New SOMA for Constrained Optimization

{Práce je věnována moderním hejnovým algoritmům v oblasti optimalizace s omezeními. Cílem je nalézt takové mechanizmy a techniky, které by přinesly zlepšení výkonu Samo-organizující se algoritmu (SOMA). Je zde popsán postupný vývoj vedoucí k nalezení vhodné úpravy. Jednotlivá dílčí řešení jsou okomentována a srovnána s původními strategiemi. Konečná úprava SOMA představuje inovativní přístup k migraci jedinců, kdy dochází ke skokům ke dvěma adaptivně se posunujícím cílovým bodům. Změněn je také způsob perturbace, který nově využívá chaoticky generovaných čísel. Přestavený algoritmus byl srovnán se state-of-art algoritmy na funkci návrhu parametrů tlakového válce, návrhu konstrukce svařovaných nosníků, návrhu parametrů pružiny a na funkcích z benchmarku CEC 2017. Na základě srovnání výkonu algoritmů dle pravidel CEC 2017 a statistických testů lze konstatovat, že nově představená strategie výrazně přispívá ke zlepšení výkonu SOMA.The thesis is focused on the modern swarm algorithms and constrained optimization. The goal of this thesis is to improve the original version of the Self-organizing migrating algorithm (SOMA). The gradual development leading to finding a suitable solution is described in this thesis. Every partial solution is commented and compared with the original SOMA strategies. The novelty of the developed algorithm lies in the principle of migration of individuals - the individuals move in the direction of two adaptively shifting target locations. The method of perturbation was modified too. In the present algorithm, the generators of chaotic numbers are utilized. The novel algorithm described in this thesis was compared with selected state-of-art algorithms. As the testing problems Pressure vessel design problem, Welded beam design problem, Tension/Compression Spring design problem and functions from the CEC 2017 benchmark were selected. Based on the experimental results, we can conclude that the innovations implemented to the original algorithm of SOMA significantly improved its performance.460 - Katedra informatikyvýborn

Helper and Equivalent Objectives:Efficient Approach for Constrained Optimization

Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation problems without any constraint, and then solve them. In this paper, we propose a new multi-objective method for constrained optimisation, which works by converting a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called ``wide gap''. In a ``wide gap'' problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the ``wide gap''. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms on IEEE CEC2017 benchmarks in constrained optimisation

Benchmarking Evolutionary Algorithms For Single Objective Real-valued Constrained Optimization - A Critical Review

Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.Comment: This manuscript is a preprint version of an article published in Swarm and Evolutionary Computation, Elsevier, 2018. Number of pages: 4

Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimization. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimization. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimization, but MOEAs based on non-dominance, such as PMODE, may not

Material Generation Algorithm: A Novel Metaheuristic Algorithm for Optimization of Engineering Problems

A new algorithm, Material Generation Algorithm (MGA), was developed and applied for the optimum design of engineering problems. Some advanced and basic aspects of material chemistry, specifically the configuration of chemical compounds and chemical reactions in producing new materials, are determined as inspirational concepts of the MGA. For numerical investigations purposes, 10 constrained optimization problems in different dimensions of 10, 30, 50, and 100, which have been benchmarked by the Competitions on Evolutionary Computation (CEC), are selected as test examples while 15 of the well-known engineering design problems are also determined to evaluate the overall performance of the proposed method. The best results of different classical and new metaheuristic optimization algorithms in dealing with the selected problems were taken from the recent literature for comparison with MGA. Additionally, the statistical values of the MGA algorithm, consisting of the mean, worst, and standard deviation, were calculated and compared to the results of other metaheuristic algorithms. Overall, this work demonstrates that the proposed MGA is able provide very competitive, and even outstanding, results and mostly outperforms other metaheuristics