The Chinese postman problem is one of the fundamental problems in operations research. This paper reviews the development of the problem, starting from its inception to its current status.
We consider the higher-order tensor eigenvalue complementarity problem (TEiCP). Since finding the largest Pareto-eigenvalue of tensor is NP-hard in general, in this paper we focus on studying the estimation of the Pareto-eigenvalue. We also present some properties for Pareto-eigenvalues of Z-tensors and M-tensors.
In this paper, we propose a new QP-free infeasible method based on the solution of nonsmooth equations which are obtained by the multipliers and the piecewise linear relationship NCP function for the KKT first-order optimality conditions. We do not use a penalty function and a filter on line search. Locally, each iteration of this method can be viewed as a perturbation of the mixed Newton-quasi Newton iteration on both primal and dual variables for the solution of KKT optimality conditions. This method is implementable and globally convergent. Without the second order correction we prove that the method has superlinear convergence rate under some mild conditions.
We propose an optimization model and its corresponding parallel algorithm for optimized signal-planning. Based on a local enumeration method, the algorithm adds a virtual guiding penalty, which is derived from the traffic weight. This makes the algorithm has a global spatial and temporal optimized property. In the situation of saturated or over-saturated traffic status, this algorithm outperforms the traditional single-point intersection control method.
According to the international price of crude oil and its change of recent data, we give the matrix of the amount of international crude oil prices change state transition probability (or frequency). According to the international crude oil price forecasting error minimum expectation and variance as the optimal target, taking the international crude oil price forecasting error minimum expectation and variance as the optimal index, a double random integer programming model to predict the price of international crude oil is proposed. Then we discuss the existence of optimal solution. According to the constraint characteristics optimization algorithm is constructed. At the same time, according to the current domestic refined oil pricing mechanism, we predict the domestic refined oil price adjustment by applying the optimization algorithm which is proposed in this paper. The empirical analysis shows that the model in this paper is of certain accuracy and practicability of the optimization algorithm.
In this paper, a novel smoothing objective penalty function is introduced for bilevel programming problems. It is proved that an optimal solution to the smoothing objective penalty optimization problem is also an optimal solution to the riginal bilevel programming problem under some mild conditions. Furthermore, for the bilevel programming problems with convexity to the lower level problem, an algorithm based on the proposed method is introduced, its convergence is proved.
In this paper we present some new results that characterize the efficient solutions of a p-dimensional multiple objective mathematical programming (MOMP). These characterizations are in terms of the optimal solutions of appropriate scalar optimization problems or in terms of efficient solutions of appropriate (p-1)-dimensional parametric MOMP.
When drawing graphs whose edges and nodes both contain text or graphics, such information needs to be displayed without overlaps, either as part of the initial layout or as a post-processing step. The core problem in removing overlaps lies in retaining the structural information inherent in a layout, minimizing the additional area required, and keeping edges as straight as possible. This paper presents a combined node and edge overlap removal algorithm that aims at offering one solution to this problem, based on minimizing a cost function that both reduces topological changes to the original drawing, and keeps edges straight.
In this paper, we indicate the reason of divergence, and illustrate the strategies which modify the alternating direction method of multipliers (ADMM) to a convergent one for the linearly constrained separable convex optimization with three individual functions. Finally, using a uniform framework, we give the simple proofs for the convergence and O(1/t) convergence rate in the ergodic sense of the ADMM-like methods.
Nonnegative matrix factorization (NMF) has become a popular data representation method and has been widely used in image processing and pattern recognition problems. However, NMF ignores the local geometric structure of data. Existing simple graph-based transductive learning only considering the image information in pairs, and they are sensitive to the radius parameter used in similarity calculation. Hypergraph learning has been investigated to solve the problems. Hypergraph models the high-order relationship of samples by using the hyperedges to link multiple samples. However, most of the existing hypergraph learning methods are unsupervised methods. Based on the discriminative hypergraph and nonnegative matrix factorization, we propose a new model and solve the new model by using the alternating direction method of multipliers. The new method, together with the nearest neighbor method, is applied to face recognition. Experimental results on several standard face datasets show the effectiveness of our method.
The automobile logistics could be divided into supply logistics (automotive parts inbound logistics), production logistics, distribution logistics and returned logistics. As part of the automobile logistics, automotive parts inbound logistics is highly technical and characterized by a high level of complexity. It is also recognized as the key point of good operation of automotive logistics system. Based on the analysis of automotive parts inbound logistics, the paper describes the optimization direction of automotive parts inbound logistics. Then it focuses on application of operations research in automotive parts inbound logistics optimization, builds a mathematical model and applies greedy algorithms to solve it.
This paper mainly focuses on the production possibility set and the production frontier for the two-stage additive DEA model. Based on the special status of the intermediate measures in the two-stage model, the production possibility set with a pair of intermediate measures and its axiom system are established. Then the production frontier is defined, which is proved to be equivalent to DEA efficiency. A multiobjective programming model is constructed to prove the equivalence of Pareto efficiency and DEA efficiency at last.
In this paper a pattern search filter algorithm for linearly equality-constrained derivative-free optimization is proposed. In this work we embed a filter technique in a derivative-free optimization algorithm which improves the efficiency of algorithms. The global convergence of new algorithm is established. Initial numerical results show that the new algorithm is efficient.
For constrained optimization problem, a class of smooth penalty algorithm is proposed. It is put forward based on L_p , a smooth function of a class of smooth exact penalty function {l_p}\left( {p\in (0,1]} \right). Under the very weak condition, a perturbationtheorem of the algorithm is set up. The global convergence of the algorithm is derived. In particular, under the hypothesis of generalized Mangasarian-Fromovitz constraint qualification, it is proved that when p=1 , after finite iterations, all iterative points of the algorithm are feasible solutions of the original problem. When {p \in (0,1)}, after finite iteration, all the iteration points are the interior points of feasible solution set of the original problem.
We study a single-machine supply chain scheduling problem with multiple unavailability intervals of equal length. The machine processes jobs in availability intervals and the length of each availability interval is no more than a given constant. The completed jobs are delivered in batches to a customer by one vehicle without capacity restriction. Our objective is to minimize the sum of total delivery time and total delivery cost by scheduling the production and delivery of every job as well as the unavailability intervals. If the interrupted job is resumable, we obtain the optimal schedule in the polynomial time O(n^2). If the interrupted job is non-resumable, we prove that the problem is strongly NP-hard and present a 2-approximation algorithm.
Indoor localization problem in geometric region from industrial practice based on noise error model is considered. With performance and comparison of traditional location algorithms and numerical experiments, we study the optimal number and distribution of anchors, improve the location theory of anchor array and furthermore present an optimization model of anchors distribution based on Delaunay triangulation and its effective algorithm.
This paper proves that when the probabilities of individuals in the group correctly judging satisfaction of alternatives are more dispersed that corresponding to the group using the majority satisfactory rule will have a higher probability. According to this result, we get the expressions of maximal probability and minimal probability of the group determined by majority satisfaction jury theorem on average probability of all individuals correctly judging satisfaction of alternatives has same.
Zhang et al recently propose another approach to Pan's face algorithm. This work gives a modification of the result.
