12 research outputs found
Explainable Benchmarking for Iterative Optimization Heuristics
Benchmarking heuristic algorithms is vital to understand under which
conditions and on what kind of problems certain algorithms perform well. In
most current research into heuristic optimization algorithms, only a very
limited number of scenarios, algorithm configurations and hyper-parameter
settings are explored, leading to incomplete and often biased insights and
results. This paper presents a novel approach we call explainable benchmarking.
Introducing the IOH-Xplainer software framework, for analyzing and
understanding the performance of various optimization algorithms and the impact
of their different components and hyper-parameters. We showcase the framework
in the context of two modular optimization frameworks. Through this framework,
we examine the impact of different algorithmic components and configurations,
offering insights into their performance across diverse scenarios. We provide a
systematic method for evaluating and interpreting the behaviour and efficiency
of iterative optimization heuristics in a more transparent and comprehensible
manner, allowing for better benchmarking and algorithm design.Comment: Submitted to ACM TEL
COCO: Performance Assessment
We present an any-time performance assessment for benchmarking numerical
optimization algorithms in a black-box scenario, applied within the COCO
benchmarking platform. The performance assessment is based on runtimes measured
in number of objective function evaluations to reach one or several quality
indicator target values. We argue that runtime is the only available measure
with a generic, meaningful, and quantitative interpretation. We discuss the
choice of the target values, runlength-based targets, and the aggregation of
results by using simulated restarts, averages, and empirical distribution
functions
Towards Dynamic Algorithm Selection for Numerical Black-Box Optimization: Investigating BBOB as a Use Case
One of the most challenging problems in evolutionary computation is to select
from its family of diverse solvers one that performs well on a given problem.
This algorithm selection problem is complicated by the fact that different
phases of the optimization process require different search behavior. While
this can partly be controlled by the algorithm itself, there exist large
differences between algorithm performance. It can therefore be beneficial to
swap the configuration or even the entire algorithm during the run. Long deemed
impractical, recent advances in Machine Learning and in exploratory landscape
analysis give hope that this dynamic algorithm configuration~(dynAC) can
eventually be solved by automatically trained configuration schedules. With
this work we aim at promoting research on dynAC, by introducing a simpler
variant that focuses only on switching between different algorithms, not
configurations. Using the rich data from the Black Box Optimization
Benchmark~(BBOB) platform, we show that even single-switch dynamic Algorithm
selection (dynAS) can potentially result in significant performance gains. We
also discuss key challenges in dynAS, and argue that the BBOB-framework can
become a useful tool in overcoming these
Integrated vs. sequential approaches for selecting and tuning CMA-ES variants
Algorithms and the Foundations of Software technolog
From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms
Estimation-of-distribution algorithms (EDAs) are optimization algorithms that
learn a distribution on the search space from which good solutions can be
sampled easily. A key parameter of most EDAs is the sample size (population
size). If the population size is too small, the update of the probabilistic
model builds on few samples, leading to the undesired effect of genetic drift.
Too large population sizes avoid genetic drift, but slow down the process.
Building on a recent quantitative analysis of how the population size leads
to genetic drift, we design a smart-restart mechanism for EDAs. By stopping
runs when the risk for genetic drift is high, it automatically runs the EDA in
good parameter regimes.
Via a mathematical runtime analysis, we prove a general performance guarantee
for this smart-restart scheme. This in particular shows that in many situations
where the optimal (problem-specific) parameter values are known, the restart
scheme automatically finds these, leading to the asymptotically optimal
performance.
We also conduct an extensive experimental analysis. On four classic benchmark
problems, we clearly observe the critical influence of the population size on
the performance, and we find that the smart-restart scheme leads to a
performance close to the one obtainable with optimal parameter values. Our
results also show that previous theory-based suggestions for the optimal
population size can be far from the optimal ones, leading to a performance
clearly inferior to the one obtained via the smart-restart scheme. We also
conduct experiments with PBIL (cross-entropy algorithm) on two combinatorial
optimization problems from the literature, the max-cut problem and the
bipartition problem. Again, we observe that the smart-restart mechanism finds
much better values for the population size than those suggested in the
literature, leading to a much better performance.Comment: Accepted for publication in "Journal of Machine Learning Research".
