Liu San-yang

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision makers preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging (C-OWA) operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Feasible direction algorithm for solving the SDP relaxations of quadratic {−1, 1} programming problems

In this article, we propose a feasible direction algorithm for solving the semidefinite programming (SDP) relaxations of quadratic {−1, 1} programming problems. This algorithms distinguishing features are that it uses a low rank factorization and searches with a constant step-size. Its convergence is also proven. Finally, we report some numerical examples to compare our method with the low rank factorization method of Burer and Monteiro on the SDP relaxation of the max-cut problem. *E-mail: xdliuhongwei@hotmail.com

Adjustable entropy function method for support vector machine

Abstract Based on KKT complementary condition in optimization theory, an unconstrained non-differential optimization model for support vector machine is proposed. An adjustable entropy function method is given to deal with the proposed optimization problem and the Newton algorithm is used to figure out the optimal solution. The proposed method can find an optimal solution with a relatively small parameter p, which avoids the numerical overflow in the traditional entropy function methods. It is a new approach to solve support vector machine. The theoretical analysis and experimental results illustrate the feasibility and efficiency of the proposed algorithm.

ISPEA: improvement for the strength Pareto evolutionary algorithm for multiobjective optimization with immunity

Recently, there arose some important multiobjective evolutionary algorithms (MOEAs), among these MOEAs, strength Pareto evolutionary algorithm (SPEA) seems the most effective technique for finding or approximating the Pareto-optimal set for multiobjective optimization problems with several characteristics. Unfortunately, there are always some basic and obvious characteristics or knowledge in pending problem, where the loss due to this negligence is sometimes considerable in dealing with complex problems. Based on these reasons, an improvement on SPEA with immunity is given to restrain degeneracy of the evolution process, where the immune operator is realized by vaccine extraction, vaccination and immune selection in turn. Simulations show the ISPEA is effective and feasible.

An infeasible-interior-point predictor-corrector algorithm for the second-order cone program

Abstract A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh—Haeberly—Overton (AHO) search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an ɛ-approximate solution of an SOCP in at most O√n ln (ɛ0/ɛ)) iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Satisfactory orthogonal array and its checking method

An orthogonal array (OA) is said to be a satisfactory orthogonal array if it is impossible to obtain another OA from it by adding one or more columns. By exploring the relationship between OAs and orthogonal decompositions of projection matrices, we present a method of checking a satisfactory OA.

A novel clonal selection for multi-modal function optimization

This paper proposes a Clonal Selection Algorithm for Multimodal function optimization (CSAM) based on the concepts of artificial immune system and antibody clonal selection theory. In CSAM, more attention is paid to locate all the peaks (both global and local ones) of multimodal optimization problems. To achieve this purpose, new clonal selection operator is put forward, dynamic population size and clustering radius are also used not only to locate all the peaks as many as possible, but assure no resource wasting, i.e., only one antibody will locate in each peak. Finally, new performances are also presented for multimodal function when there is no prior idea about it in advance. Our experiments demonstrated that CSAM is very effective in dealing with multimodal optimization regardless of global or local peaks.

New method to option pricing for the general black-scholes model—An actuarial approach

Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black-Scholes model is generalized to the case where the risk-less asset (bond or bank account) earns a time-dependent interest rate and risk asset (stock) has time-dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put-call parity of European option are obtained. The general approach of option pricing is given for the general Black-Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback (O-U) process are given by actuarial approach.

Mobile Agent Routing Algorithm in Dynamic Sensor Network

An ant colony optimization-based dynamic energy efficient mobile agent routing algorithm (ADEEMA) is presented in this paper. In this algorithm, mobile agent (MA) has the character of an ant, and a novel probabilistic model is constructed to make MA can find an energy efficient route from processing node (PN) to target nodes (TN). The route considers both the energy consumption and the node residual energy, and a new concept: route optimal degree (ROD) is presented to evaluate the performance of the chosen route. In order to adapt to the topology changes in dynamic sensor network, a new local pheromone re-initialization rule is presented, the rule reinitializes the pheromone in the local area where the sensor network topology changes, so most information of the old optimization route can be reserved and meanwhile the ant can search new route in local area, thus the optimization route can be modified fast. The simulation shows that a route with minimum energy consumption and maximum node residual energy can be obtained by our method. In addition, a new optimization route can be found fast when topology changes by our algorithm.

On the Generalized Fritz John Optimality Conditions of Vector Optimization With Set-Valued Maps Under Benson Proper Efficiency

A kind of tangent derivative and the concepts of strong and weak pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the setvalued map is specialized to be a single-valued map.