Improved particle swarm optimization combined with chaos

As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality.  

Nonmonotonic trust region algorithm

A nonmonotonic trust region method for unconstrained optimization problems is presented. Although the method allows the sequence of values of the objective function to be nonmonotonic, convergence properties similar to those for the usual trust region method are proved under certain conditions, including conditions on the approximate solutions to the subproblem. To make the solution satisfy these conditions, an algorithm to solve the subproblem is also established. Finally, some numerical results are reported which show that the nonmonotonic trust region method is superior to the usual trust region method according to both the number of gradient evaluations and the number of function evaluations.The authors would like to thank Professor L. C. W. Dixon for his useful suggestions.  

A survey of credibility theory

This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.  

Fuzzy Random Variables: A Scalar Expected Value Operator

Fuzzy random variable has been defined in several ways in literature. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. Some properties concerning the measurability of fuzzy random variable are also discussed. In addition, the concept of independent and identically distributed fuzzy random variables is introduced. Finally, a type of law of large numbers is proved.  

A note on chance constrained programming with fuzzy coefficients

This paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives. We also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints. Finally, a fuzzy simulation based genetic algorithm is employed to solve a numerical example.  

Toward Fuzzy Optimization without Mathematical Ambiguity

Fuzzy programming has been discussed widely in literature and applied in such various disciplines as operations research, economic management, business administration, and engineering. The main purpose of this paper is to present a brief review on fuzzy programming models, and classify them into three broad classes: expected value model, chance-constrained programming and dependent-chance programming. In order to solve general fuzzy programming models, a hybrid intelligent algorithm is also documented. Finally, some related topics are discussed.  

Filled functions for unconstrained global optimization

This paper is concerned with filled function techniques for unconstrained global minimization of a continuous function of several variables. More general forms of filled functions are presented for smooth and non-smooth optimization problems. These functions have either one or two adjustable parameters. Conditions on functions and on the values of parameters are given so that the constructed functions have the desired properties of filled functions.  

On transcendental meromorphic functions with radially distributed values

The growth of transcendental meromorphic functions in terms of their ordersis investigated in this paper when they and their derivatives have radially distributed valuesfollowing the discussion of the author. A simple and elementary way to study such subjectsis exhibited in this paper; that is, once an estimation of B(r, *) in terms of a few c(r, **) inthe Nevanlinna theory on angular domains is established, we can produce one result thatthe order of a mermorphic function with radially distributed values related to C(r, **) canbe estimated under the assumption of existence of suitable deficient value. The results ob-tained in this paper lead us to a new singular direction in terms of Nevanlinna charactersticinstead of the order of meromorphic functions.