Implementation of a fixing strategy and parallelization in a recent global optimization method

Electromagnetism-like Mechanism (EM) heuristic is a population-based stochastic global optimization method inspired by the attraction-repulsion mechanism of the electromagnetism theory. EM was originally proposed for solving continuous global optimization problems with bound constraints and it has been shown that the algorithm performs quite well compared to some other global optimization methods. In this work, we propose two extensions to improve the performance of the original algorithm: First, we introduce a fixing strategy that provides a mechanism for not being trapped in local minima, and thus, improves the effectiveness of the search. Second, we use the proposed fixing strategy to parallelize the algorithm and utilize a cooperative parallel search on the solution space. We then evaluate the performance of our study under three criteria: the quality of the solutions, the number of function evaluations and the number of local minima obtained. Test problems are generated by an algorithm suggested in the literature that builds test problems with varying degrees of difficulty. Finally, we benchmark our results with that of the Knitro solver with the multistart option set

Lipschitz gradients for global optimization in a one-point-based partitioning scheme

A global optimization problem is studied where the objective function $f(x)$ is a multidimensional black-box function and its gradient $f'(x)$ satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant $K$. Different methods for solving this problem by using an a priori given estimate of $K$, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for $f'(x)$ (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.Comment: 25 pages, 4 figures, 5 tables. arXiv admin note: text overlap with arXiv:1103.205

Vector Form Implementation in Three-Phase Power Flow Analysis Based on Power Injection Rectangular Coordinate

This paper aims to propose the vector form implementation into three-phase power flow analysis. The developed algorithm is based on Newton-Raphson method with voltage is represented in rectangular coordinate. The Python programming language and its mathematical libraries are used in this works. Three-phase power flow analysis in vector form utilizes sparse matrix ordering algorithm, so the elements of the coefficient correction matrix can be rearranged easily. This method was used to solve three-phase power flow for balance or unbalance network in two actual distribution system feeders in Lampung, i.e. 119 nodes and 191 nodes. Comparison with traditional Newton-Raphson method (non-vector) shows the vector form is able to solve computation up to eight times faster than non-vector

Solving Global Optimization Problems Using MANGO

Traditional approaches for solving global optimization problems generally rely on a single algorithm. The algorithm may be hybrid or applied in parallel. Contrary to traditional approaches, this paper proposes to form teams of algorithms to tackle global optimization problems. Each algorithm is embodied and ran by a software agent. Agents exist in a multiagent system and communicate over Our proposed MultiAgent ENvironment for Global Optimization (MANGO). Through Communication and cooperation, the agents complement each other in tasks that they cannot do on their own. This paper gives a formal description of MANGO and Outlines design principles for developing agents to execute Oil MANGO. Our case study shows the effectiveness of multiagent teams in solving global optimization problems

Using landscape topology to compare continuous metaheuristics: a framework and case study on EDAs and ridge structure

In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behavior of continuous metaheuristic optimization algorithms. In particular, we generate twodimensional landscapes with parameterized, linear ridge structure, and perform pairwise comparisons of algorithms to gain insight into what kind of problems are easy and difficult for one algorithm instance relative to another.We apply thismethodology to investigate the specific issue of explicit dependency modeling in simple continuous estimation of distribution algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modeling is useful, harmful, or has little impact on mean algorithm performance. Heat maps are used to compare algorithm performance over a large number of landscape instances and algorithm trials. Finally, we perform ameta-search in the landscape parameter space to find landscapes which maximize the performance between algorithms. The results are related to some previous intuition about the behavior of these algorithms, but at the same time lead to new insights into the relationship between dependency modeling in EDAs and the structure of the problem landscape. The landscape generator and overall methodology are quite general and extendable and can be used to examine specific features of other algorithms

