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In the paper, we give a new non-parameter filled function method for finding global minimizer of global optimization programming problems, the filled function consists of a inverse cosine function and a logarithm function, and without parameter. Its theoretical residences are proved. A new filled function algorithm is given based on the proposed new parameterless filled function, The results of numerical with ten experiments verify the efficient and reliability for the algorithm. [ABSTRACT FROM AUTHOR]

Founded on the idea of subdividing the (p − 1) -dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Let be a compact metric space and be an -tuple of continuous selfmaps on . This paper investigates Hausdorff metric Li-Yorke chaos, distributional chaos and distributional chaos in a sequence from a set-valued view. On the basis of this research, we draw the main conclusions as follows: (i) If has a distributionally chaotic pair, especially is distributionally chaotic, the strongly nonwandering set contains at least two points. (ii) We give a sufficient condition for to be distributionally chaotic in a sequence and chaotic in the strong sense of Li-Yorke. Finally, an example to verify (ii) is given. [ABSTRACT FROM AUTHOR]

A co-evolutionary algorithm based on particle swarm optimization (PSO) and ant colony optimization (ACO) is given to solve the bound constrained mixed-integer programming problem (BCMIP). For the specificity of the problem, the hybrid coding includes the real coding and the integer coding. The real coding part is evolved by PSO while the integer coding part is evolved by ACO. The entire population is co-evolved by PSO and ACO. Numerical experiments show that the proposed algorithm is feasible and effective to solve BCMIP. We also obtain satisfactory result to solve MIP when the proposed algorithm is combined with penalty function method. [ABSTRACT FROM AUTHOR]