An efficient second-order cone programming approach for optimal selection in tree breeding

TL;DR

This paper introduces a second-order cone programming method for optimal tree breeding selection that significantly reduces computation time while maintaining solution accuracy, compared to previous semidefinite programming approaches.

Contribution

The paper presents a novel SOCP formulation for tree breeding selection that exploits matrix sparsity, achieving faster computation without sacrificing optimality.

Findings

Reduced computation time from 39,200 seconds to under 2 seconds.

Maintained solution quality equivalent to SDP approach.

Demonstrated efficiency gains through numerical case study.

Abstract

An important problem in tree breeding is optimal selection from candidate pedigree members to produce the highest performance in seed orchards, while conserving essential genetic diversity. The most beneficial members should contribute as much as possible, but such selection of orchard parents would reduce performance of the orchard progeny due to serious inbreeding. To avoid inbreeding, we should include a constraint on the numerator relationship matrix to keep a group coancestry under an appropriate threshold. Though an SDP (semidefinite programming) approach proposed by Pong-Wong and Woolliams gave an accurate optimal value, it required rather long computation time. In this paper, we propose an SOCP (second-order cone programming) approach to reduce this computation time. We demonstrate that the same solution is attained by the SOCP formulation, but requires much less time. Since a simple SOCP formulation is not much more efficient compared to the SDP approach, we exploit a sparsity structure of the numerator relationship matrix, and formulate the SOCP constraint using Henderson's algorithm. Numerical results show that the proposed SOCP approach reduced computation time in a case study from 39,200 seconds under the SDP approach to less than 2 seconds.