A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces

In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ−norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.

Study of League Championship Algorithm Efficiency for Global Optimization Problem

The article objective is to study a new League Championship Algorithm (LCA) algorithm efficiency by its comparing with the efficiency of the Particle Swarm optimization (PSO) algorithm.The article presents a brief description of the terms used in the League Championship algorithm, describes the basic rules of the algorithm, on the basis of which the iterative process for solving the global optimization problem is built.Gives a detailed description of the League Championship algorithm, which comprises a flowchart of the algorithm, as well as a formalization of all its main steps.Depicts an exhaustive description of the software developed to implement the League Championship algorithm to solve global optimization problems.Briefly describes the modified particle swarm algorithm. Presents the values of all free parameters of the algorithm and the algorithm modifications, which make it different from the classical version, as well.The main part of the article shows the results of a great deal of computational experiments using two abovementioned algorithms. All the performance criteria, used for assessment of the algorithms efficiency, are given.Computational experiments were performed using the spherical function, as well as the Rosenbrock, Rastrigin, and Ackley functions. The results of the experiments are summarized in Tables, and also illustrated in Figures. Experiments were performed for the vector dimension of the variable parameters that is equal to 2, 4, 8, 16, 32, and 64.An analysis of the results of computational experiments involves a full assessment of the efficiency of the League Championship algorithm, and also provides an answer about expediency for further algorithm development.It is shown that the League Championship algorithm presented in the article has a high development potential and needs further work for its study.

OPTIMIZATION OF THE GLOBAL OBJECTIVES OF THE SYSTEM

Issues of optimizing the technological modes of operation of multi-stage processes are considered. It is noted that decomposition and the creation of local control subsystems according to the stages of processes is one of the possible ways to solve the global optimization problem. The sequence of optimization procedures is determined that allow to achieve such controlled values at each stage technological parameters at which the state of the process will be capable of completing production tasks. KEYWORDS: Multi-stage processes, optimization, decomposition, control loop, optimization procedure.

Optimal Switching Instants for the Control of Hybrid Systems

The problem of determining optimal switching instants for the control of hybrid systems under reachability constraints is considered. This optimization problem is cast into an interval global optimization problem with differential constraints, where validated simulation techniques and dynamic time meshing are used for its solution. The approach is applied on two examples, one being the well-known example of the Goddard's problem where a rocket has to reach a given altitude while consuming the smallest amount of fuel.