5 1 Overview of the Thesis 7 2 Global Optimization 11 2.1 The Global Optimization Problem . . . . . . . . . . . 12 2.2 Global Optimization Methods . . . . . . . . . . . . . . 14 2.3 Selected Optimization Methods . . . . . . . . . . . . . 17 2.3.1 Monte Carlo . . . . . . . . . . . . . . . . . . . 18 2.3.2 Hill Climbing . . . . . . . . . . . . . . . . . . . 19 2.3.3 Simulated Annealing . . . . . ...

This paper considers general rank-constrained optimization problems that minimize a objective function ${f}( {X})$ over the set of rectangular notation="LaTeX">${n}\times {m}$ matrices have rank at most r. To tackle constraint and als...

This paper proposes an enhanced dung beetle optimization (EDBO) algorithm in order to address the issues of (DBO) which include easy convergence local optimal, slow speed, and poor global search capability. The improvements EDBO are implemented via following four aspects. Firstly, SPM chaotic mapping designed through combing Sine Piece-Wise Linear Chaotic Mapping is introduced initialize popula...

The efficient search of global optimal solutions is an important contemporary subject. Different optimization methods tackle the search in different ways. The gradient based methods are among the fastest optimization methods but the final optimal solution depends on the starting point. The global search using these methods is carried out by providing many starting points. Other optimization met...

This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decomposition-based primal dual methods, (ii) methods for generalized geometric programming problems, and (iii) global optimization methods for general nonlinear programming problems. The classes of m...

A deterministic global optimization algorithm is proposed for locating the global minimum potentialenergy conformationsof oligopeptide chains. The ECEPP/3 detailed potential energy model is utilized to model the energetics of the atomic interactions. The minimization of the total potential energy is formulated on the set of peptide dihedral angles. Based on previous work on the microcluster and...

In this paper, we study various supervised learning methods for training feed-forward neural networks. In general, such learning can be considered as a nonlinear global optimization problem in which the goal is to minimize a nonlinear error function that spans the space of weights using heuristic strategies that look for global optima (in contrast to local optima). We survey various global opti...

The purpose of this paper is to present a new method of design which is an extension of previous works combining analytical models with exact global optimization algorithms. The idea here is to associate analytical and numerical models of electrical machines with an extension of the exact global optimization algorithm previously used in order to solve more general design problems. Some examples...

Following from part I, which presents a retrospective on optimization, we focus here on areas that are recent active research topics and are likely to strongly influence the future of optimization algorithms and formulations. First, we discuss recent developments in deterministic global optimization algorithms applied to both nonlinear programs and mixed-integer programs. Second, we discuss log...

A novel approach for enclosing all heterogeneous and reactive azeotropes in multi-component mixtures is presented. The thermodynamic conditions for azeotropy form a system of nonlinear equations. A deterministic global optimization approach is introduced in which the global optimization problem may contain multiple global minima and there is a one-to-one correspondence between each global minim...