BENCHMARK PROBLEMS FOR TESTING OPTIMIZATION METHODS APPLIED AT WATER RESOURCES MANAGEMENT PROBLEMS

Στην εργασία αυτή παρουσιάζονται δύο προβλήματα βελτιστοποίησης, που σχετίζονται με θέματα διαχείρισης υδατικών πόρων και έχουν τα ακόλουθα χαρακτηριστικά: α) Το ολικό βέλτιστο είναι γνωστό β) Η περιοχή διακύμανσης των τιμών της αντικειμενικής συνάρτησης είναι γνωστή γ) Παρουσιάζουν άπειρα τοπικά ακρότατα δ) Η εφαρμογή τους είναι εύκολη και ε) Ο υπολογιστικός όγκος για την εύρεση τιμών της αντικειμενικής συνάρτησης είναι περιορισμένος. Επιπλέον, ο βαθμός δυσκολίας του ενός από αυτά είναι μεταβλητός και μπορεί να ρυθμιστεί μέσω των δεδομένων, χωρίς να αλλάξει το ολικό βέλτιστο. Λόγω αυτών των χαρακτηριστικών, τα παρουσιαζόμενα προβλήματα είναι κατάλληλα για την αξιολόγηση μεθόδων βελτιστοποίησης, ιδιαίτερα μάλιστα κατά την εφαρμογή τους σε θέματα διαχείρισης υδατικών πόρων.In this paper, two problems are presented and investigated, which are relevant to water resources management. These problems have the following features: a) Their global optimum is known b) The range of the values of the objective function is known c) The number of local optima is infinite d) Their application is easy and e) The computational effort that is required for the calculation of objective function values is low. Moreover, the difficulty of one of them can be adjusted, through the input parameters, without changing global optimum. Due to these favourite features, the two presented problems are suitable for evaluation of the performance of optimization techniques, in particular when applied to water resources management issues

Metaheuristic optimization of power and energy systems: underlying principles and main issues of the 'rush to heuristics'

In the power and energy systems area, a progressive increase of literature contributions containing applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods based on weak comparisons. This 'rush to heuristics' does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter, but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems, and aims at providing a comprehensive view of the main issues concerning the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls found in literature contributions are identified, and specific guidelines are provided on how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

Global optimization algorithms for image registration and clustering

Global optimization is a classical problem of finding the minimum or maximum value of an objective function. It has applications in many areas, such as biological image analysis, chemistry, mechanical engineering, financial analysis, deep learning and image processing. For practical applications, it is important to understand the efficiency of global optimization algorithms. This dissertation develops and analyzes some new global optimization algorithms and applies them to practical problems, mainly for image registration and data clustering. First, the dissertation presents a new global optimization algorithm which approximates the optimum using only function values. The basic idea is to use the points at which the function has been evaluated to decompose the domain into a collection of hyper-rectangles. At each step of the algorithm, it chooses a hyper-rectangle according to a certain criterion and the next function evaluation is at the center of the hyper-rectangle. The dissertation includes a proof that the algorithm converges to the global optimum as the number of function evaluations goes to infinity, and also establishes the convergence rate. Standard test functions are used to experimentally evaluate the algorithm. The second part focuses on applying algorithms from the first part to solve some practical problems. Image processing tasks often require optimizing over some set of parameters. In the image registration problem, one attempts to determine the best transformation for aligning similar images. Such problems typically require minimizing a dissimilarity measure with multiple local minima. The dissertation describes a global optimization algorithm and applies it to the problem of identifying the best transformation for aligning two images. Global optimization algorithms can also be applied to the data clustering problem. The basic purpose of clustering is to categorize data into different groups by their similarity. The objective cost functions for clustering usually are non-convex. $k$-means is a popular algorithm which can find local optima quickly but may not obtain global optima. The different starting points for $k$-means can output different local optima. This dissertation describes a global optimization algorithm for approximating the global minimum of the clustering problem. The third part of the dissertation presents variations of the proposed algorithm that work with different assumptions on the available information, including a version that uses derivatives