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.
This report presents benchmarking results of the latest version of the Hill-Valley Evolutionary Algorithm (HillVallEA) on the CEC2013 niching benchmark suite. The benchmarking follows restrictions required by the GECCO 2018 competition on Niching methods for Multimodal Optimization. In particular, no problem dependent parameter tuning is performed. A number of adjustments have been made to original publication of HillVallEA that are discussed in this report.
MToP: A MATLAB Benchmarking Platform for Evolutionary Multitasking
School of Computer Science, China University of Geosciences（中国地质大学计算机学院）；Trustworthy and General Artificial Intelligence Laboratory, School of Engineering, Westlake University（西湖大学工学院可信与通用人工智能实验室）；College of Systems Engineering, National University of Defense Technology（国防科技大学系统工程学院）；School of Computer Engineering, Hubei University of Arts and Science（湖北文理学院计算机工程学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research（新加坡科技研究局前沿人工智能研究中心）
Real-valued genotypes together with the variation operators, mutation and crossover, constitute some of the fundamental building blocks of Evolutionary Algorithms. Real-valued genotypes are utilized in a broad range of contexts, from weights in Artificial Neural Networks to parameters in robot control systems. Shared between most uses of real-valued genomes is the need for limiting the range of individual parameters to allowable bounds. In this paper we will illustrate the challenge of limiting the parameters of real-valued genomes and analyse the most promising method to properly limit these …
This report presents benchmarking results of the Hill-Valley Evolutionary Algorithm version 2019 (HillVallEA19) on the CEC2013 niching benchmark suite under the restrictions of the GECCO 2019 niching competition on multimodal optimization. Performance is compared to algorithms that participated in previous editions of the niching competition.
The stochastic nature of iterative optimization heuristics leads to inherently noisy performance measurements. Since these measurements are often gathered once and then used repeatedly, the number of collected samples will have a significant impact on the reliability of algorithm comparisons. We show that care should be taken when making decisions based on limited data. Particularly, we show that the number of runs used in many benchmarking studies, e.g., the default value of 15 suggested by the COCO environment, can be insufficient to reliably rank algorithms on well-known numerical optimizat…
Neural architecture search (NAS), which automatically designs the architectures of deep neural networks, has achieved breakthrough success over many applications in the past few years. Among different classes of NAS methods, evolutionary computation based NAS (ENAS) methods have recently gained much attention. Unfortunately, the issues of fair comparisons and efficient evaluations have hindered the development of ENAS. The current benchmark architecture datasets designed for fair comparisons only provide the datasets, not the ENAS algorithms or the platform to run the algorithms. The existing …
Southern University of Science and Technology（南方科技大学）
In the evolutionary multi-objective optimization (EMO) field, the standard practice is to present the final population of an EMO algorithm as the output. However, it has been shown that the final population often includes solutions which are dominated by other solutions generated and discarded in previous generations. Recently, a new EMO framework has been proposed to solve this issue by storing all the non-dominated solutions generated during the evolution in an archive and selecting a subset of solutions from the archive as the output. The key component in this framework is the subset select…
First Mathematical Runtime Analyses of Multi-Objective Evolutionary Algorithms for Multi-Valued Decision Variables
School of Computer Science and Technology, National Key Laboratory of Smart Farm Technologies and Systems, International Research Institute for Artificial Intelligence（计算机科学与技术学院，智慧农业技术与系统国家重点实验室，人工智能国际研究院）；Pengcheng Laboratory, Shenzhen, China（鹏城实验室）；Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Institut Polytechnique de Paris, Palaiseau, France（巴黎理工学院）；Laboratoire d’Informatique (LIX), CNRS, École Polytechnique（计算机实验室（LIX），法国国家科学研究中心，巴黎综合理工学院）
Theoretical and empirical research on evolutionary computation methods complement each other by providing two fundamentally different approaches towards a better understanding of black-box optimization heuristics. In discrete optimization, both streams developed rather independently of each other, but we observe today an increasing interest in reconciling these two sub-branches. In continuous optimization, the COCO (COmparing Continuous Optimisers) benchmarking suite has established itself as an important platform that theoreticians and practitioners use to exchange research ideas and question…
Model-based evolutionary algorithms (EAs) adapt an underlying search model to features of the problem at hand, such as the linkage between problem variables. The performance of EAs often deteriorates as multiple modes in the fitness landscape are modelled with a unimodal search model. The number of modes is however often unknown a priori, especially in a black-box setting, which complicates adaptation of the search model. In this work, we focus on models that can adapt to the multi-modality of the fitness landscape. Specifically, we introduce Hill-Valley Clustering, a remarkably simple approac…
We present IOHexperimenter, the experimentation module of the IOHprofiler project, which aims at providing an easy-to-use and highly customizable toolbox for benchmarking iterative optimization heuristics such as local search, evolutionary and genetic algorithms, Bayesian optimization techniques, etc. IOHexperimenter can be used as a stand-alone tool or as part of a benchmarking pipeline that uses other components of IOHprofiler such as IOHanalyzer, the module for interactive performance analysis and visualization. IOHexperimenter provides an efficient interface between optimization problems a…
