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Memes as building blocks: a case study on evolutionary optimization + transfer learning for routing problems

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Abstract

A significantly under-explored area of evolutionary optimization in the literature is the study of optimization methodologies that can evolve along with the problems solved. Particularly, present evolutionary optimization approaches generally start their search from scratch or the ground-zero state of knowledge, independent of how similar the given new problem of interest is to those optimized previously. There has thus been the apparent lack of automated knowledge transfers and reuse across problems. Taking this cue, this paper presents a Memetic Computational Paradigm based on Evolutionary Optimization \(+\) Transfer Learning for search, one that models how human solves problems, and embarks on a study towards intelligent evolutionary optimization of problems through the transfers of structured knowledge in the form of memes as building blocks learned from previous problem-solving experiences, to enhance future evolutionary searches. The proposed approach is composed of four culture-inspired operators, namely, Learning, Selection, Variation and Imitation. The role of the learning operator is to mine for latent knowledge buried in past experiences of problem-solving. The learning task is modelled as a mapping between past problem instances solved and the respective optimized solution by maximizing their statistical dependence. The selection operator serves to identify the high quality knowledge that shall replicate and transmit to future search, while the variation operator injects new innovations into the learned knowledge. The imitation operator, on the other hand, models the assimilation of innovated knowledge into the search. Studies on two separate established NP-hard problem domains and a realistic package collection/deliver problem are conducted to assess and validate the benefits of the proposed new memetic computation paradigm.

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Notes

  1. A meme is defined as the basic unit of cultural transmission in [31] stored in brains. In the context of computational intelligence, memes are defined as recurring real-world patterns or knowledge encoded in computational representations for the purpose of effective problem-solving [33].

  2. Optimized solution here denotes the best solution found by the evolutionary solvers.

  3. If a database of knowledge memes that are learned from relevant past problem solving experiences in the same domain is available, it can be loaded and leveraged upon.

  4. Note that as the learning operation is conducted offline, it does not incur additional cost to the evolutionary optimization of \(\mathbf {p}^j_{new}\).

  5. Dependency is a measure of the correlation of two random variables [63]. Here our interest on knowledge meme \(\mathbf {M}\) is in the form of a maximization of the statistical dependency, so as to ensure a maximal alignment between the transformed tasks distribution and the tasks distribution of the optimized solution. The trace of \(\mathbf {HKHY}\) is the empirical estimation of HSIC criterion [63], which is a nonlinear statistical dependence measures defined on two sets of random variables \(\mathbf {X}\) and \(\mathbf {Y}\), in their feature spaces, \(\phi (\mathbf {X})\) and \(\psi (\mathbf {Y})\). Mathematically, it tries to measure \(||C_{\mathbf {XY}}||^2\), where \(C_{\mathbf {XY}}:=E_{\mathbf {X,Y}}[(\phi (\mathbf {X})-\mu _{\mathbf {X}})\otimes (\psi (\mathbf {Y})-\mu _{\mathbf {Y}})]\), \(\mu _{\mathbf {X}}\) and \(\mu _{\mathbf {Y}}\) are the mean measures of \(\phi (\mathbf {X})\) and \(\psi (\mathbf {Y})\). A higher HSIC thus implies a higher nonlinear dependence between X and Y in the sense of the \(\phi (\mathbf {X})\) and \(\psi (\mathbf {Y})\) feature spaces.

  6. From our experimental study, the problems in the benchmark set are mostly verified to be positively correlated.

  7. Maximum mean discrepancy measures the distribution differences between two data sets, which can come in the form of vectors, sequences, graphs, and other common structured data types.

  8. Due to page limit constraints, only representatives of each series have been shown.

  9. Similar trends on enhancements in search efficiency of CAMA-M over CAMA has been obtained on all the other problem instances. However, due to the page limit constraint, only representatives of instances in each benchmark problem class can be presented in this paper.

  10. Due to page limit constraints, only representatives of each series have been shown.

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Acknowledgments

This work is partially supported under the A*Star-TSRP funding, by the Singapore Institute of Manufacturing Technology-Nanyang Technological University (SIMTech-NTU) Joint Laboratory and Collaborative research Programme on Complex Systems, and the Computational Intelligence Graduate Laboratory at NTU.

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, China

    Liang Feng

  2. Center for Computational Intelligence, School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Yew-Soon Ong & Ah-Hwee Tan

  3. Centre for Quantum Computation and Intelligent Systems, University of Technology, Sydney, Australia

    Ivor W. Tsang

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  1. Liang Feng
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  2. Yew-Soon Ong
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  4. Ivor W. Tsang
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Correspondence to Liang Feng.

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Feng, L., Ong, YS., Tan, AH. et al. Memes as building blocks: a case study on evolutionary optimization + transfer learning for routing problems. Memetic Comp. 7, 159–180 (2015). https://doi.org/10.1007/s12293-015-0166-x

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