Empirical and analytical study of many-objective optimization problems: analysing distribution of nondominated solutions and population size for scalability of randomized heuristics

Joshi, Ramprasad; Deshpande, Bharat M.

doi:10.1007/s12293-014-0133-y

Cited by 13 publications

(6 citation statements)

References 20 publications

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“…Knowing this probability would allow to predict the expected number of non-dominated solutions in a population and hence facilitate the design of more efficient initialization strategies for many-objective problems. This line of research has been considered, for example, by Knowles and Corne (2007); Joshi and Deshpande (2014). Research related to heterogeneous objectives in a many-objective setup is still in its infancy and forms another direction of future research in terms of theory and algorithms.…”

Section: Future Workmentioning

confidence: 99%

What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

Allmendinger

Jaszkiewicz

Liefooghe

et al. 2022

Computers & Operations Research

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Section: Future Workmentioning

confidence: 99%

What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

Allmendinger

Jaszkiewicz

Liefooghe

et al. 2022

Computers & Operations Research

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“…There are few works in the continuous multiobjective domain related to behavior analysis. Some of the few examples with works on the relations between behavior and population size [24] and between behavior and solution quality and time [39]. In contrast more works studied the behavior of multiobjective algorithms in the combinatorial domain.…”

Section: Behavior Analysis In the Continuous Multiobjective Domainmentioning

confidence: 99%

Component-wise analysis of automatically designed multiobjective algorithms on constrained problems

Lavinas¹,

Ochoa²,

Aranha³

2022

Proceedings of the Genetic and Evolutionary Computation Conference

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The performance of multiobjective evolutionary algorithms (MOEAs) varies across problems, making it hard to develop new algorithms or apply existing ones to new problems. To simplify the development and application of new multiobjective algorithms, there has been an increasing interest in their automatic design from their components. These automatically designed metaheuristics can outperform their human-developed counterparts. However, it is still unknown what are the most influential components that lead to performance improvements. This study specifies a new methodology to investigate the effects of the final configuration of an automatically designed algorithm. We apply this methodology to a tuned Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) designed by the iterated racing (irace) configuration package on constrained problems of 3 groups: (1) analytical real-world problems, (2) analytical artificial problems and (3) simulated real-world. We then compare the impact of the algorithm components in terms of their Search Trajectory Networks (STNs), the diversity of the population, and the anytime hypervolume values. Looking at the objective space behavior, the MOEAs studied converged before half of the search to generally good HV values in the analytical artificial problems and the analytical real-world problems. For the simulated problems, the HV values are still improving at the end of the run. In terms of decision space behavior, we see a diverse set of the trajectories of the STNs in the analytical artificial problems. These trajectories are more similar and frequently reach optimal solutions in the other problems.

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“…Knowing this probability would allow to predict the expected number of nondominated solutions in a population and hence facilitate the design of more efficient initialization strategies for manyobjective problems. This line of research has been considered, for example, by Joshi and Deshpande (2014). Research related to heterogeneous objectives in a many-objective setup is still in its infancy and forms another direction of future research in terms of theory and algorithms.…”

Section: Future Workmentioning

confidence: 99%

What if we Increase the Number of Objectives? Theoretical and Empirical Implications for Many-objective Optimization

Allmendinger,

Jaszkiewicz,

Liefooghe

et al. 2021

Preprint

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The difficulty of solving a multi-objective optimization problem is impacted by the number of objectives to be optimized. The presence of many objectives typically introduces a number of challenges that affect the choice/design of optimization algorithms. This paper investigates the drivers of these challenges from two angles: (i) the influence of the number of objectives on problem characteristics and (ii) the practical behavior of commonly used procedures and algorithms for coping with many objectives. In addition to reviewing various drivers, the paper makes theoretical contributions by quantifying some drivers and/or verifying these drivers empirically by carrying out experiments on multi-objective NK landscapes and other typical benchmarks. We then make use of our theoretical and empirical findings to derive practical recommendations to support algorithm design. Finally, we discuss remaining theoretical gaps and opportunities for future research in the area of multi-and many-objective optimization.

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Empirical and analytical study of many-objective optimization problems: analysing distribution of nondominated solutions and population size for scalability of randomized heuristics

Cited by 13 publications

References 20 publications

What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

Component-wise analysis of automatically designed multiobjective algorithms on constrained problems

What if we Increase the Number of Objectives? Theoretical and Empirical Implications for Many-objective Optimization

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