1,853 research outputs found
Multiplicative Approximations, Optimal Hypervolume Distributions, and the Choice of the Reference Point
Many optimization problems arising in applications have to consider several
objective functions at the same time. Evolutionary algorithms seem to be a very
natural choice for dealing with multi-objective problems as the population of
such an algorithm can be used to represent the trade-offs with respect to the
given objective functions. In this paper, we contribute to the theoretical
understanding of evolutionary algorithms for multi-objective problems. We
consider indicator-based algorithms whose goal is to maximize the hypervolume
for a given problem by distributing {\mu} points on the Pareto front. To gain
new theoretical insights into the behavior of hypervolume-based algorithms we
compare their optimization goal to the goal of achieving an optimal
multiplicative approximation ratio. Our studies are carried out for different
Pareto front shapes of bi-objective problems. For the class of linear fronts
and a class of convex fronts, we prove that maximizing the hypervolume gives
the best possible approximation ratio when assuming that the extreme points
have to be included in both distributions of the points on the Pareto front.
Furthermore, we investigate the choice of the reference point on the
approximation behavior of hypervolume-based approaches and examine Pareto
fronts of different shapes by numerical calculations
Pareto Optimization for Subset Selection with Dynamic Cost Constraints
We consider the subset selection problem for function with constraint
bound that changes over time. Within the area of submodular optimization,
various greedy approaches are commonly used. For dynamic environments we
observe that the adaptive variants of these greedy approaches are not able to
maintain their approximation quality. Investigating the recently introduced
POMC Pareto optimization approach, we show that this algorithm efficiently
computes a -approximation, where
is the submodularity ratio of , for each possible constraint
bound . Furthermore, we show that POMC is able to adapt its set of
solutions quickly in the case that increases. Our experimental
investigations for the influence maximization in social networks show the
advantage of POMC over generalized greedy algorithms. We also consider EAMC, a
new evolutionary algorithm with polynomial expected time guarantee to maintain
approximation ratio, and NSGA-II as an advanced multi-objective
optimization algorithm, to demonstrate their challenges in optimizing the
maximum coverage problem. Our empirical analysis shows that, within the same
number of evaluations, POMC is able to outperform NSGA-II under linear
constraint, while EAMC performs significantly worse than all considered
algorithms in most cases.Comment: A preliminary version of this article has been presented at the
Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019
Plateaus can be harder in multi-objective optimization
AbstractIn recent years a lot of progress has been made in understanding the behavior of evolutionary computation methods for single- and multi-objective problems. Our aim is to analyze the diversity mechanisms that are implicitly used in evolutionary algorithms for multi-objective problems by rigorous runtime analyses. We show that, even if the population size is small, the runtime can be exponential where corresponding single-objective problems are optimized within polynomial time. To illustrate this behavior we analyze a simple plateau function in a first step and extend our result to a class of instances of the well-known SetCover problem
Analysis of the (1+1) EA on LeadingOnes with Constraints
Understanding how evolutionary algorithms perform on constrained problems has
gained increasing attention in recent years. In this paper, we study how
evolutionary algorithms optimize constrained versions of the classical
LeadingOnes problem. We first provide a run time analysis for the classical
(1+1) EA on the LeadingOnes problem with a deterministic cardinality
constraint, giving as the tight bound. Our
results show that the behaviour of the algorithm is highly dependent on the
constraint bound of the uniform constraint. Afterwards, we consider the problem
in the context of stochastic constraints and provide insights using
experimental studies on how the (+1) EA is able to deal with these
constraints in a sampling-based setting
COORDINATIVE THRESHOLD IN RACE WALKING
According to the international competition rules race walkers have to keep contact to the ground and their knee straightened. In order to investigate the influence of adhering to the rules 20 race walkers performed a step test on a treadmill. Depending on velocity, movement coordination changed from a correct walking technique to an incorrect one and afterwards to running. Incorrect walking begins with occurrence of flight time and bending knee dependent on performance level between velocities of 2.75 to 4.0 m/s. The investigation shows a linear function between velocity and flight time, and a nonlinear one between velocity and knee straightening. To mark the maximum increase of offence against knee rule in course of velocity the term of coordinative threshold is introduced
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