scholarly journals Average convergence rate of evolutionary algorithms in continuous optimization

2021 ◽  
Vol 562 ◽  
pp. 200-219
Author(s):  
Yu Chen ◽  
Jun He
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Continuous Optimization

scholarly journals Heliostat Field Layout Optimization with Evolutionary Algorithms

10.29007/7p6t ◽  
2018 ◽  
Author(s):  
Pascal Richter ◽  
David Laukamp ◽  
Levin Gerdes ◽  
Martin Frank ◽  
Erika Ábrahám
Keyword(s):  
Power Plant ◽  
Convex Optimization ◽  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Computer Science ◽  
Energy Supply ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
New Genotype

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant.We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals.Experimental results show the applicability of our approach.

scholarly journals A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems

2020 ◽  
Vol 28 (1) ◽  
pp. 55-85
Author(s):  
Bo Song ◽  
Victor O.K. Li
Keyword(s):  
Population Dynamics ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Analytical Framework ◽  
Population Models ◽  
Initial Population ◽  
Infinite Population ◽  
Continuous Optimization Problems

Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the [Formula: see text]-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed.

scholarly journals On the Hardness of Offline Multi-objective Optimization

2007 ◽  
Vol 15 (4) ◽  
pp. 475-491 ◽  
Author(s):  
Olivier Teytaud
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Random Search ◽  
Computational Cost ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Insight Into ◽  
Better Than

It has been empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. This paper shows that the convergence rate of all comparison-based multi-objective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search under certain conditions. The number of objectives must be very moderate and the framework should hold the following assumptions: the objectives are conflicting and the computational cost is lower bounded by the number of comparisons is a good model. Our conclusions are: (i) the number of conflicting objectives is relevant (ii) the criteria based on comparisons with random-search for multi-objective optimization is also relevant (iii) having more than 3-objectives optimization is very hard. Furthermore, we provide some insight into cross-over operators.

Evolutionary algorithms and elliptical copulas applied to continuous optimization problems

2016 ◽  
Vol 369 ◽  
pp. 419-440 ◽  
Author(s):  
Harold Dias de Mello Junior ◽  
Luis Martí ◽  
André V. Abs da Cruz ◽  
Marley M.B. Rebuzzi Vellasco
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Continuous Optimization Problems

scholarly journals Automatically Designing State-of-the-Art Multi- and Many-Objective Evolutionary Algorithms

2020 ◽  
Vol 28 (2) ◽  
pp. 195-226 ◽  
Author(s):  
Leonardo C. T. Bezerra ◽  
Manuel López-Ibáñez ◽  
Thomas Stützle
Keyword(s):  
Evolutionary Algorithms ◽  
Performance Metrics ◽  
State Of The Art ◽  
Continuous Optimization ◽  
Parameter Tuning ◽  
High Performing ◽  
Performance Metric ◽  
Wide Range ◽  
Algorithmic Framework ◽  
Art Performance

A recent comparison of well-established multiobjective evolutionary algorithms (MOEAs) has helped better identify the current state-of-the-art by considering (i) parameter tuning through automatic configuration, (ii) a wide range of different setups, and (iii) various performance metrics. Here, we automatically devise MOEAs with verified state-of-the-art performance for multi- and many-objective continuous optimization. Our work is based on two main considerations. The first is that high-performing algorithms can be obtained from a configurable algorithmic framework in an automated way. The second is that multiple performance metrics may be required to guide this automatic design process. In the first part of this work, we extend our previously proposed algorithmic framework, increasing the number of MOEAs, underlying evolutionary algorithms, and search paradigms that it comprises. These components can be combined following a general MOEA template, and an automatic configuration method is used to instantiate high-performing MOEA designs that optimize a given performance metric and present state-of-the-art performance. In the second part, we propose a multiobjective formulation for the automatic MOEA design, which proves critical for the context of many-objective optimization due to the disagreement of established performance metrics. Our proposed formulation leads to an automatically designed MOEA that presents state-of-the-art performance according to a set of metrics, rather than a single one.

