Adaptive Global Optimization Based on a Block-Recursive Dimensionality Reduction Scheme

Local Tuning in Peano Curves-based Global Optimization Scheme

It has recently been important to obtain optimal solutions to multidimensional nonlinear integer programming problems with multiple constraints. The surrogate constraint method is very effective in obtaining high-quality solutions of the original multidimensional problems. The surrogate constraint method translates a multidimensional problem into a one-dimensional problem by using a surrogate multiplier. But when there exists a surrogate duality gap between the translated one-dimensional problem and the original multidimensional problem, the optimal solution to the surrogate problem is not optimal with respect to the original problem. Nakagawa has recently proposed an improved surrogate constraint (ISC) method that can reduce the surrogate duality gap and provide an exact solution to the original problem. By using this method, we can obtain exact solutions to separable nonlinear integer programming problems with 1000 variables and 5 or 6 constraints. The ISC method requires an optimal surrogate multiplier. However, there are problems of calculation time and memory requirements in the algorithm for obtaining the optimal surrogate multiplier when the number of constraints is large. In this paper, the Dyer algorithm and Nakagawa's Cutting-Off Polyhedron (COP) algorithm for an algorithm that obtains the optimal surrogate multiplier in the ISC method are compared in computational experiments, and the advantages and disadvantages of these algorithms are investigated. In addition, an improved Dyer algorithm is proposed and computational experiments show that the improved algorithm is more effective than the original algorithm. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(8): 38–48, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20114

Parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems via a hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm

We consider multidimensional optimization problems in the framework of tropical mathematics. The problems are formulated to minimize a nonlinear objective function that is defined on vectors over an idempotent semifield and calculated by means of multiplicative conjugate transposition. We start with an unconstrained problem and offer two complete direct solutions to demonstrate different practicable argumentation schemes. The first solution consists of the derivation of a sharp lower bound for the objective function and the solving of an equation to find all vectors that yield the bound. The second is based on extremal properties of the spectral radius of matrices and involves the evaluation of this radius for a certain matrix. This solution is then extended to problems with boundary constraints that specify the feasible solution set by a double inequality, and with a linear inequality constraint given by a matrix. To illustrate one application of the results obtained, we solve problems in project scheduling under the minimum makespan criterion subject to various precedence constraints on the time of initiation and completion of activities in the project. Simple numerical examples are given to show the computational technique used for solutions.

Whale Optimization Algorithm (WOA) proposed by Seyedali Mirjalili and Andrew Lewis in 2016 is popular and powerful metaheuristic algorithm to search the global solution of optimization problems. WOA is nature-inspired, metaheuristic (randomization and deterministic) algorithm, which has been widely used to solve various single objective, multi objective and multidimensional optimization problems. WOA and its variant have been introduced in engineering applications, bioinformatics, multi-level image segmentation, clustering applications, design of low pass filter, Email classification, Diabetes classification, heterogeneous networks, machine learning etc. WOA is gradient free, easy to represent, capable to explore, exploit the search space and able to avoid local optima. This paper presents overview of WOA, its variants and applications. The performance of WOA is enhanced by introducing hybridization of other methods with WOA such as WOA-PSO, WOA-Levy, WOA-BAT, WOA-ANN, WOA-SVM etc. Objective of metaheuristic algorithm is tofind best position or leader position X* which is near to optimal solution for target prey over successive iteration. Objective function could be based on minimization or maximization approach.

The article proposes an approach to parametric identification of interval nonlinear models of static systems based on the standard problem of minimizing the root mean square deviation between the values ​​of the modeled characteristics of the static object and the values ​​belonging to the experimental intervals. As a result of expanding the parameter space of nonlinear models by introducing additional coefficients to match the predicted and experimental values into the objective function, a multidimensional optimization problem with a nonlinear multiextremal objective function is obtained. The paper examines the characteristics of the objective function and the convergence of its optimization.

The eigenimage filter generates a composite image in which a desired feature is segmented from interfering features. The signal-to-noise ratio (SNR) of the eigenimage equals its contrast-to-noise ratio (CNR) and is directly proportional to the dissimilarity between the desired and interfering features. Since image gray levels are analytical functions of magnetic resonance imaging (MRI) parameters, it is possible to maximize this dissimilarity by optimizing these parameters. For optimization, the authors consider four MRI pulse sequences: multiple spin-echo (MSE); spin-echo (SE); inversion recovery (IR); and gradient-echo (GE). The authors use the mathematical expressions for MRI signals along with intrinsic tissue parameters to express the objective function (normalized SNR of the eigenimage) in terms of MRI parameters. The objective function along with a set of diagnostic or instrumental constraints define a multidimensional nonlinear constrained optimization problem, which the authors solve by the fixed point approach. The optimization technique is demonstrated through its application to phantom and brain images. The authors show that the optimal pulse sequence parameters for a sequence of four MSE and one IR images almost doubles the smallest normalized SNR of the brain eigenimages, as compared to the conventional brain protocol.

