2,468 research outputs found
On the Construction of Pareto-Compliant Combined Indicators
The most relevant property that a quality indicator (QI) is expected to have is Pareto compliance, which means that every time an approximation set strictly dominates another in a Pareto sense, the indicator must reflect this. The hypervolume indicator and its variants are the only unary QIs known to be Pareto-compliant but there are many commonly used weakly Pareto-compliant indicators such as R2, IGD+,andÉ›+. Currently, an open research area is related to finding new Pareto-compliant indicators whose preferences are different from those of the hypervolume indicator. In this article, we propose a theoretical basis to combine existing weakly Pareto-compliant indicators with at least one being Pareto-compliant, such that the resulting combined indicator is Pareto-compliant as well. Most importantly, we show that the combination of Paretocompliant QIs with weakly Pareto-compliant indicators leads to indicators that inherit properties of the weakly compliant indicators in terms of optimal point distributions. The consequences of these new combined indicators are threefold: (1) to increase the variety of available Pareto-compliant QIs by correcting weakly Pareto-compliant indicators, (2) to introduce a general framework for the combination of QIs, and (3) to generate new selection mechanisms for multiobjective evolutionary algorithms where it is possible to achieve/adjust desired distributions on the Pareto front
Indicator Based Ant Colony Optimization for Multi-objective Knapsack Problem
AbstractThe use of metaheuristics to solve multi-objective optimization problems (MOP) is a very active research topic. Ant Colony Optimization (ACO) has received a growing interest in the last years for such problems. Many algorithms have been proposed in the literature to solve different MOP. This paper presents an indicator-based ant colony optimization algorithm called IBACO for the multi-objective knapsack problem (MOKP). The IBACO algorithm proposes a new idea that uses binary quality indicators to guide the search of artificial ants. These indicators were initially used by Zitzler and KĂĽnzli in the selection process of their evolutionary algorithm IBEA. In this paper, we use the indicator optimization principle to reinforce the best solutions by rewarding pheromone trails. We carry out a set of experiments on MOKP benchmark instances by applying the two binary indicators: epsilon indicator and hypervolume indicator. The comparison of the proposed algorithm with IBEA, ACO and other state-of-the-art evolutionary algorithms shows that IBACO is significantly better on most instances
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
Multi-Objective Archiving
Most multi-objective optimisation algorithms maintain an archive explicitly
or implicitly during their search. Such an archive can be solely used to store
high-quality solutions presented to the decision maker, but in many cases may
participate in the search process (e.g., as the population in evolutionary
computation). Over the last two decades, archiving, the process of comparing
new solutions with previous ones and deciding how to update the
archive/population, stands as an important issue in evolutionary
multi-objective optimisation (EMO). This is evidenced by constant efforts from
the community on developing various effective archiving methods, ranging from
conventional Pareto-based methods to more recent indicator-based and
decomposition-based ones. However, the focus of these efforts is on empirical
performance comparison in terms of specific quality indicators; there is lack
of systematic study of archiving methods from a general theoretical
perspective. In this paper, we attempt to conduct a systematic overview of
multi-objective archiving, in the hope of paving the way to understand
archiving algorithms from a holistic perspective of theory and practice, and
more importantly providing a guidance on how to design theoretically desirable
and practically useful archiving algorithms. In doing so, we also present that
archiving algorithms based on weakly Pareto compliant indicators (e.g.,
epsilon-indicator), as long as designed properly, can achieve the same
theoretical desirables as archivers based on Pareto compliant indicators (e.g.,
hypervolume indicator). Such desirables include the property limit-optimal, the
limit form of the possible optimal property that a bounded archiving algorithm
can have with respect to the most general form of superiority between solution
sets.Comment: 21 pages, 4 figures, journa
Quality Indicators for Preference-based Evolutionary Multi-objective Optimization Using a Reference Point: A Review and Analysis
Some quality indicators have been proposed for benchmarking preference-based
evolutionary multi-objective optimization algorithms using a reference point.
