Table of Content

15 December 2018, Volume 22 Issue 4

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A globally convergent SSDP algorithm without a penalty function or a filter for nonlinear semidefinite programming

LI Jianling, ZHANG Hui, YANG Zhenping, JIAN Jinbao

2018, 22(4):  1-16.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.001

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In this paper, we present a sequence quadratic semidefinite programming (SSDP) algorithm method without a penalty function or a filter for nonlinear  semidefinite programming. At each iteration, the search direction is determined by solving a specially quadratic semidefinite programming subproblem. The nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. The proposed algorithm is globally convergent under some mild conditions. The preliminary numerical results are reported at the end of the paper.

Model and algorithms of the distributed permutation flow shop scheduling problem with machine eligibility constraints

CAI Shuang, YANG Ke, LIU Ke

2018, 22(4):  17-30.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.002

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This paper considers the distributed permutation flow shop scheduling problem with eligibility constraints, which means that there exists an available factory set for each job. The processing time of each job in different factories may not be the same. We present a mixed integer linear programming based on position of jobs in all factories. The general problem and three special cases are analyzed and several heuristic algorithms are proposed with performance guarantee. A heuristic algorithm based on greedy algorithm, LFJ and NEH is carried out to obtain an approximate solution. The branch and bound method based on the approximate value is proposed to find optimal scheduling. At last, an example is used to explain the computing process of NEHg2 and the branch and bound method; numerous experiments prove the effectiveness of the NEHg heuristics.

Optimal consumption-investment-insurance purchase strategy under the condition of stochastic interest rate

GUO Wenjing, LI Xiaojun

2018, 22(4):  31-44.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.003

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With the development of interest rate liberalization in China, the stochastic volatility of interest rates will exert significant influence on the investor's optimal investment strategy. Besides, with the improvement of our insurance market, the investor has paid a lot of attention to the life insurance purchase, so the optimal strategy of the investor will change a lot; This paper studies the optimal consumption-investment-insurance purchase strategy under the condition of stochastic interest rate driven by Vasicek Model. The objective of the investor is to maximize the expected discount utility. With the method of Legendre transform, we get the closed-form solution to the optimal consumption-investment-insurance purchase strategy. By means of numerical analysis, the effects of the changes of variables on the optimal portfolio and life insurance strategy are analyzed.

General equivalence problem of multi-loss WCVaR

XU Leiyan, MENG Zhiqing

2018, 22(4):  45-56.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.004

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Under multi-probability distribution cluster, equivalence of multi-loss WCVaR (Worst Conditional Value-at-Risk, MCVaR) problem is studied. According to the VaR measure under multi-probability distribution cluster, the multi-objective optimization problem (MWCVaR) is defined by the WCVaR risk measurement. It is proved that the optimization problem (MWCVaR) is equivalent to solve another multi-objective optimization problem. In the case of a finite distributions cluster, under certain conditions, we prove that the Pareto effective solution of the problem (MWCVaR) can be approximated by a finite distributions cluster.

Multi-stage active portfolio management with multiple constraints and its empirical study

XU Weijun, YU Canbin, XU Zhongyue

2018, 22(4):  57-68.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.005

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When measuring the risk of the portfolio, the investment manager will consider not only the risk exposed by the portfolio itself, but also the risked exposed compared to a benchmark, i.e. active risk. In addition, the manager will set some constraints according to the rules of the market. Taking account of the risk and the transaction constraints in real market, we consider the absolute risk (CVaR) and the relative risk (Tracking Error) as the risk constraints while we consider the transaction costs, short-sale constraint and the multiple weight constraints as the transaction constraints. Then, we construct a new model of portfolio based on the constraints above and use the nonlinear algorithm and dynamic programming to solve it. Finally, an empirical study is presented based on the benchmark of SSE 50 in empirical study. The result proves the priority of the multi-stage portfolio compared to the single-stage one in terms of the return of the portfolio. Although adding the multiple weight constraints reduces the return of the portfolio in in-sample, we prove that the portfolio can be more efficient by using the multiple weight constraints incorporated by the correct forecast of the investment manager. The portfolio proposed not only conforms to the rules in reality but also shows advantages on the return and risk.

The preventive maintenance policy for a two-component series system with delay repair

GAO Qiaoqiao, YUE Dequan, ZHAO Bing

2018, 22(4):  69-78.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.006

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In this paper, we study the preventive maintenance policy for a two-component series system. When the working time of the system reaches T, the system will be preventive repaired. The preventive maintenance restores every component to the state which is the same as the last failure repair. When the failure occurs, the repair may be delayed for every component. The successive survival times of the component form a stochastically decreasing geometric process and the consecutive repair times after component failures form a stochastically increasing geometric process. We look for a bivariate policy (T,N), which T is the working time of the system before preventive maintenance, N is the failure time of the component before replacement. By using the renewal process theory and geometric process theory, the explicit expression of the long-run expected cost per unit time is derived. Finally, a numerical example is given.

A global optimization algorithm for polynomial programming

TIAN Mingyu, YANG Yongjian

2018, 22(4):  79-88.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.007

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This paper presents a global optimization algorithm for solving the general polynomial programming with box constraint. The algorithm includes two phases. In the first phase, a local optimal solution is found by a local optimization algorithm. In the second phase, with a density vector sequence on the unit ball, we transform the multivariate polynomial into univariate polynomial, and find a point which is smaller than the current local optimal point by solving the roots of univariate polynomial. We use it as the new initial point, and return to the first phase. Therefore we can get a better local optimal solution. Through repeating the two phases, we can find the global optimal solution of the problem eventually. And the convergence of the algorithm is analyzed. Finally, the numerical results show that the algorithm is effective.

