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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 ...
Context 4
... 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 5
... 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 6
... 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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