A multi-stop routing problem

The problem of determining the sequence of stops and the amount of load to carry in each segment route, named the Multi-Stop Routing Problem (MSRP) is addressed. A 0/1 mixed integer linear program and formulation refinements which facilitate the solution process are presented. Since the constraint set of the MSRP includes 0/1 mixed rows, valid inequalities for this type of regions are presented. Then these results are applied to the constraint set of the routing problem, presenting additional valid inequalities. In addition, polynomial separation algorithms associated with the valid inequalities are given, computational results are also included.     

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt^*, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.     

Neural network control of seat vibrations of a non-linear full vehicle model using PMSM

In this paper, the dynamic behaviour of a non-linear eight degrees of freedom vehicle model having active suspensions and passenger seat using Permanent Magnet Synchronous Motor (PMSM) controlled by a Neural Network (NN) controller is examined. A robust NN structure is established by using principle design data from the Matlab diagrams of system functions. In the NN structure, Fast Back-Propagation Algorithm (FBA) is employed. The user inputs a set of 16 variables while the output from the NN consists of f₁–f₁₆ non-linear functions. Further, the PMSM controller is also determined using the same NN structure. Various tests of the NN structure demonstrated that the model is able to give highly sensitive outputs for vibration condition, even using a more restricted input data set. The non-linearity occurs due to dry friction on the dampers. The vehicle body and the passenger seat using PMSM are fully controlled at the same time. The time responses of the non-linear vehicle model due to road disturbance and the frequency responses are obtained. Finally, uncontrolled and controlled cases are compared. It is seen that seat vibrations of a non-linear full vehicle model are controlled by a NN-based system with almost zero error between desired and achieved outputs.     

On estimating the distribution of optimal traveling salesman tour lengths using heuristics

The traveling salesman problem is an important combinatorial optimization problem due to its significance in academic research and its real world applications. The problem has been extensively studied and much is known about its polyhedral structure and algorithms for exact and heuristic solutions. While most work is concentrated on solving the deterministic version of the problem, there also has been some research on the stochastic TSP. Research on the stochastic TSP has concentrated on asymptotic properties and estimation of the TSP-constant. Not much is, however, known about the probability distribution of the optimal tour length. In this paper, we present some empirical results based on Monte Carlo simulations for the symmetric Euclidean and Rectilinear TSPs. We derive regression equations for predicting the first four moments of the distribution of estimated TSP tour lengths using heuristics. We then show that a Beta distribution gives excellent fits for small to moderate sized TSP problems. We derive regression equations for predicting the parameters of the Beta distribution. Finally we predict the TSP constant using two alternative approaches.     

完全域上矩阵多项式方程的可解性

本文利用一般域上的λ-矩阵理论，研究了矩阵多项式方程的可解性，证明了完全域上矩阵多项式方程有解的充要条件，这些条件同时提供了解此类矩阵方程的方法。     

A branch-and-cut algorithm for the Undirected Rural Postman Problem

The well-known Undirected Rural Postman Problem is considered and a binary linear problem using new dominance relations is presented. Polyhedral properties are investigated and a branch-and-cut algorithm is developed. Extensive computational results indicate that the algorithm is capable of solving much larger instances than previously reported. Received: December 1, 1997 / Accepted: October 13, 1999?Published online January 27, 2000     

圆型限制性三体问题中双恒星系统的存在性

在圆型限制性三体问题的研究中,研究较多的是在其中一体附近的运动。本文研究远离两个大质量恒星的行星的运行情况,在此范围内,使用KAM理论研究大振幅轨道的存在性,说明了星系中双恒星系统的存在性,而这一现象已被天文学家所观察到。     

A necessary and sufficient condition to a pareto optimal without optimizing the weighting criterion

The easiest thecnique to reduce the classical multiple criteria decision problem into a reasonable single criterion decision problem is the weighting method. Po-Lung Yu (1985) gives a well known necessary condition fory ⁰ to be a Pareto optimal, namelyy ⁰ maximizes λ^ty overY, for some λ ∈ℝ ^p, such that λ_i≥0 for alli and some λ_j>0. In this brief note we generalize the necessary condition of Po-Lung Yu.     

The steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.     

线性方程组Ax=b的反问题的一般解

给出了线性方程组Ax=b的反问题在n阶矩阵类中解的一般形式．