A key challenge in the application of evolutionary algorithms in practice is the selection of an algorithm instance that best suits the problem at hand. What complicates this decision further is that different algorithms may be best suited for different stages of the optimization process. Dynamic algorithm selection and configuration are therefore well-researched topics in evolutionary computation. However, while hyper-heuristics and parameter control studies typically assume a setting in which the algorithm needs to be chosen while running the algorithms, without prior information, AutoML app…
In model-based evolutionary algorithms (EAs), the underlying search distribution is adapted to the problem at hand, for example based on dependencies between decision variables. Hill-valley clustering is an adaptive niching method in which a set of solutions is clustered such that each cluster corresponds to a single mode in the fitness landscape. This can be used to adapt the search distribution of an EA to the number of modes, exploring each mode separately. Especially in a black-box setting, where the number of modes is a priori unknown, an adaptive approach is essential for good performanc…
The development, assessment, and comparison of randomized search algorithms heavily rely on benchmarking. Regarding the domain of constrained optimization, the number of currently available benchmark environments bears no relation to the number of distinct problem features. The present paper advances a proposal of a scalable linear constrained optimization problem that is suitable for benchmarking Evolutionary Algorithms. By comparing two recent EA variants, the linear benchmarking environment is demonstrated.
Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A meta-heuristic algorithm is a problem-independent technique that can be applied to a broad range of problems. In this experiment, some of the evolutionary algorithms will be tested, evaluated, and compared with each other. We will go through the Genetic Algorithm\, Differential Evolution, Particle Swarm Optimization Algorithm, Grey Wolf Optimizer, and Simulated An…
The University of Adelaide（阿德莱德大学）；Nanjing University（南京大学）；Leiden University（莱顿大学）
Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for a wide class of submodular problems under various types of constraints while clearly outperforming standard greedy approximation algorithms. This paper introduces a setup for benchmarking algorithms for submodular optimization problems with the aim to provide researchers with a framework to enhance and compare the performance of new algorithms for submodular…
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem, and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.
In this paper, we first propose a graph neural network encoding method for multiobjective evolutionary algorithm to handle the community detection problem in complex attribute networks. In the graph neural network encoding method, each edge in an attribute network is associated with a continuous variable. Through non-linear transformation, a continuous valued vector (i.e. a concatenation of the continuous variables associated with the edges) is transferred to a discrete valued community grouping solution. Further, two objective functions for single- and multi-attribute network are proposed to …
This paper presents a comparative analysis of the performance of the Incremental Ant Colony algorithm for continuous optimization ($IACO_\mathbb{R}$), with different algorithms provided in the NLopt library. The key objective is to understand how the various algorithms in the NLopt library perform in combination with the Multi Trajectory Local Search (Mtsls1) technique. A hybrid approach has been introduced in the local search strategy by the use of a parameter which allows for probabilistic selection between Mtsls1 and a NLopt algorithm. In case of stagnation, the algorithm switch is made bas…
We propose a new approach for building recommender systems by adapting surrogate-assisted interactive genetic algorithms. A pool of user-evaluated items is used to construct an approximative model which serves as a surrogate fitness function in a genetic algorithm for optimizing new suggestions. The surrogate is used to recommend new items to the user, which are then evaluated according to the user's liking and subsequently removed from the search space. By updating the surrogate model after new recommendations have been evaluated by the user, we enable the model itself to evolve towards the u…
Babeş-Bolyai University（巴比什-博雅依大学）；Faculty of Mathematics and Computer Science（数学与计算机科学学院）
A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for generating the individuals of a new generation. The evolved pattern is embedded into a standard evolutionary scheme that is used for solving a particular problem. Several evolutionary algorithms for function optimization are evolved by using the considered model. The evolved evolutionary algorithms are compared with a human-designed Genetic Algorithm. Numerical ex…
We have employed a recent implementation of genetic algorithms to study a range of standard benchmark functions for global optimization. It turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters. The latter properties seem to be simulated better by two other types of benchmark functions. One type is designed to be decept…
Most experimental studies initialize the population of evolutionary algorithms with random genotypes. In practice, however, optimizers are typically seeded with good candidate solutions either previously known or created according to some problem-specific method. This "seeding" has been studied extensively for single-objective problems. For multi-objective problems, however, very little literature is available on the approaches to seeding and their individual benefits and disadvantages. In this article, we are trying to narrow this gap via a comprehensive computational study on common real-val…
Block-Bench: A Framework for Controllable and Transparent Discrete Optimization Benchmarking
LIACS, Leiden University（莱顿大学）；Optimisation and Logistics, School of Computer Science and Information Technology, Adelaide University（阿德莱德大学）；Adelaide University（阿德莱德大学）