The paper studies multidimensional optimization problems with a polynomial objective function and constraints in the form of polynomial matrix inequalities. The author suggests a transformation of the solution method based on the theory of moments. This transformation allows to reduce appreciably the computational complexity of the method, still preserving its applicability to optimization problems of the above class.

In this study, we introduce a new global optimization technique for a multi-dimensional unconstrained optimization problem. First, we present a new smoothing auxiliary function. Second, we transform the multi-dimensional problem into a one-dimensional problem by using an auxiliary function to reduce the number of local minimizers and then we find the global minimizer of the one-dimensional problem. Finally, we find the global minimizer of the multi-dimensional smooth objective function with the help of a new algorithm.

Long-term scheduling of large cascade hydropower stations in Jinsha River, China

The computational efficiency of the quantum particle swarm optimization (QPSO) is significantly higher than that of the traditional particle swarm optimization when solving the parameters of the optimization problem model. However, the exploration and exploitation abilities of the QPSO are weak, based on the historical best position and the global best position. Enlightened by the multi-stage search strategies of marine predators algorithm, we propose a novel hybrid quantum particle swarm optimization algorithm with marine predators (HMPQPSO) in this paper. The evolutionary process of the algorithm is divided two stages: firstly, the Brownian motion of the predator is introduced to the exploration. The randomness and uniformity of which can expand the solution space of particles; secondly, the Levy motion strategy and dynamic parameter strategy are used to update the position, which can accelerate the convergence of the algorithm and enhance the diversity of the algorithm. Meanwhile, both fish aggregation devices(FADs) and opposition-based learning strategy incorporated are used to increase the diversity of the population and prevent the phenomenon of premature particle aggregation. The algorithm is applied to distinct types of CEC2017 benchmark test functions and four multidimensional nonlinear structure design optimization problems, as compared to other recent algorithms. The results demonstrate that the convergence speed and accuracy of HMPQPSO are notably superior to that of other algorithms.

This article studies the exact G-penalty function method to solve a multi-dimensional control optimization problem with non-linear dynamical system involving G-convex functionals. Particularly, the exact G-penalized unconstrained problem associated with the aforementioned problem is constructed using the exact penalty approach. Further, the equivalence relation between an optimal solution of the constrained problem and the minimizer of its related unconstrained problem is established imposing the suitable assumptions on the involved functionals. In addition, several numerical examples are formulated to better illustrate the main results, and an informative algorithm is also constructed to specify the certain steps of the solution procedure.

In order to cope with the multidimensional non-linear optimization problems which involved a great number of discrete variables and continuous variables, a self-organizing learning algorithm (SOLA) was proposed in this paper, in which the parallel search strategy of genetic algorithm(GA) and the serial search strategy of simulated annealing (SA) were involved. Additionally, the learning principle of particle swarm optimization(PSO) and the tabu search strategy were adopted into the SOLA, wherein the integrated frame work was different from traditional optimization methods and the interactive learning strategy was involved in the process of random searching. SOLA was divided into two handling courses: self-learning and interdependent-learning. The local optimal solution would be achieved through self-learning in the process of local searching and the global optimal solution would be achieved via the interdependent learning based on the information sharing mechanism. The search strategies and controlled parameters of SOLA were adaptively fixed according to the feedback information from interactive learning with the environments thus SOLA is self-organizing and intelligent. Experiments for the multidimensional testbed functions showed that SOLA was far superior to traditional optimization methods at the robustness and the global search capability while the solution space ranged from low-dimensional space to the high-dimensional space.Keywordsself-organizinglearning principlehigh-dimensional spacegenetic algorithm

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.

As outlined in chapter 1, integrated optimum structural design represents an optimization problem with both equality constraints and inequality constraints. In this method the analysis and optimal design of the structure are carried out simultaneously. The disadvantage of this approach, however, is that the formulation results in a large size problem. Generalized geometric programming is a powerful mathematical tool that can be used to solve the multidimensional optimization problems with nonlinear equations, Burns (1985). In this chapter we will present the generalized geometric programming (GGP) and its extensions to the solution of problems with equality constraints (GGPE). We will also describe the IGGP solver, Burns (1982), and the added extensions for the optimal solution.