Models and algorithms for simple disjunctive temporal problems

TL;DR

This paper introduces the simple disjunctive temporal problem, providing new models and algorithms for efficiently solving complex temporal constraints with multiple release and due dates, supported by extensive empirical evaluation.

Contribution

It defines the simple disjunctive temporal problem, develops three models, proposes two novel algorithms, and offers the first comprehensive empirical comparison of solution methods.

Findings

New algorithms significantly reduce space complexity.

Empirical results identify the most effective solving methods.

Source code and data are publicly available.

Abstract

Simple temporal problems represent a powerful class of models capable of describing the temporal relations between events that arise in many real-world applications such as logistics, robot planning and management systems. The classic simple temporal problem permits each event to have only a single release and due date. In this paper, we focus on the case where events may have an arbitrarily large number of release and due dates. This type of problem, however, has been referred to by various names. In order to simplify and standardize nomenclatures, we introduce the name Simple Disjunctive Temporal Problem. We provide three mathematical models to describe this problem using constraint programming and linear programming. To efficiently solve simple disjunctive temporal problems, we design two new algorithms inspired by previous research, both of which exploit the problem's structure to significantly reduce their space complexity. Additionally, we implement algorithms from the literature and provide the first in-depth empirical study comparing methods to solve simple disjunctive temporal problems across a wide range of experiments. Our analysis and conclusions offer guidance for future researchers and practitioners when tackling similar temporal constraint problems in new applications. All results, source code and instances are made publicly available to further assist future research.