1,681 research outputs found
On the Impact of Multiobjective Scalarizing Functions
Recently, there has been a renewed interest in decomposition-based approaches
for evolutionary multiobjective optimization. However, the impact of the choice
of the underlying scalarizing function(s) is still far from being well
understood. In this paper, we investigate the behavior of different scalarizing
functions and their parameters. We thereby abstract firstly from any specific
algorithm and only consider the difficulty of the single scalarized problems in
terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes.
Secondly, combining the outcomes of independent single-objective runs allows
for more general statements on set-based performance measures. Finally, we
investigate the correlation between the opening angle of the scalarizing
function's underlying contour lines and the position of the final solution in
the objective space. Our analysis is of fundamental nature and sheds more light
on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives
The properties of local optimal solutions in multi-objective combinatorial
optimization problems are crucial for the effectiveness of local search
algorithms, particularly when these algorithms are based on Pareto dominance.
Such local search algorithms typically return a set of mutually nondominated
Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper
investigates two aspects of PLO-sets by means of experiments with Pareto local
search (PLS). First, we examine the impact of several problem characteristics
on the properties of PLO-sets for multi-objective NK-landscapes with correlated
objectives. In particular, we report that either increasing the number of
objectives or decreasing the correlation between objectives leads to an
exponential increment on the size of PLO-sets, whereas the variable correlation
has only a minor effect. Second, we study the running time and the quality
reached when using bounding archiving methods to limit the size of the archive
handled by PLS, and thus, the maximum size of the PLO-set found. We argue that
there is a clear relationship between the running time of PLS and the
difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII,
Ljubljana : Slovenia (2014
Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes
In multiobjective combinatorial optimization, there exists two main classes
of metaheuristics, based either on multiple aggregations, or on a dominance
relation. As in the single objective case, the structure of the search space
can explain the difficulty for multiobjective metaheuristics, and guide the
design of such methods. In this work we analyze the properties of
multiobjective combinatorial search spaces. In particular, we focus on the
features related the efficient set, and we pay a particular attention to the
correlation between objectives. Few benchmark takes such objective correlation
into account. Here, we define a general method to design multiobjective
problems with correlation. As an example, we extend the well-known
multiobjective NK-landscapes. By measuring different properties of the search
space, we show the importance of considering the objective correlation on the
design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Shift-based density estimation for pareto-based algorithms in many-objective optimization
It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation that only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Pareto-based algorithms demonstrates its usefulness in handling many-objective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle many-objective problems, but also present a general extension of Pareto-based algorithms in many-objective optimization. © 2013 IEEE
Global vs local search on multi-objective NK-landscapes: contrasting the impact of problem features
Best paper award (ECOM track)International audienc
On the Combined Impact of Population Size and Sub-problem Selection in MOEA/D
This paper intends to understand and to improve the working principle of
decomposition-based multi-objective evolutionary algorithms. We review the
design of the well-established Moea/d framework to support the smooth
integration of different strategies for sub-problem selection, while
emphasizing the role of the population size and of the number of offspring
created at each generation. By conducting a comprehensive empirical analysis on
a wide range of multi-and many-objective combinatorial NK landscapes, we
provide new insights into the combined effect of those parameters on the
anytime performance of the underlying search process. In particular, we show
that even a simple random strategy selecting sub-problems at random outperforms
existing sophisticated strategies. We also study the sensitivity of such
strategies with respect to the ruggedness and the objective space dimension of
the target problem.Comment: European Conference on Evolutionary Computation in Combinatorial
Optimization, Apr 2020, Seville, Spai
Shake them all! Rethinking Selection and Replacement in MOEA/D
International audienceWe build upon the previous efforts to enhance the search ability of Moead (a decomposition-based algorithm), by investigating the idea of evolving the whole population simultaneously at once. We thereby propose new alternative selection and replacement strategies that can be combined in different ways within a generic and problem-independent framework. To assess the performance of our strategies, we conduct a comprehensive experimental study on bi-objective combinatorial optimization problems. More precisely, we consider ρMNK-landscapes and knapsack problems as a benchmark, and experiment a wide range of parameter configurations for Moead and its variants. Our analysis reveals the effectiveness of our strategies and their robustness to parameter settings. In particular, substantial improvements are obtained compared to the conventional Moead
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