多目标、多约束工程系统可靠度的一种求解方法

为进一步研究工程实际问题中，当系统受多方面限制的情况下，提高系统多方面功能的能力，本研究了系统多目标、多约束可靠度的一种求解的方法，其思想是：首先将系统多目标可靠度的数学模型转化为单目标的数学模型，然后由单目标问题的求解来实现多目标问题的解。     

On a multiple credit rating migration model with stochastic interest rate

In this paper, we explore a pricing model for corporate bond accompanied with multiple credit rating migration risk and stochastic interest rate. The bond price volatility strongly depends on potentially multiple credit rating migration and stochastic change of interest rate. A free boundary problem of partial differential equation is presented, which is the equivalent transformation of the pricing model. The existence, uniqueness, and regularity for the free boundary problem are established to guarantee the rationality of the pricing model. Due to the stochastic change of interest rate, the discontinuous coefficient in the free boundary problem depends explicitly on the time variable but is convergent as time tends to infinity. Accordingly, an auxiliary free boundary problem is constructed, whose coefficient is the convergent limit of the coefficient in the original free boundary problem. With some constraint on the risk discount rate satisfied, we prove that a unique traveling wave exists in the auxiliary free boundary problem. The inductive method is adopted to fit the multiplicity of credit rating. Then we show that the solution of the original free boundary problem converges to the traveling wave in the auxiliary free boundary problem. Returning to the pricing model with multiple credit rating migration and stochastic interest rate, we conclude that the bond price profile can be captured by a traveling wave pattern coupling with a guaranteed bond price with face value equal to one at the maturity.     

定量型多指标决策的层次分析法探讨

本文采用等级标度与层次分析综合的方法对定量型多指标决策问题进行了讨论，它既是层次分析法在定量型多指标决策中的合理推广，同时也为定量型多指标决策问题提供了一种行之有效的方法．     

Maximizing a concave function over the efficient or weakly-efficient set

An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.     

多时滞线性切换系统的H_∞控制

研究了连续的多时滞线性切换系统的H_∞控制问题,用Lyapunov函数和凸组合技术,给出了连续的多时滞切换系统满足H_∞性能指标的充分条件和切换律的设计方案,并且进一步讨论了离散的多时滞线性切换系统的H_∞控制问题.     

Continuity Properties of Optimal Multiple Stopping Value

This article is concerned with the optimal multiple stopping problem for discrete time finite stage stochastic processes. We study lower semicontinuity and continuity properties of optimal stopping values with respect to the topology of convergence in distribution. Also, we formulate the multiple stopping version of the prophet inequality for the optimal stopping problem and apply the lower semicontinuity property of optimal stopping values to the prophet inequality for the optimal multiple stopping problem.     

Upper and lower bounding procedures for the multiple knapsack assignment problem

We formulate the multiple knapsack assignment problem (MKAP) as an extension of the multiple knapsack problem (MKP), as well as of the assignment problem. Except for small instances, MKAP is hard to solve to optimality. We present a heuristic algorithm to solve this problem approximately but very quickly. We first discuss three approaches to evaluate its upper bound, and prove that these methods compute an identical upper bound. In this process, reference capacities are derived, which enables us to decompose the problem into mutually independent MKPs. These MKPs are solved euristically, and in total give an approximate solution to MKAP. Through numerical experiments, we evaluate the performance of our algorithm. Although the algorithm is weak for small instances, we find it prospective for large instances. Indeed, for instances with more than a few thousand items we usually obtain solutions with relative errors less than 0.1% within one CPU second.     

An Interactive Multiple Criteria Approach to Ranking Alternatives

In this paper we are concerned with ranking various orderings of a set of alternatives to a composite order as a multiple criteria problem. The orderings (called preference orderings) can be real preference orderings or any natural orderings. The objective is to find the most preferred order of the decision maker using the preference orderings as criteria.In principle, the problem can be formulated as a multiple objective linear programming problem using the model of Bowman and Colantoni and then solved with the interactive method proposed by Zionts and Wallenius. However, the fact that we are dealing with integer variables prohibits us from applying this approach as such. We discuss the problem formulation and propose a modified approach to that of Zionts and Wallenius for solving the problem.     

EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM

In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.     

Mapping DNA by stochastic relaxation

The multiple digest mapping problem arising in molecular biology can be stated roughly as follows. A linear or circular segment of DNA is cut at all occurrences of a specific short pattern by restriction enzymes. By using restriction enzymes singly and in combination it is required to construct a map showing the location of cleavage sites. In this paper we first consider the efficacy of a simulated annealing algorithm towards the solution to the multiple digest problem. Second, the double digest problem, the simplest version of the multiple digest problem with only two restriction enzymes used, is shown to admit an exponentially increasing number of solutions as a function of the length of the segment under a particular probability model. Next, the double digest problem is shown to lie in the class of NP complete problems which are conjectured to have no polynomial time solution. Last, the construction of circular maps is considered and the problem of measurement error is discussed.     