An exploration-enhanced elephant herding optimization

2019 ◽  
Vol 36 (9) ◽  
pp. 3029-3046 ◽  
Author(s):  
Islam A. ElShaarawy ◽  
Essam H. Houssein ◽  
Fatma Helmy Ismail ◽  
Aboul Ella Hassanien
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Search Space ◽  
Exploration And Exploitation ◽  
Content Type ◽  
Discrepancy Measure ◽  
The One ◽  
Star Discrepancy ◽  
Exploration Phase

Purpose The purpose of this paper is to propose an enhanced elephant herding optimization (EEHO) algorithm by improving the exploration phase to overcome the fast-unjustified convergence toward the origin of the native EHO. The exploration and exploitation of the proposed EEHO are achieved by updating both clan and separation operators. Design/methodology/approach The original EHO shows fast unjustified convergence toward the origin specifically, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms. Furthermore, the star discrepancy measure is adopted to quantify the quality of the exploration phase of evolutionary algorithms in general. Findings In experiments, EEHO has shown a better performance of convergence rate compared with the original EHO. Reasons behind this performance are: EEHO proposes a more exploitative search method than the one used in EHO and the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Operator γ is added to EEHO assists to escape from local optima, which commonly exist in the search space. The proposed EEHO controls the convergence rate and the random walk independently. Eventually, the quantitative and qualitative results revealed that the proposed EEHO outperforms the original EHO. Research limitations/implications Therefore, the pros and cons are reported as follows: pros of EEHO compared to EHO – 1) unbiased exploration of the whole search space thanks to the proposed update operator that fixed the unjustified convergence of the EHO toward the origin and the proposed separating operator that fixed the tendency of EHO to introduce new elephants at the boundary of the search space; and 2) the ability to control exploration–exploitation trade-off by independently controverting the convergence rate and the random walk using different parameters – cons EEHO compared to EHO: 1) suitable values for three parameters (rather than two only) have to be found to use EEHO. Originality/value As the original EHO shows fast unjustified convergence toward the origin specifically, the search method adopted in EEHO is more exploitative than the one used in EHO because of the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Further, the star discrepancy measure is adopted to quantify the quality of exploration phase of evolutionary algorithms in general. Operator γ that added EEHO allows the successive local and global searching (exploration and exploitation) and helps escaping from local minima that commonly exist in the search space.

scholarly journals OPTIMIZATION OF FIRE MONITORING SYSTEM USING THE DEFORMED STARS METHOD

2020 ◽  
pp. 60-66
Author(s):  
Vitaliy Snityuk ◽  
Marina Antonevich ◽  
Anna Didyk
Keyword(s):  
Evolutionary Algorithms ◽  
Monitoring System ◽  
Optimization Problem ◽  
Continuous Optimization ◽  
Function Optimization ◽  
Evolutionary Strategies ◽  
Fire Load ◽  
Material Loss ◽  
Fire Monitoring ◽  
Fire Alarm System

In this paper are being considered the aspects of two variables function optimization problem solving, which, in general, is poly-extremal and undifferentiated. The classic methods of continuous optimization are not applicable in this case. One of the most commonly used methods of solving this problem is evolutionary algorithms, which can be divided into two classes. The first class includes algorithms where a potential offspring-solution is generated by two parent-solutions solutions, in the second case, the offspring-solution is generated by one parent-solution. There is deformed star method proposed where the population of parental solutions is 3, 4, and 5 point groups. The application of proposed method is shown to solve the optimization problem of fire monitoring system for buildings, which minimizes the time of its operation. The buildings where fire load can be both permanent and variable are considered. Such buildings include concert halls, nightclubs, supermarkets, logistics facilities and more. Fires at such buildings result in human sacrifice and serious material loss. Timely activation of the fire alarm system have great importance. The objective function of the problem is determined by the distance from the horizontal projections of the detectors to the sources of fire and the probability of triggering the detectors. The solution is optimizing location of fire detectors, taking into account their number and the fire load of the room. The advantages of the developed method over genetic algorithms, evolutionary strategies and differential evolution as the most typical evolutionary algorithms are shown. Numerical experiments were carried out, which showed the increased accuracy of calculations and the increased speed of method convergence.

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