Multi-objective optimization approach of the optimal performance allocation

YU Ke, ZHANG Xiaoqing, ZHAO Kequan

2018, 22(4):  89-98.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.008

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How to reflect some degree of incentive and take into account fairness is one of the key problem of performance allocation. In this paper, all assessment objects are classified based on the individual difference, by introducing conversion function and desirability function regarding the control parameters to reflect the degree of incentive and basic workload of all assessment objects as variables, a multi-objective optimization model is formulated  with the objectives of maximizing the total desirability and the tradeoff of all assessment objects' desirability. Furthermore,  by means of the epsilon-constraint scalarization method, the existence is proved for weakly efficient solution. As its application, the optimal performance allocation of is studied.

Graph games and edge density of graphs

LI Li, SHAN Erfang

2018, 22(4):  99-107.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.009

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A cooperative game with transferable utility, shortly TU game, is a pair consisting of a finite set of players and a characteristic function assigning a worth to each coalition of players. Myerson (1977) introduced TU games with restricted cooperative structure represented by an undirected graph, or simply graph games, and presented an allocation rule, called the Myerson value, which  extended the well-known Shapley value. Under the assumption that only coalitions of connected players can cooperate and realize  gains from cooperation. However, the structures of  connected coalitions in the model are ignored. To measure the degree of closeness among the members of each connected set, we introduce the (local) edge density that is regarded as the income coefficient of the members of the connected set and define the Myerson value with  edge density. We show the Myerson value with edge density can be uniquely determined by component efficiency with the edge density and fairness.

A new class of exact penalty functions for equality constrained smooth optimization

LIAN Shujun, TANG Jiahui, DU Aihua

2018, 22(4):  108-116.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.010

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The penalty function method is one of the main approaches to transform the constrained optimization problems into unconstrained optimization problems. If the gradient of the objective function and constrained functions is not involved in the penalty function, the penalty function is simple. For the traditional exact penalty function, it can not be simple and smooth. For equality constrained optimization problems, a new class of simple penalty functions is constructed by adding a new variable to control the penalty terms. In this paper, the simple penalty functions have been proved smooth and exact. An algorithm based on the class of simple exact functions is proposed. Some numerical examples are given to show the efficiency of the algorithm. 

An identification method to estimate the thickness of sea ice

LV Wei, WANG Weiping

2018, 22(4):  117-126.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.011

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This study intended to provide an identification method to estimate the thickness of sea ice with the temperature of sea ice and sea water, which avoids the limitations of using thickness data directly. Firstly, a quasi-linear thermodynamic system with unknown thickness of sea ice is established, which proved the existence and uniqueness of its solution. Secondly, a parameter identification model is constructed which takes the thickness of sea ice as the identified variable, and takes the temperature deviation between the system output and practical observations as an objective function. Finally, a new algorithm, containing of the semi-implicit difference scheme, Genetic Algorithm and Hooke-Jeeves Algorithm, is established for  obtaining the thickness of sea ice. We proved our method is effective and feasible by analysing the sensitivity of identification variable.

An M/M/c queue with customer interjections and balking

WU Wenqing, HE Gang, TANG Yinghui, YU Miaomiao

2018, 22(4):  127-134.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.012

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This paper studies an M/M/c queueing system with customer interjections and balking. Arriving customers are divided into normal customers and interjecting customers, in which the normal customers join the queue at the end, and the interjecting customers try to cut in the queue and occupy a position as close to the head of the queue as possible. The behavior of the interjecting customers is described by the percentage of customers interjecting and the tolerance level of interjection by individual customer. By using the theory of the exponential distributions, the Laplace-Stieltjes transform and the formula of the total probability, we obtain the waiting time of a customer in position n, the waiting time of a normal customer, and the waiting time of an interjecting customer. Furthermore, we discuss the influence of system parameters on the system performance measures.

Laplacian spectral characterizations of graphs with even cyclic

DING Chao, YU Guidong

2018, 22(4):  135-140.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.013

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Let H(K_{1,5},P_n,C_l) be a unicyclic graph obtained from a path P_n by attaching a star K_{1,5} and a cyclic C_l to its two pendent vertices respectively. If two bipartite graphs are Laplacian cospectral, then their line graphs are adjacency cospectral. The numbers of the same length walks are equal in two adjacency cospectral graphs. A graph G is called to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G.  Using the relation between graphs and line graphs, it is proved that the unicyclic graphs H(K_{1,5},P_n,C_4), H(K_{1,5},P_n,C_6) are determined by their Laplacian spectra.

Pareto efficiency in robust optimization

WANG Feng, LIU Sanyang

2018, 22(4):  141-147.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.014

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In this paper, we study the Pareto efficiency of robust solutions to general optimization problems under uncertainty. Firstly, we prove that the set of Pareto robust solutions is the Pareto efficient set of the robust solution set, by which to obtain Pareto robust solutions reduces to find Pareto efficient elements of the robust solution set. Then on the basis of an extension of epsilon-constraint method, we get two ways of generating Pareto robust solutions.

The basis number of join graphs

LV Xuezheng, WEI Erling, SONG Hongye

2018, 22(4):  148-152.  doi:10.15960/j.cnki.issn.1007-6093.2018.04.015

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In 1937 MacLane gave the important theory on cycle basis: gaph G is planar if and only if G  has a 2-basis. The join G = G_1\vee G_2 of graphs G_1 and G_2 is obtained from  G_1\bigcup G_2 by adding all the edges in {(u,v)|u\in V(G_1), v\in V(G_2)}. In this paper we investigate the  basis number of G = G_1\vee G_2 and obtain an upper bound which improves the bound given by Zare. Based on this, a better bound of C_m \vee C_n is derived too.