Extended version of our GECCO 2020 paper. This article supersedes
arXiv:2004.0714
A model of anytime algorithm performance for bi-objective optimization
International audienceAnytime algorithms allow a practitioner to trade-off runtime for solution quality. This is of particular interest in multi-objective combinatorial optimization since it can be infeasible to identify all efficient solutions in a reasonable amount of time. We present a theoretical model that, under some mild assumptions, characterizes the “optimal” trade-off between runtime and solution quality, measured in terms of relative hypervolume, of anytime algorithms for bi-objective optimization. In particular, we assume that efficient solutions are collected sequentially such that the collected solution at each iteration maximizes the hypervolume indicator, and that the non-dominated set can be well approximated by a quadrant of a superellipse. We validate our model against an “optimal” model that has complete knowledge of the non-dominated set. The empirical results suggest that our theoretical model approximates the behavior of this optimal model quite well. We also analyze the anytime behavior of an ε-constraint algorithm, and show that our model can be used to guide the algorithm and improve its anytime behavior
関数最適化問題に対する適応型差分進化法の研究
学位の種別: 課程博士審査委員会委員 : (主査)東京大学准教授 福永 アレックス, 東京大学教授 池上 高志, 東京大学教授 植田 一博, 東京大学教授 山口 泰, 東京大学教授 伊庭 斉志University of Tokyo(東京大学
Globally convergent evolution strategies with application to Earth imaging problem in geophysics
Au cours des dernières années, s’est développé un intérêt tout particulier pour l’optimisation sans dérivée. Ce domaine de recherche se divise en deux catégories: une déterministe et l’autre stochastique. Bien qu’il s’agisse du même domaine, peu de liens ont déjà été établis entre ces deux branches. Cette thèse a pour objectif de combler cette lacune, en montrant comment les techniques issues de l’optimisation déterministe peuvent améliorer la performance des stratégies évolutionnaires, qui font partie des meilleures méthodes en optimisation stochastique. Sous certaines hypothèses, les modifications réalisées assurent une forme de convergence globale, c’est-à-dire une convergence vers un point stationnaire de premier ordre indépendamment du point de départ choisi. On propose ensuite d’adapter notre algorithme afin qu’il puisse traiter des problèmes avec des contraintes générales. On montrera également comment améliorer les performances numériques des stratégies évolutionnaires en incorporant un pas de recherche au début de chaque itération, dans laquelle on construira alors un modèle quadratique utilisant les points où la fonction coût a déjà été évaluée. Grâce aux récents progrès techniques dans le domaine du calcul parallèle, et à la nature parallélisable des stratégies évolutionnaires, on propose d’appliquer notre algorithme pour résoudre un problème inverse d’imagerie sismique. Les résultats obtenus ont permis d’améliorer la résolution de ce problème. ABSTRACT : In recent years, there has been significant and growing interest in Derivative-Free Optimization (DFO). This field can be divided into two categories: deterministic and stochastic. Despite addressing the same problem domain, only few interactions between the two DFO categories were established in the existing literature. In this thesis, we attempt to bridge this gap by showing how ideas from deterministic DFO can improve the efficiency and the rigorousness of one of the most successful class of stochastic algorithms, known as Evolution Strategies (ES’s). We propose to equip a class of ES’s with known techniques from deterministic DFO. The modified ES’s achieve rigorously a form of global convergence under reasonable assumptions. By global convergence, we mean convergence to first-order stationary points independently of the starting point. The modified ES’s are extended to handle general constrained optimization problems. Furthermore, we show how to significantly improve the numerical performance of ES’s by incorporating a search step at the beginning of each iteration. In this step, we build a quadratic model using the points where the objective function has been previously evaluated. Motivated by the recent growth of high performance computing resources and the parallel nature of ES’s, an application of our modified ES’s to Earth imaging Geophysics problem is proposed. The obtained results provide a great improvement for the problem resolution