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A generic method to compose an algorithm portfolio with a problem set of unknown distribution

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Abstract

As an individual algorithm rarely outperforms all kinds of optimization problems, algorithm portfolios are proposed to combine algorithms and take advantage of their strengths which fits well the prevalent theme of memetic computing. When there are many algorithms to choose from, the possibilities of algorithm combinations are numerous. Therefore, composing an algorithm portfolio which performs well for a given problem class is essential. In this paper, based on a problem set drawn from any unknown problem class according to an unknown probability distribution, we propose a general method to automatically accomplish portfolio construction. The problem set is used as training data for our method to learn an algorithm portfolio suitable for solving the underlying problem class. To construct the portfolio, algorithms are chosen and added one by one. We first find the best-performing algorithm based on its average rank of solving the training problem set. Its most complementary algorithm is then selected by applying the Pearson correlation coefficient of fitness values at the first hitting time. The method iterates to compose the portfolio with more and more algorithms until there is no more improvement. The experimental results indicate the effectiveness of this approach to select well-cooperated algorithms, and the composed portfolio is shown to have the best rank compared to individual algorithms, elite portfolios and comparison algorithms.

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Authors and Affiliations

  1. Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China

    Wenwen Liu, Shiu Yin Yuen & Chi Wan Sung

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  1. Wenwen Liu
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  2. Shiu Yin Yuen
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  3. Chi Wan Sung
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Correspondence to Shiu Yin Yuen.

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Appendix

Appendix

There are three experiments conducted to verify the abilities of the approach proposed in this paper. The problem sets for both composing and testing the portfolios are all randomly sampled by the given distributions. The detailed information of problem sets is recorded in Appendix.

Table 18 Problem set for composing the algorithm portfolio of Experiment 4.3, the first column of Table 7
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Table 19 Problem set for composing the algorithm portfolio of Experiment 4.3, the second column of Table 7
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Table 20 Problem set for composing the algorithm portfolio of Experiment 4.3, the third column of Table 7
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Table 21 Testing Problem set of Experiment 4.3 for 14 algorithms in Table 9
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Table 22 Testing Problem set of Experiment 4.3 for 6 algorithm portfolios in Fig. 5
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Tables 10, 11, 12 and 13 cover problem sets in experiment 4.1. In the first experiment, the problems in each problem set is uniformly sampled from BBOB.

Tables 15 and 16 cover problem sets in experiment 4.2. In the second experiment, the problem sets are non-uniformly sampled. The occurrence distribution of problems is that 90% of the problems are sampled from unimodal and linear problems, which are functions 1, 2, 5, 6, 10, 12 of BBOB [49], while the rest of the problems (10%) are randomly selected from other problems.

From Tables 10, 11, 12, 13, 14, 15, 16 and 17 “fxx” represents the function numbers of BBOB and the number following is the instance number. For example, “f15-80” is BBOB suite problem f15 instance 80 in 20D.

Tables 18, 19, 20, 21 and 22 record values of nGaussian, which is the number of Gaussians used in the landscape in experiment 4.3. In the third experiment, the problems in the problem sets are randomly generated from the MSG landscape generator.

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Liu, W., Yuen, S.Y. & Sung, C.W. A generic method to compose an algorithm portfolio with a problem set of unknown distribution. Memetic Comp. 14, 287–304 (2022). https://doi.org/10.1007/s12293-022-00367-8

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