A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems

A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

A Compromise Approach to Lexicographic Optimal Solution in Multiple Objective Programming

In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.

Global Optimization Method for Linear Multiplicative Programming

In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming（LMP）. The problem（LMP） is firstly converted into an equivalent programming problem（LMP（H））by introducing p auxiliary variables. Then by exploiting structure of（LMP（H））, a linear relaxation programming（LP（H）） of（LMP（H）） is obtained with a problem（LMP） reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems（LP（H））. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

Regularized multiple criteria linear programs for classification

Although multiple criteria mathematical program （MCMP）, as an alternative method of classification, has been used in various real-life data mining problems, its mathematical structure of solvability is still challengeable. This paper proposes a regularized multiple criteria linear program （RMCLP） for two classes of classification problems. It first adds some regularization terms in the objective function of the known multiple criteria linear program （MCLP） model for possible existence of solution. Then the paper describes the mathematical framework of the solvability. Finally, a series of experimental tests are conducted to illustrate the performance of the proposed RMCLP with the existing methods： MCLP, multiple criteria quadratic program （MCQP）, and support vector machine （SVM）. The results of four publicly available datasets and a real-life credit dataset all show that RMCLP is a competitive method in classification. Furthermore, this paper explores an ordinal RMCLP （ORMCLP） model for ordinal multigroup problems. Comparing ORMCLP with traditional methods such as One-Against-One, One-Against-The rest on large-scale credit card dataset, experimental results show that both ORMCLP and RMCLP perform well.

Inter-cell downlink co-channel interference management through cognitive sensing in heterogeneous network for LTE-A

Heterogeneous network for long term evolution advanced（LTE-A） creates severe interference.It is an urgent task to overcome the interference in macro cellular with low-power base stations（BSs）,such as relay,pico,and femto called subnet nodes.In this paper,the cognitive interference model in interference zone（IZ） of the practical heterogeneous scenario is proposed.Based on investigation of interaction between the macro BS and subnet nodes in this model,the strategy framework of the cognitive critical ratio and power reward factor is set up for interference management aiming to get the maximum net saving power.The study of interference management is transformed into a multiple objective non-linear programming（MONLP） of the maximum saving power for the macro BS and subnet nodes.To facilitate the best compromise solution for both,the MONLP is changed into single objective programming and genetic algorithm（GA） is employed to obtain the global optimum solution.In addition,the practical implementation using the proposed algorithm in heterogeneous network for LTE-A is designed.Finally,numerical evaluation is used to test the applicability of the proposed algorithm,and system level simulation results demonstrate the effectiveness of the proposed interference management scheme.

多尺度视角下中国西部城市网络空间演化与演化机制

Globalization and informatization promote the evolution of urban spatial organization from a hierarchical structure mode to a network structure mode,forming a complex network system.This study considers the coupling of“space of flows”and“spaces of places”as the core and“embeddedness”as the link and a relevant theoretical basis;then we construct a conceptual model of urban networks and explore the internal logic of enterprise networks and city networks.Using the interlocking-affiliate network model and data from China’s top 500 listed companies,this study constructs a directed multi-valued relational matrix between cities in western China from 2005 to 2015.Using social network analysis and the multiple regression of quadratic assignment program model(MRQAP),this study adopts a“top-down”research perspective to analyze the spatio-temporal evolution and growth mechanism of the city network in western China from three nested spatial scales:large regions,intercity agglomerations,and intracity agglomerations.The results show the following:(1)Under the large regional scale,the city network has good symmetry,obvious characteristics of hierarchical diffusion,neighborhood diffusion,and cross-administrative regional connection,presenting the“core-periphery”structural pattern.(2)The network of intercity agglomerations has the characteristics of centralization,stratification,and geographical proximity.(3)The internal network of each urban agglomeration presents a variety of network structure modes,such as dual-core,single-core,and multicore modes.(4)Administrative subordination and economic system proximity have a significant positive impact on the city network in western China.The differences in internet convenience,investment in science and technology,average time distance,and economic development have negative effects on the growth and development of city networks.(5)The preferential attachment is the internal driving force of the city network development.

A Multi-Criteria Optimization Method for Electrical Distribution System and Its Analysing in Practice

In this paper, the author explains the problem that we have to consider multiple goals and multiple factors which are usually affected by others at the same time in practical work for electrical power distribution system programming. A new mathematics model is set up here for the multiple goals programming of electrical power distribution system which includes various load control alternatives. An arithmetic and current software for the multi-criteria optimization of electrical power distribution system are given here. The author calculates and analyses the optimal programming projects and the optimal operation strategies for a practical system, which show that the model, the arithmetic and the current software are all correct and effective. The outcome of researches has been adopted by the authoritative persons.