[Paper Review] Selection of training populations (and other subset selection problems) with an accelerated genetic algorithm (STPGA: An R-package for selection of training populations with a genetic algorithm)

Deniz Akdemir|arXiv (Cornell University)|Feb 26, 2017

Genetic and phenotypic traits in livestock50 references3 citations

TL;DR

This paper introduces STPGA, an R package implementing an accelerated genetic algorithm (LA-GA-T) for optimal subset selection in high-dimensional data, particularly for training population selection in genomic prediction. The method integrates tabu memory and fitness-based look-ahead heuristics to enhance convergence and avoid local optima, demonstrating strong performance across diverse applications including variable selection, influential observation detection, and mixed integer quadratic programming.

ABSTRACT

Optimal subset selection is an important task that has numerous algorithms designed for it and has many application areas. STPGA contains a special genetic algorithm supplemented with a tabu memory property (that keeps track of previously tried solutions and their fitness for a number of iterations), and with a regression of the fitness of the solutions on their coding that is used to form the ideal estimated solution (look ahead property) to search for solutions of generic optimal subset selection problems. I have initially developed the programs for the specific problem of selecting training populations for genomic prediction or association problems, therefore I give discussion of the theory behind optimal design of experiments to explain the default optimization criteria in STPGA, and illustrate the use of the programs in this endeavor. Nevertheless, I have picked a few other areas of application: supervised and unsupervised variable selection based on kernel alignment, supervised variable selection with design criteria, influential observation identification for regression, solving mixed integer quadratic optimization problems, balancing gains and inbreeding in a breeding population. Some of these illustrations pertain new statistical approaches.

Motivation & Objective

• To address the challenge of optimal subset selection in high-dimensional data, especially for training population design in genomic prediction.
• To develop a scalable, parallelizable algorithm that outperforms traditional heuristic and exact methods in computational efficiency and solution quality.
• To provide a flexible, extensible framework for subset selection applicable beyond genomics, including variable selection, influential observation detection, and mixed integer quadratic programming.
• To enable researchers to efficiently select informative subsets using customizable objective functions through a user-friendly R interface.

Proposed method

• The LA-GA-T algorithm combines a genetic algorithm with tabu memory to track and avoid revisiting previously evaluated solutions and their fitness values.
• It incorporates a fitness regression model on solution coding to predict ideal solutions, enabling a 'look-ahead' strategy that guides search toward high-quality regions.
• The algorithm uses adaptive mutation and elite retention to maintain diversity and convergence, with configurable parameters for population size, mutation probability, and stopping criteria.
• It supports parallel execution via the 'mc.cores' parameter, leveraging multi-core architectures to accelerate computation.
• The method is designed to be extensible, allowing users to define custom objective functions through the 'errorstat' parameter.
• It is implemented in pure R, ensuring accessibility and ease of customization, while supporting integration with existing R workflows.

Experimental results

Research questions

• RQ1 Can a modified genetic algorithm with tabu memory and look-ahead heuristics outperform standard heuristic and exact methods in solving optimal subset selection problems?
• RQ2 How effective is the LA-GA-T algorithm in selecting training populations that maximize genomic prediction accuracy in high-dimensional marker data?
• RQ3 To what extent can the STPGA package be generalized to other subset selection problems such as variable selection, influential observation detection, and mixed integer quadratic programming?
• RQ4 How does parallelization impact the performance and scalability of the LA-GA-T algorithm on large-scale genomic and statistical problems?
• RQ5 Can the algorithm reliably identify influential observations in regression by selecting subsets that minimize coefficient instability?

Key findings

• The LA-GA-T algorithm successfully identified the six manipulated observations (5, 30, 55, 80, 105, 130) as the most influential in a regression model, as evidenced by a sharp increase in criterion value when excluding them from a 144-sample subset.
• The algorithm demonstrated robustness in detecting influential observations, with the solution for n=144 including all six manipulated points, confirming the method's sensitivity to high-leverage cases.
• A speedup of up to 3.5 times was observed with 256 processors when parallelization efficiency increased by just 1%, highlighting the algorithm’s strong parallel scalability.
• The method achieved stable convergence across multiple runs, with minimal variation in best criterion values over iterations, indicating reliable performance.
• The package successfully solved diverse problems including supervised and unsupervised variable selection, inbreeding-balanced breeding population design, and mixed integer quadratic programming.
• The use of user-defined objective functions enabled flexible adaptation to novel statistical criteria, extending the tool’s applicability beyond default genomic selection metrics.