Adaptive Constraint Partition based Optimization Framework for Large-scale Integer Linear Programming(Student Abstract)

TL;DR

This paper introduces an adaptive constraint partition framework for large-scale integer linear programming that improves optimization efficiency and solution quality over traditional methods like large neighborhood search.

Contribution

The paper proposes a novel adaptive constraint partitioning framework (ACP) that enhances large-scale IP solving by dynamically adjusting constraint blocks and leveraging existing solvers.

Findings

ACP outperforms LNS in solution quality within the same time frame.

ACP demonstrates better performance than SCIP and Gurobi on tested IPs.

The adaptive partitioning effectively avoids local optima.

Abstract

Integer programming problems (IPs) are challenging to be solved efficiently due to the NP-hardness, especially for large-scale IPs. To solve this type of IPs, Large neighborhood search (LNS) uses an initial feasible solution and iteratively improves it by searching a large neighborhood around the current solution. However, LNS easily steps into local optima and ignores the correlation between variables to be optimized, leading to compromised performance. This paper presents a general adaptive constraint partition-based optimization framework (ACP) for large-scale IPs that can efficiently use any existing optimization solver as a subroutine. Specifically, ACP first randomly partitions the constraints into blocks, where the number of blocks is adaptively adjusted to avoid local optima. Then, ACP uses a subroutine solver to optimize the decision variables in a randomly selected block of constraints to enhance the variable correlation. ACP is compared with LNS framework with different subroutine solvers on four IPs and a real-world IP. The experimental results demonstrate that in specified wall-clock time ACP shows better performance than SCIP and Gurobi.