The most common representation in evolutionary computation are bit strings. This is ideal to model binary decision variables, but less useful for variables taking more values. With very little theoretical work existing on how to use evolutionary algorithms for such optimization problems, we study the run time of simple evolutionary algorithms on some OneMax-like functions defined over $Ω= \{0, 1, \dots, r-1\}^n$. More precisely, we regard a variety of problem classes requesting the component-wise minimization of the distance to an unknown target vector $z \in Ω$. For such problems we see a cru…
Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently embedded in many evolutionary algorithms. In this paper, we identify such a relation by proposing a unified analysis framework for a generalized simple multi-objective evolutionary algorithm (GSEMO), and apply it on a minimum weight general cover problem. For a wide range of problems (including the the minimum submodular cover problem in which the submodular fu…
Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the dimensions increase. In this paper, we will use the dimensionality reduction method Principal component analysis (PCA) to reduce the dimension during the iteration of Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is a good Evolutionary Algorithm that is presented as the numeric type and useful for different kinds of problems. We assess the p…
Institute of Automation and Computer Science, Brno University of Technology（布尔诺理工大学自动化与计算机科学学院）
The center-bias (or zero-bias) operator has recently been identified as one of the problems plaguing the benchmarking of evolutionary computation methods. This operator lets the methods that utilize it easily optimize functions that have their respective optima in the center of the feasible set. In this paper, we describe a simple procedure that can be used to identify methods that incorporate a center-bias operator and use it to investigate 90 evolutionary computation methods that were published between 1987 and 2022. We show that more than half (47 out of the 90) of the considered methods ha…
Research on new optimization algorithms is often funded based on the motivation that such algorithms might improve the capabilities to deal with real-world and industrially relevant optimization challenges. Besides a huge variety of different evolutionary and metaheuristic optimization algorithms, also a large number of test problems and benchmark suites have been developed and used for comparative assessments of algorithms, in the context of global, continuous, and black-box optimization. For many of the commonly used synthetic benchmark problems or artificial fitness landscapes, there are ho…
Designing optimisation algorithms that perform well in general requires experimentation on a range of diverse problems. Training neural networks is an optimisation task that has gained prominence with the recent successes of deep learning. Although evolutionary algorithms have been used for training neural networks, gradient descent variants are by far the most common choice with their trusted good performance on large-scale machine learning tasks. With this paper we contribute CORNN (Continuous Optimisation of Regression tasks using Neural Networks), a large suite for benchmarking the perform…
In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets (PSS) in the variable space. Such problems are practically relevant when a decision maker (DM) is interested in identifying alternative designs with similar performance. There has been significant research interest in recent years to develop efficient algorithms to deal with MMOPs. However, the existing algorithms still require prohibitive number of function e…
The Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA) has been proven effective and efficient in solving real-world problems. A prime example is optimizing treatment plans for prostate cancer brachytherapy, an internal form of radiation treatment, for which equally important clinical aims from a base protocol are grouped into two objectives and bi-objectively optimized. This use of MO-RV-GOMEA was recently successfully introduced into clinical practice. Brachytherapy can also play an important role in treating cervical cancer. However, using the same app…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic grating design problem. Unfortunately, most traditional optimization techniques focus on solving for a single optimal solution. They need to be applied several times; yet all solutions are not guaranteed to be found. Thus the multimodal optimization problem was proposed. In that problem, we are interested in not only a single optimal point, but also the others. …
The unit commitment (UC) problem is a nonlinear, high-dimensional, highly constrained, mixed-integer power system optimization problem and is generally solved in the literature considering minimizing the system operation cost as the only objective. However, due to increasing environmental concerns, the recent attention has shifted to incorporating emission in the problem formulation. In this paper, a multi-objective evolutionary algorithm based on decomposition (MOEA/D) is proposed to solve the UC problem as a multi-objective optimization problem considering minimizing cost and emission as the…
This paper presents the main characteristics of the evolutionary optimization code named EOS, Evolutionary Optimization at Sapienza, and its successful application to challenging, real-world space trajectory optimization problems. EOS is a global optimization algorithm for constrained and unconstrained problems of real-valued variables. It implements a number of improvements to the well-known Differential Evolution (DE) algorithm, namely, a self-adaptation of the control parameters, an epidemic mechanism, a clustering technique, an $\varepsilon$-constrained method to deal with nonlinear constr…
Yandex；National Research University Higher School of Economics（俄罗斯国立高等经济研究大学）
Most decision tree induction algorithms are based on a greedy top-down recursive partitioning strategy for tree growth. In this paper, we propose several methods for induction of decision trees and their ensembles based on evolutionary algorithms. The main difference of our approach is using real-valued vector representation of decision tree that allows to use a large number of different optimization algorithms, as well as optimize the whole tree or ensemble for avoiding local optima. Differential evolution and evolution strategies were chosen as optimization algorithms, as they have good resu…
