SimplifEx: Simplifying and Explaining Linear Programs

IF 2.1 3区心理学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Cognitive Systems Research Pub Date : 2024-10-11 DOI:10.1016/j.cogsys.2024.101298

Claire Ott, Frank Jäkel

{"title":"SimplifEx: Simplifying and Explaining Linear Programs","authors":"Claire Ott, Frank Jäkel","doi":"10.1016/j.cogsys.2024.101298","DOIUrl":null,"url":null,"abstract":"<div><div>Linear Programming is one of the most common methods for finding optimal solutions to complex problems. Despite its extensive use, solutions are not usually accompanied by explanations, especially explanations for non-experts. Our new tool SimplifEx combines well-known preprocessing techniques with cognitively adequate heuristics to simplify a given linear program, structure its variables, and explain the optimal solution that was found. SimplifEx is meant to improve intuitive understanding of linear programs. In addition, we introduce a generalization of the classical dominance relation in Linear Programming. The order of dominant and dominated variables in an optimal solution can give valuable insights into the structure of a problem and fits well with how humans approach linear programs. The resulting, automatically generated explanations include detailed step-wise listings of processing steps and graphs that provide an overview. The heuristics are based on historical and experimental observations of people solving linear programs by hand. We apply SimplifEx to Stigler’s diet problem as a running example.</div></div>","PeriodicalId":55242,"journal":{"name":"Cognitive Systems Research","volume":"88 ","pages":"Article 101298"},"PeriodicalIF":2.1000,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cognitive Systems Research","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1389041724000925","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

Abstract

Linear Programming is one of the most common methods for finding optimal solutions to complex problems. Despite its extensive use, solutions are not usually accompanied by explanations, especially explanations for non-experts. Our new tool SimplifEx combines well-known preprocessing techniques with cognitively adequate heuristics to simplify a given linear program, structure its variables, and explain the optimal solution that was found. SimplifEx is meant to improve intuitive understanding of linear programs. In addition, we introduce a generalization of the classical dominance relation in Linear Programming. The order of dominant and dominated variables in an optimal solution can give valuable insights into the structure of a problem and fits well with how humans approach linear programs. The resulting, automatically generated explanations include detailed step-wise listings of processing steps and graphs that provide an overview. The heuristics are based on historical and experimental observations of people solving linear programs by hand. We apply SimplifEx to Stigler’s diet problem as a running example.

Abstract Image

查看原文本刊更多论文

SimplifEx：简化和解释线性规划

线性规划是为复杂问题寻找最优解的最常用方法之一。尽管线性规划被广泛使用，但其解决方案通常并不附带解释，尤其是针对非专业人士的解释。我们的新工具 SimplifEx 结合了著名的预处理技术和认知启发式方法，可简化给定的线性规划、构建变量结构并解释找到的最优解。SimplifEx 旨在提高对线性规划的直观理解。此外，我们还引入了线性规划中经典支配关系的一般化。最优解中支配变量和被支配变量的顺序可以让人深入了解问题的结构，非常符合人类处理线性规划的方式。由此自动生成的解释包括处理步骤的详细分步列表和提供概览的图表。启发式方法基于人们手工解决线性程序的历史和实验观察。我们将 SimplifEx 作为一个运行示例应用于斯蒂格勒的饮食问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Cognitive Systems Research 工程技术-计算机：人工智能

CiteScore

9.40

自引率

5.10%

发文量

审稿时长

>12 weeks

期刊介绍： Cognitive Systems Research is dedicated to the study of human-level cognition. As such, it welcomes papers which advance the understanding, design and applications of cognitive and intelligent systems, both natural and artificial. The journal brings together a broad community studying cognition in its many facets in vivo and in silico, across the developmental spectrum, focusing on individual capacities or on entire architectures. It aims to foster debate and integrate ideas, concepts, constructs, theories, models and techniques from across different disciplines and different perspectives on human-level cognition. The scope of interest includes the study of cognitive capacities and architectures - both brain-inspired and non-brain-inspired - and the application of cognitive systems to real-world problems as far as it offers insights relevant for the understanding of cognition. Cognitive Systems Research therefore welcomes mature and cutting-edge research approaching cognition from a systems-oriented perspective, both theoretical and empirically-informed, in the form of original manuscripts, short communications, opinion articles, systematic reviews, and topical survey articles from the fields of Cognitive Science (including Philosophy of Cognitive Science), Artificial Intelligence/Computer Science, Cognitive Robotics, Developmental Science, Psychology, and Neuroscience and Neuromorphic Engineering. Empirical studies will be considered if they are supplemented by theoretical analyses and contributions to theory development and/or computational modelling studies.