On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.Comment: 8 pages, 9 figure

Evolutionary Dynamic Optimization Laboratory: A MATLAB Optimization Platform for Education and Experimentation in Dynamic Environments

Many real-world optimization problems possess dynamic characteristics. Evolutionary dynamic optimization algorithms (EDOAs) aim to tackle the challenges associated with dynamic optimization problems. Looking at the existing works, the results reported for a given EDOA can sometimes be considerably different. This issue occurs because the source codes of many EDOAs, which are usually very complex algorithms, have not been made publicly available. Indeed, the complexity of components and mechanisms used in many EDOAs makes their re-implementation error-prone. In this paper, to assist researchers in performing experiments and comparing their algorithms against several EDOAs, we develop an open-source MATLAB platform for EDOAs, called Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform also contains an education module that can be used for educational purposes. In the education module, the user can observe a) a 2-dimensional problem space and how its morphology changes after each environmental change, b) the behaviors of individuals over time, and c) how the EDOA reacts to environmental changes and tries to track the moving optimum. In addition to being useful for research and education purposes, EDOLAB can also be used by practitioners to solve their real-world problems. The current version of EDOLAB includes 25 EDOAs and three fully-parametric benchmark generators. The MATLAB source code for EDOLAB is publicly available and can be accessed from [https://github.com/EDOLAB-platform/EDOLAB-MATLAB].Comment: This work was submitted to ACM Transactions on Mathematical Software on December 7, 202

GNBG: A Generalized and Configurable Benchmark Generator for Continuous Numerical Optimization

As optimization challenges continue to evolve, so too must our tools and understanding. To effectively assess, validate, and compare optimization algorithms, it is crucial to use a benchmark test suite that encompasses a diverse range of problem instances with various characteristics. Traditional benchmark suites often consist of numerous fixed test functions, making it challenging to align these with specific research objectives, such as the systematic evaluation of algorithms under controllable conditions. This paper introduces the Generalized Numerical Benchmark Generator (GNBG) for single-objective, box-constrained, continuous numerical optimization. Unlike existing approaches that rely on multiple baseline functions and transformations, GNBG utilizes a single, parametric, and configurable baseline function. This design allows for control over various problem characteristics. Researchers using GNBG can generate instances that cover a broad array of morphological features, from unimodal to highly multimodal functions, various local optima patterns, and symmetric to highly asymmetric structures. The generated problems can also vary in separability, variable interaction structures, dimensionality, conditioning, and basin shapes. These customizable features enable the systematic evaluation and comparison of optimization algorithms, allowing researchers to probe their strengths and weaknesses under diverse and controllable conditions

Investigating bound handling schemes and parameter settings for the interior search algorithm to solve truss problems

The interior search algorithm (ISA) is an optimization algorithm inspired by esthetic techniques used for interior design and decoration. The algorithm has only one parameter, controlled by θ, and uses an evolutionary boundary constraint handling (BCH) strategy to keep itself within an admissible solution space while approaching the optimum. We apply the ISA to find optimal weight design of truss structures with frequency constraints. Sensitivity of the ISA's performance to the θ parameter and the BCH strategy is investigated by considering different values of θ and BCH techniques. This is the first study in the literature on the sensitivity of truss optimization problems to various BCH approaches. Moreover, we also study the impact of different BCH methods on diversification and intensification. Through extensive numerical simulations, we identified the best BCH methods that provide consistently better results for all truss problems studied, and obtained a range of θ that maximizes the ISA's performance for all problem classes studied. However, results also recommend further fine-tuning of parameter settings for specific case studies to obtain the best results

