Advances in Answer Set Planning: A Comprehensive Survey and Integration with Mixed Integer Programming

This paper presents a comprehensive survey of the progress made in the field, spanning from its foundational concepts to its application in challenging planning domains. The survey delves into the strengths and weaknesses of answer set planning, exploring its typical applications and outlining key challenges for future research. One notable contribution of this paper is the integration of answer set programming with mixed integer programming, a widely applied paradigm. Theoretical results establish translations from non-disjunctive logic programs to linear constraints in mixed integer programming, aligning solutions to these constraints with the answer sets of the original programs. This integration forms the basis for an extended answer set programming language that incorporates linear constraints as a primitive, facilitating more concise problem encodings. To validate the theoretical findings, a prototype system has been implemented, utilizing a state-of-the-art mixed integer programming solver to compute answer sets. Experimental results showcase the effectiveness of this approach in addressing optimization problems and those with variables spanning large domains. This research not only contributes to the theoretical foundations of answer set planning but also introduces a practical and efficient approach for solving complex problems in various domains.