Linear Ordering Problem: Time for a Change

2026-05-29

AI Summary

This study addresses the limitations of existing algorithms for the Linear Ordering Problem (LOP), which rely on outdated macroeconomic data and struggle to handle real-world scenarios characterized by multiple significantly distinct global optima. To bridge this gap, the authors construct the first LOP benchmark dataset based on up-to-date real-world economic data and propose a novel approach that integrates advanced metaheuristic techniques with diversity-aware optimization strategies to generate high-quality, diverse solution sets. A new evaluation metric is also introduced, explicitly balancing solution quality and diversity. Experimental results demonstrate that the proposed method performs effectively under both single-solution and multi-solution settings, yielding solution ensembles that better align with the requirements of contemporary economic applications.

Abstract

The Linear Ordering Problem (LOP) is a fundamental combinatorial optimization problem with important applications in areas such as economics, social choice, and machine learning. Its most prominent use is the triangulation of economic input-output tables, which helps identify critical industries in an economy. Most existing algorithms have been evaluated on benchmarks derived from outdated macroeconomic data, which no longer reflect the structure of contemporary economies. Furthermore, LOP instances often exhibit many distinct global optima that can differ substantially from one another, creating challenges for applications that rely on a single solution. To address these limitations, we introduce a novel benchmark suite derived from up-to-date real-world economic data and an algorithmic scheme that leverages state-of-the-art LOP metaheuristics to generate diverse sets of high-quality solutions, together with metrics for assessing both quality and diversity. Experiments were conducted to report results on the proposed benchmark suite under both the traditional single-solution setting and the newly introduced multi-solution scenario

Problem

• Linear Ordering Problem
• combinatorial optimization
• economic input-output tables
• solution diversity
• benchmark data

Innovation

• Linear Ordering Problem
• benchmark suite
• solution diversity
• metaheuristics
• economic input-output tables