Polyhedral-based Methods for Mixed-Integer SOCP in Tree Breeding

TL;DR

This paper introduces polyhedral-based methods, including lifted polyhedral programming relaxation and cone-decomposition, to efficiently solve mixed-integer second-order cone programs in forest tree breeding, significantly reducing computation time.

Contribution

It presents novel linear approximation techniques for MI-SOCP in tree breeding, enabling faster solutions compared to traditional solvers.

Findings

Cone-decomposition method accelerates OCS problem solving

LPP relaxation provides effective linear approximations

Approach applicable to other MI-SOCP problems

Abstract

Optimal contribution selection (OCS) is a mathematical optimization problem that aims to maximize the total benefit from selecting a group of individuals under a constraint on genetic diversity. We are specifically focused on OCS as applied to forest tree breeding, when selected individuals will contribute equally to the gene pool. Since the diversity constraint in OCS can be described with a second-order cone, equal deployment in OCS can be mathematically modeled as mixed-integer second-order cone programming (MI-SOCP). If we apply a general solver for MI-SOCP, non-linearity embedded in OCS requires a heavy computation cost. To address this problem, we propose an implementation of lifted polyhedral programming (LPP) relaxation and a cone-decomposition method (CDM) to generate effective linear approximations for OCS. In particular, CDM successively solves OCS problems much faster than generic approaches for MI-SOCP. The approach of CDM is not limited to OCS, so that we can also apply the approach to other MI-SOCP problems.