Although a systematic review and analysis of the quality indicators are helpful
for both benchmarking and practical decision-making, neither has been
conducted. In this context, first, this paper reviews existing regions of
interest and quality indicators for preference-based evolutionary
multi-objective optimization using the reference point. We point out that each
quality indicator was designed for a different region of interest. Then, this
paper investigates the properties of the quality indicators. We demonstrate
that an achievement scalarizing function value is not always consistent with
the distance from a solution to the reference point in the objective space. We
observe that the regions of interest can be significantly different depending
on the position of the reference point and the shape of the Pareto front. We
identify undesirable properties of some quality indicators. We also show that
the ranking of preference-based evolutionary multi-objective optimization
algorithms depends on the choice of quality indicators
BOtied: Multi-objective Bayesian optimization with tied multivariate ranks
Many scientific and industrial applications require joint optimization of
multiple, potentially competing objectives. Multi-objective Bayesian
optimization (MOBO) is a sample-efficient framework for identifying
Pareto-optimal solutions. We show a natural connection between non-dominated
solutions and the highest multivariate rank, which coincides with the outermost
level line of the joint cumulative distribution function (CDF). We propose the
CDF indicator, a Pareto-compliant metric for evaluating the quality of
approximate Pareto sets that complements the popular hypervolume indicator. At
the heart of MOBO is the acquisition function, which determines the next
candidate to evaluate by navigating the best compromises among the objectives.
Multi-objective acquisition functions that rely on box decomposition of the
objective space, such as the expected hypervolume improvement (EHVI) and
entropy search, scale poorly to a large number of objectives. We propose an
acquisition function, called BOtied, based on the CDF indicator. BOtied can be
implemented efficiently with copulas, a statistical tool for modeling complex,
high-dimensional distributions. We benchmark BOtied against common acquisition
functions, including EHVI and random scalarization (ParEGO), in a series of
synthetic and real-data experiments. BOtied performs on par with the baselines
across datasets and metrics while being computationally efficient.Comment: 10 pages (+5 appendix), 9 figures. Submitted to NeurIP
Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study
The permutation flowshop scheduling problem has been thoroughly studied in recent decades, both from single objective as well as from multi-objective perspectives. To the best of our knowledge, little has been done regarding the multi-objective flowshop with Pareto approach when sequence dependent setup times are considered. As setup times and multi-criteria problems are important in industry, we must focus on this area. We propose a simple, yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria. The presented method is referred to as Restarted Iterated Pareto Greedy or RIPG and is compared against the best performing approaches from the relevant literature. Comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed RIPG method clearly outperforms all other algorithms and, as a consequence, it is a state-of- art method for this important and practical scheduling problemThe authors thank the anonymous referees for their careful and detailed comments which have helped improve this manuscript considerably. This work is partially financed by the Spanish Ministry of Science and Innovation, under the projects "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theorerical Advances" with reference DPI2008-03511/DPI and "RESULT-Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 and by the Small and Medium Industry of the Generalitat Valenciana (IMPIVA) and by the European Union through the European Regional Development Fund (FEDER) inside the R+D program "Ayudas dirigidas a Institutos Tecnologicos de la Red IMPIVA" during the year 2011, with project numbers IMDEEA/2011/142 and IMDEEA/2012/143.Ciavotta, M.; Minella, GG.; Ruiz GarcĂa, R. (2013). Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study. European Journal of Operational Research. 227(2):301-313. https://doi.org/10.1016/j.ejor.2012.12.031S301313227
Evolutionary algorithms for the multi-objective test data generation problem
Software: Practice & Experience, 42(11):1331-1362Automatic test data generation is a very popular domain in the field of search-based software engineering. Traditionally, the main goal has been to maximize coverage. However, other objectives can be defined, such as the oracle cost, which is the cost of executing the entire test suite and the cost of checking the system behavior. Indeed, in very large software systems, the cost spent to test the system can be an issue, and then it makes sense by considering two conflicting objectives: maximizing the coverage and minimizing the oracle cost. This is what we did in this paper. We mainly compared two approaches to deal with the multi-objective test data generation problem: a direct multi-objective approach and a combination of a mono-objective algorithm together with multi-objective test case selection optimization. Concretely, in this work, we used four state-of-the-art multi-objective algorithms and two mono-objective evolutionary algorithms followed by a multi-objective test case selection based on Pareto efficiency. The experimental analysis compares these techniques on two different benchmarks. The first one is composed of 800 Java programs created through a program generator. The second benchmark is composed of 13 real programs extracted from the literature. In the direct multi-objective approach, the results indicate that the oracle cost can be properly optimized; however, the full branch coverage of the system poses a great challenge. Regarding the mono-objective algorithms, although they need a second phase of test case selection for reducing the oracle cost, they are very effective in maximizing the branch coverage.Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)
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