Solution of Mixed-Integer Optimization Problems in Bioinformatics with Differential Evolution Method

Sergey Salihov, Dmitriy Maltsov, Maria Samsonova and Konstantin Kozlov
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Sergey Salihov: Mathematical Biology and Bioinformatics Lab, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia
Dmitriy Maltsov: Mathematical Biology and Bioinformatics Lab, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia
Maria Samsonova: Mathematical Biology and Bioinformatics Lab, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia
Konstantin Kozlov: Mathematical Biology and Bioinformatics Lab, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia

Mathematics, 2021, vol. 9, issue 24, 1-20

Abstract: The solution of the so-called mixed-integer optimization problem is an important challenge for modern life sciences. A wide range of methods has been developed for its solution, including metaheuristics approaches. Here, a modification is proposed of the differential evolution entirely parallel (DEEP) method introduced recently that was successfully applied to mixed-integer optimization problems. The triangulation recombination rule was implemented and the recombination coefficients were included in the evolution process in order to increase the robustness of the optimization. The deduplication step included in the procedure ensures the uniqueness of individual integer-valued parameters in the solution vectors. The developed algorithms were implemented in the DEEP software package and applied to three bioinformatic problems. The application of the method to the optimization of predictors set in the genomic selection model in wheat resulted in dimensionality reduction such that the phenotype can be predicted with acceptable accuracy using a selected subset of SNP markers. The method was also successfully used to optimize the training set of samples for such a genomic selection model. According to the obtained results, the developed algorithm was capable of constructing a non-linear phenomenological regression model of gene expression in developing a Drosophila eye with almost the same average accuracy but significantly less standard deviation than the linear models obtained earlier.

Keywords: differential evolution; genomic selection; gene expression; integer-valued parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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