Dağıtım transformatörlerinin metasezgisel algoritmalarla tasarım optimizasyonu

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Dünyadaki pek çok ekonomi, yüksek verimli transformatörlerin kullanımını zorunlu kılan veya teşvik eden enerji verimliliği yönetmelikleri veya teşvik programları kabul etmiştir. Öte yandan, transformatör verimliliğindeki artışlar, transformatör ağırlık ve boyutunda bazen % 50 hatta daha fazla bir artışı gerektirmektedir. Transformatör endüstrisi bu nedenle gerçekten en iyi tasarımları geliştirme uğraşısı ile karşı karşıyadır. Transformatör tasarım optimizasyonu (TDO) problemi, karmaşık ve süreksiz amaç fonksiyonlu ve kısıtlı karma-tamsayılı bir doğrusal olmayan programlama problemidir. TDO'nun amacı, ulusal ve/veya ulusal standartlar ve müşteri şartnameleri uyarıca, mevcut malzemeleri ekonomik olarak kullanarak daha düşük boyut, ağırlık ve maliyet ve daha yüksek işletme performansı elde etmek üzere transformatörün tüm bileşenlerinin niteliklerinin detaylı olarak hesaplanmasıdır. Bu çalışmada TDO probleminin çözümü için beş modern metasezgisel optimizasyon algoritması uygulamasının ayrıntılı karşılaştırmalı analizi üç test vakası üzerinde gösterilmiş ve iki algoritma önerilmiştir önerilen bu algoritmaların, rassal özelliklerine rağmen, garanti edilmiş küresel yakınsama özelliklerine sahip oldukları doğrulanmıştır. Algoritmaların karşılaştırılması için pragmatik bir kıyaslama yöntemi geliştirilmiştir. Literatürde sunulan TDO yöntemleri nadiren üretimde doğrudan uygulanabilir çözümler üretir. tasarım mühendisinin genellikle teorik çözümü pratik olarak uygulanabilir bir hale dönüştürmek için ek çaba harcaması gerekir. Bu problem bu çalışmada ele alınmış ve piyasada mevcut veya üretime uygun boyutlara sahip çözümler üreten bir ayrık transformatör tasarım optimizasyon yöntemi önerilmiştir Ayrıca, amaç fonksiyonu ve kısıt hesaplamalarını azaltmak için basit bir yöntem önerilmiştir. Yöntem, önbellekleme tekniği kullanılarak arama işlemi sırasında yinelenen tasarım vektörleri için hesaplamaların atlanması esasına dayanmaktadır. Performans testleri, teorik TDO için Rekabetçi-Uyarlamalı Diferansiyel Gelişim ve Guguk Kuşu Arama, Pratik TDO için de Guguk Kuşu Arama ve Çiçek Tozlaşma algoritmaları kullanıldığında küresel optimum ve ona çok yakın sonuçlar elde edildiğini göstermiştir.Many economies in the world have adopted energy-efficiency requirements or incentive programs mandating or promoting the use of energy-efficient transformers. On the other hand, increases in transformer efficiency are subject to increases in transformer weight and size, sometimes as much as 50% or even more. The transformer manufacturing industry is therefore faced with the challenge to develop truly optimum designs. Transformer design optimization (TDO) is a mixed-integer nonlinear programming problem having complex and discontinuous objective function and constraints, with the objective of detailed calculation of the characteristics of a transformer based on national and/or international standards and transformer user and two algorithms are proposed, for which it has been verified that they possess guaranteed global convergence properties in spite of their inherent stochastic nature. A pragmatic benchmarking scheme is used for comparison of the algorithms. Transformer design optimization methods presented in the literature rarely yield solutions directly applicable in productionrequirements, using available materials and manufacturing processes, to minimize manufacturing cost or total owning cost, while maximizing operating performance. Detailed comparative analysis of the application of five modern metaheuristic optimization algorithms for the solution of TDO problem are carried out in this study, demonstrated on three test cases the design engineer usually needs to convert the theoretical solution to a practical one. This problem is addressed in this study, and a discrete transformer design optimization method is proposed which yields solutions with commercially available or productionally feasible dimensions Furthermore, a simple method is proposed to reduce the number of objective function and constraint calculations. The method is based on skipping calculations for design vectors recurring during the search process, by the use of caching technique Performance tests showed that global or near-global optimum solutions can be obtained with b6e6rl and CS for TDO, and CS and FPA algorithms for DTDO

Evolutionary boundary constraint handling scheme

The performance of an optimization tool is largely determined by the efficiency of the search algorithms used in the process as well as the proper handling of complex constraints. From the implementation point of view, an important part of task ensuring an efficient algorithm to work to its best capability is to handle the boundary constraints properly and effectively. Asmost studies in the literature have focused on the development of algorithms and performance evaluation and comparison of optimization algorithms, this crucial step has not been explored very well, and consequently only limited studies have been carried out in this field. This paper intends to propose a simple and yet efficient evolutionary scheme for handling boundary constraints. The simplicity of this approach means that the proposed scheme is very easy to implement and thus can be suitable for many applications. We demonstrate this approach with an efficient algorithm, differential evolution, and we also compare it with other boundary constraint handling approaches for a wide set of benchmark problems. Based on statistical parameters and especially mean values, the results obtained by the evolutionary scheme are better than the best known solutions obtained by the existing methods