propose a branch and bound method (BBM), based on the sensitivity analysis algorithm (SAA), to find the optimal turning restriction strategy. A branch strategy and a bound strategy are applied to accelerate the solution process of the TRDP. The computational experiments give promising results, showing that the optimal turning restriction strategy can obviously reduce system congestion and are robust to the variations of both the dispersion parameter of the SUE problem and the level of demand.     

The Optimal Control of a Train

We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.     

一类多对多物流系统的运送频率选择优化问题研究

多供应商多客户物流系统的周期运送库存决策问题是一个非常复杂的问题,但它在供应链管理中又极其重要.本文主要考虑一个由多个供应商、一个联运中心和多个客户组成的三级物流系统的运送频率选择优化问题.假定两级库存均采用周期补货策略,且补货周期满足二次幂(POT)策略,每个客户处的产品需求为确定性需求.假设给定一套可行频率的情况下,选择使整个系统总的长期平均成本最小化的联运中心的补货策略和联运中心到各客户的配送策略.分为单频率配送和多频率配送两种情况分别建立了数学模型,并设计了相应的近似算法——基于支配性的邻域搜索启发式算法和基于饱和性的邻域搜索启发式算法.计算试验显示,本文所设计的近似算法对于求解多对多配送这样的大型组合优化问题是有效的.     

Benchmark and mean-variance problems for insurers

We consider the classical Cramér-Lundberg model with dynamic proportional reinsurance and solve the problem of finding the optimal reinsurance strategy which minimizes the expected quadratic distance of the risk reserve to a given benchmark. This result is extended to a mean-variance problem.     

On a pursuit-evasion problem under a linear change of the pursuer resource

We study a pursuit-evasion problem in the case when an integral constraint is imposed on the pursuer control class which is a generalization of integral as well as geometric constraints and only a geometric constraint is imposed on the evader control class. We prove the theorem of alternative. The optimal pursuit problem is solved by a generalized parallel pursuit strategy, and lower bounds for the distance between the pursuer and the evader are established in the pursuit problem.     

Improving constants of strong convexity in linear stochastic programming

We derive formulas for constants of strong convexity (CSCs) of expectation functions encountered in two-stage stochastic programs with linear recourse. One of them yields a CSC as the optimal value of a certain quadratically constrained quadratic program, another one in terms of the thickness of the feasibility polytope of the dual problem associated to the recourse problem. CSCs appear in Hoelder-type estimates relating the distance of optimal solution sets of stochastic programs to a suitable distance of underlying probability distributions.     

Feature extraction algorithms for constrained global optimization II. Batch process scheduling application

The feature extraction algorithms developed in part I of this series are applied to solve nonconvex mixed integer nonlinear programming problems which arise in the optimal scheduling of multipurpose chemical plants. A general formulation of the multipurpose plant scheduling problem is developed which considers the allocation of plant equipment and secondary, limited resources to recipe operations so as to satisfy given production requirements while minimizing cost. Results obtained with a test example involving 135 binary and 922 continuous variables show that the successive refinement strategy is effective in identifying dominant regions of the solution space. Furthermore it is shown that multiple moment based characterization methods are superior to the interval analysis method reported in the literature. Trials using a second, larger nonlinear test problem involving 356 binary and 2402 continuous variables demonstrate that the focused successive refinement strategy is more efficient than a constant resolution strategy which employs genetic algorithm constructions. Although the conventional genetic algorithm can be significantly improved by introducing a heuristic mutation strategy which increases the likelihood of constant feasibility, the successive refinement strategy remains dominant. These studies demonstrate that the feature extraction strategy employing successive refinements and relatively low order moment based region characterization methods, offers an effective approach to solving an important class of large scale MINLP problems with multiple local optima.     

On the adjustment problem for linear programs

We propose a generalization of the inverse problem which we will call the adjustment problem. For an optimization problem with linear objective function and its restriction defined by a given subset of feasible solutions, the adjustment problem consists in finding the least costly perturbations of the original objective function coefficients, which guarantee that an optimal solution of the perturbed problem is also feasible for the considered restriction. We describe a method of solving the adjustment problem for continuous linear programming problems when variables in the restriction are required to be binary.     

A bi-objective turning restriction design problem in urban road networks

This paper introduces a bi-objective turning restriction design problem (BOTRDP), which aims to simultaneously improve network traffic efficiency and reduce environmental pollution by implementing turning restrictions at selected intersections. A bi-level programming model is proposed to formulate the BOTRDP. The upper level problem aims to minimize both the total system travel time (TSTT) and the cost of total vehicle emissions (CTVE) from the viewpoint of traffic managers, and the lower level problem depicts travelers’ route choice behavior based on stochastic user equilibrium (SUE) theory. The modified artificial bee colony (ABC) heuristic is developed to find Pareto optimal turning restriction strategies. Different from the traditional ABC heuristic, crossover operators are captured to enhance the performance of the heuristic. The computational experiments show that incorporating crossover operators into the ABC heuristic can indeed improve its performance and that the proposed heuristic significantly outperforms the non-dominated sorting genetic algorithm (NSGA) even if different operators are randomly chosen and used in the NSGA as in our proposed heuristic. The results also illustrate that a Pareto optimal turning restriction strategy can obviously reduce the TSTT and the CTVE when compared with those without implementing the strategy, and that the number of Pareto optimal turning restriction designs is smaller when the network is more congested but greater network efficiency and air quality improvement can be achieved. The results also demonstrate that traffic information provision does have an impact on the number of Pareto optimal turning restriction designs. These results should have important implications on traffic management.     

Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints

In this paper, we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel; the resulting problem is called the multiple traveling repairmen problem with distance constraints (MTRPD). In the MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once. The objective is to minimize the total waiting time of all customers after the vehicles leave the depot. To optimally solve the MTRPD, we propose a new exact branch-and-price-and-cut algorithm, where the column generation pricing subproblem is a resource-constrained elementary shortest-path problem with cumulative costs. An ad hoc label-setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem. Computational results show the effectiveness of the proposed method. The optimal solutions to 179 out of 180 test instances are reported in this paper. Our computational results serve as benchmarks for future researchers on the problem.     

Quickest search over Brownian channels

In this paper we resolve an open problem proposed by Lai, Vincent Poor, Xin, and Georgiadis [Quickest search over multiple sequences. IEEE Trans. Inf. Theory 57(8) (2011), pp. 5375–5386]. Consider a sequence of Brownian motions with unknown drift equal to one or zero, which may be observed one at a time. We give a procedure for finding, as quickly as possible, a process which is a Brownian motion with non-zero drift. This original quickest search problem, in which the filtration itself is dependent on the observation strategy, is reduced to a single filtration impulse control and optimal stopping problem, which is in turn reduced to an optimal stopping problem for a reflected diffusion, which can be explicitly solved.     

Effectiveness-based Voronoi partition: a new tool for solving a class of location optimization problems

In this article we provide a framework for optimal placement or deployment of facilities in a region of interest. We present a generalization of Voronoi partition, where functions modeling the effectiveness of facilities are used in the place of the usual distance measure used in the standard Voronoi partition and its variations. We illustrate the usefulness of the generalization in designing strategies for optimal deployment of multiple vehicles equipped with sensors, optimal placement of base stations in a cellular network design problem, and locational optimization of power plants.     

Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal dali alignments for the very first time.     

考虑两个风险情形的项目风险应对策略选择方法

项目风险应对是风险管理的一个值得关注的重要研究问题。本文是在文献[11]研究单一风险情形的项目风险应对策略选择方法的基础上,进一步给出了考虑两个风险情形的项目风险应对策略选择方法。在本文中,首先给出了项目风险应对策略的相关概念及数学描述;然后,考虑到针对一个风险所采取的应对策略会对另一个风险发生作用,给出了项目风险应对策略选择问题的分析,并在此基础上,构建了项目风险应对策略选择的优化模型,进而通过求解模型可进行选择最优风险应对策略;最后,通过一个实例分析说明了本文给出方法的可行性和有效性。     

Optimal parking of idle elevators under myopic and state-dependent policies

In this paper we discuss the problem of optimally parking single and multiple idle elevators under light-traffic conditions. The problem is analyzed from the point of view of the elevator owner whose objective is to minimize the expected total cost of parking and dispatching the elevator (which includes the cost incurred for waiting passengers). We first consider the case of a single elevator and analyze a (commonly used but suboptimal) state-independent myopic policy that always positions the idle elevator at the same floor. Building on the results obtained for the myopic policy, we then show that the optimal non-myopic (state-dependent) policy calls for dispatching the idle elevator to the state-dependent median of a weight distribution. Next, we consider the more difficult case of two elevators and develop an expression for the expected dispatching distance function. We show that the objective function for the myopic policy is non-convex. The non-myopic policy is found to be dependent on the state of the two idle elevators. We compute the optimal state-dependent policy for two elevators using the results developed for the myopic policy. Next, we examine the case of multiple elevators and provide a general recursive formula to find the expected dispatching distance functions. Finally, we generalize the previous models by incorporating a fixed cost for parking the idle elevators that results in a two-sided optimal policy with different regions. Every policy that we introduce and analyze is illustrated by an example. The paper concludes with a short summary and suggestions for future research.     

Strategic oscillation for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to different tasks when their ability to cooperate may affect the results. Strategic oscillation (SO) is a search strategy that operates in relation to a critical boundary associated with important solution features (such as feasibility). Originally proposed in the context of tabu search, it has become widely applied as an efficient memory-based methodology. We apply strategic oscillation to the quadratic multiple knapsack problem, disclosing that SO effectively exploits domain-specific knowledge, and obtains solutions of particularly high quality compared to those obtained by current state-of-the-art algorithms.     

A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements

We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer??s demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm for the case in which a customer??s demand may be split among an arbitrary number of supply facilities. The Benders subproblem takes the form of an uncapacitated, nonlinear transportation problem, a relevant and interesting problem in its own right. We provide analysis and insight on this subproblem, which allows us to devise a hybrid algorithm based on an outer approximation of this subproblem to accelerate the generalized Benders decomposition algorithm. We also provide computational results for the general model that permit characterizing the costs that arise from a single-sourcing strategy.     

Robust optimal strategies in Markov decision problems

An optimal strategy in a Markov decision problem is robust if it is optimal in every decision problem (not necessarily stationary) that is close to the original problem. We prove that when the state and action spaces are finite, an optimal strategy is robust if and only if it is the unique optimal strategy.