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Quality vs. number of selected sub-problems (λ) w.r.t. budget (μ = 500).

Quality vs. number of selected sub-problems (λ) w.r.t. budget (μ = 500).

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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 o...

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Context 1
... order to fairly compare the different selection strategies, we analyze the impact of λ, i.e., the number of selected sub-problems, independently for each strategy. It is worth-noticing that both the value of λ and the selection strategy impact the probability of selecting a weigh vector. Our results are depicted in Fig. 2 for sps Dra and sps Rnd , for different budgets and on a representative subset of instances. Other instances are not reported due to space restrictions. The main observation is that the best setting for λ depends on the considered budget, on the instance type, and on the sub-problem selection strategy ...
Context 2
... of λ on sps Rnd . For the random strategy sps Rnd (Fig. 2, top), and for smooth problems (K = 0), a small λ value is found to perform better for a small budget. As the available budget grows, the λ value providing the best performance starts to increase until it reaches the population size μ. In other words, for small budgets one should select very few sub-problems at each generation, whereas for ...
Context 3
... of λ on sps Dra . The impact of λ appears to be different when analyzing the sps Dra strategy (Fig. 2, bottom). In fact, the effect of λ seems relatively uniform, and its optimal setting less sensitive to the available budget and instance type. More precisely, the smallest value of λ = 1 is always found to perform better, while an increasing λ value leads to a decrease in the overall approximation quality. We attribute this to the adaptive ...

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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 o...

Citations

... Notre but est de permettre une compréhension plus systématique de facteurs importants dans la conception de l'algorithme, à savoir, l'impact du nombre de sous-problèmes définis par décomposition, le nombre de sous-problèmes optimisés à chaque génération et la méthode de sélection de ces sous-problèmes. Ces travaux ont fait l'objet d'une publication à la conférence internationale EvoCOP 2020 [82]. ...
Thesis
In this thesis, we are interested in multi-objective combinatorial optimization, and in particular in evolutionary algorithms based on decomposition. This type of approaches consists in decomposing the original multi-objective problem into multiple single-objective sub-problems that are then solved cooperatively. In this context, we consider the design and the analysis of new algorithmic components contributing to the establishment of the foundations of an optimization framework based on decomposition for multi-objective combinatorial problems known as "black box", i.e., for which the analytical form of the objective functions is not available to the solving algorithm. First of all, we investigate the key components for a better distribution of the computational efforts during the optimization process. To this end, we study the joint impact of the population size and of the number of solutions generated at each iteration, while proposing different strategies for selecting one ore multiple sub-problem(s) to be optimized at each stage. We then study different mechanisms allowing to escape from local optima. They are inspired by techniques from single-objective optimization, and we show they can significantly improve the convergence profile of the considered approaches. Finally, we consider the context of expensive optimization, where the evaluation of each solution is particularly intensive in terms of computational resources. This hence drastically restrict the budget allocated to the optimization process. As such, we investigate new components based on combinatorial meta-models, and we consider their integration within decomposition-based multi-objective evolutionary approaches.
... However, the use of larger populations does not improve the solution accuracy and only increase the needed computational resources in the ant colony optimization [28]. Very recently, Geoffrey et al. investigated the combined impact of population sizing and sub-problem selection in MOEA/D, suggesting that a larger population performs better as the problem difficulty increases [27]. ...
Chapter
Large-scale multiobjective optimization problems (LSMOPs) are emerging and widely existed in real-world applications, which involve a large number of decision variables and multiple conflicting objectives. Evolutionary algorithms (EAs) are naturally suitable for multiobjective optimization due to their population-based property, allowing the search of optima simultaneously. Nevertheless, LSMOPs are challenging for conventional EAs, mainly due to the huge volume of search space in LSMOPs. Thus, it is important to explore the impact of the population sizing on the performance of conventional multiobjective EAs (MOEAs) in solving LSMOPs. In this work, we compare several representative MOEAs with different settings of population sizes on some transformer ratio error estimation (TREE) problems in the power system. These test cases are defined on combinations of three population sizes, three TREE problems, and five MOEAs. Our results indicate that the performances of conventional MOEAs with different population sizes in solving LSMOPs are different. The impact of population sizing is most significant for differential evolution based and particle swarm based MOEAs.
... The key idea of the MOEA/D is to decompose the multi-objective optimization problem into a set of single-objective subproblems, which are solved simultaneously by a population-based evolutionary approach. While the original MOEA/D and some of its earlier variants did not discriminate between subproblems, it has since become clear that focusing computational effort on certain subsets of these subproblems can substantially improve the performance of the algorithm [5]- [9]. It has been noted that the MOEA/D may sometimes waste computational effort by trying to improve solutions that are not very promising [10]. ...
... Interestingly enough, Pruvost et. al [9] also found that selecting a subset of subproblems at random on MOEA/D performs well on combinatorial domain. This suggests that increasing the inertia of the population dynamics in the MOEA/D can be beneficial in itself, regardless of the Resource Allocation strategy. ...
Article
In this paper, we propose a test-and-apply based adaptive operator selection strategy (TAOS) towards significant improvement of decomposition-based multi-objective optimization. In this approach, the entire evolutionary process is structured into several continuous sections, each of which is designed to run a test-and-apply procedure, in order to pave the way for adaptive selection of the best possible operators. In the phase of test, the adopted operators are tested by running sequentially on individuals and then the operators credits are assigned by their successful update of counts to replace the parent solutions. In the phase of apply, the best operator is selected to run on the remaining time of this section. In comparison with the existing state of the arts, our introduced two phases with the test-and-apply strategy not only achieve a better fairness, but also a more appropriate balance between exploration and exploitation for the decomposition-based multi-objective evolutionary algorithms, where the decomposition approach is convenient for credit assignment in the test phase. To evaluate our proposed strategy, we have carried out extensive experiments and the results support that our proposed outperforms the existing state of the arts on three sets of multi-objective optimization problems.