Criteria and dimension reduction of linear multiple criteria optimization problems

Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential) objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions. Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria. This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple objective optimization.     

Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

A metaheuristic based on a pool of routes for the vehicle routing problem with multiple trips and time windows

This paper studies the vehicle routing problem with multiple trips and time windows, in which vehicles are allowed to perform multiple trips during a scheduling period and each customer must be served within a given time interval. The problem is of particular importance for planning fleets of hired vehicles in common practices, such as e-grocery distributions, but this problem has received little attention in the literature. As a result of the multi-layered structure characteristic of the problem solution, we propose a pool-based metaheuristic in which various routes are first constructed to fill a pool, following which some of the routes are selected and combined to form vehicle working schedules. Finally, we conduct a series of experiments over a set of benchmark instances to evaluate and demonstrate the effectiveness of the proposed metaheuristic.     

灾后运输网络中的最短路修复合作博弈

在最短路修复合作博弈中,当灾后运输网络规模较大时,最优成本分摊问题难以直接求解。基于拉格朗日松弛理论,提出了一种最短路修复合作博弈成本分摊算法。该算法将最短路修复合作博弈分解为两个具有特殊结构的子博弈,进而利用两个子博弈的结构特性,可以{高效地}求解出二者的最优成本分摊,将这两个成本分摊相加,可以获得原博弈的一个近乎最优的稳定成本分摊。结果部分既包含运输网络的随机仿真,也包含玉树地震灾区的现实模拟,无论数据来源于仿真还是现实,该算法都能在短时间内为最短路修复合作博弈提供稳定的成本分摊方案。     

Fuzzy approaches for multiple objective linear fractional optimization

The problem of finding a solution to a multiple objective linear fractional program arises in several real world situations.In this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness.After representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program, techniques of fuzzy linear programming may be used to reach a satisfactory solution.It is shown that under reasonable restrictions, this solution is efficient (Pareto optimal) for the original problem. Numerical examples are also included for illustration.     

Strictly feasible solutions and strict complementarity in multiple objective linear optimization

Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established. Here, we use these results to prove some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are established. We show that primal-dual (weakly) efficient solutions satisfying strictly complementary conditions exist. Furthermore, we consider Isermann’s and Kolumban’s dual problems and establish conditions for the existence of strictly primal and dual feasible points. We show the existence of primal-dual feasible points satisfying strictly complementary conditions for Isermann’s dual problem. Also, we give an alternative proof to establish necessary conditions for weakly efficient solutions of multiple objective programs, assuming the Kuhn–Tucker (KT) constraint qualification. We also provide a new condition to ensure the KT constraint qualification.     

带多重选择的最短路问题:复杂性和算法

本文提出了带出重选择的是短路问题,建立了该问题的数学模型,利用背包问题的一个变形问题－带限制选择的背包问题,证明了该问题是ＮＰ－Ｃ的,最后利用动态规则给出了一个伪多项式算法,其时间复杂性Ｏ（Ｃｈｍｎ）,其中ｈ是最大的选择重数。     

An exact algorithm for the fixed-charge multiple knapsack problem

We formulate the fixed-charge multiple knapsack problem (FCMKP) as an extension of the multiple knapsack problem (MKP). The Lagrangian relaxation problem is easily solved, and together with a greedy heuristic we obtain a pair of upper and lower bounds quickly. We make use of these bounds in the pegging test to reduce the problem size. We also present a branch-and-bound (B&B) algorithm to solve FCMKP to optimality. This algorithm exploits the Lagrangian upper bound as well as the pegging result for pruning, and at each terminal subproblem solve MKP exactly by invoking MULKNAP code developed by Pisinger [Pisinger, D., 1999. An exact algorithm for large multiple knapsack problems. European Journal of Operational Research 114, 528–541]. As a result, we are able to solve almost all test problems with up to 32,000 items and 50 knapsacks within a few seconds on an ordinary computing environment, although the algorithm remains some weakness for small instances with relatively many knapsacks.     

Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm

Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we address the problem of finding all roots of a system of equations. Our method makes use of a biased random-key genetic algorithm (BRKGA). Given a nonlinear system, we construct a corresponding optimization problem, which we solve multiple times, making use of a BRKGA, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on seven nonlinear equations systems with multiple roots from the literature.