A Combinatorial Search Perspective on Diverse Solution Generation

Abstract

Finding diverse solutions has become important in many combinatorial search domains, including Automated Planning, Path Planning and Constraint Programming. Much of the work in these directions has however focussed on coming up with appropriate diversity metrics and compiling those metrics in to the solvers/planners. Most approaches use linear-time greedy algorithms for exploring the state space of solution combinations for generating a diverse set of solutions, limiting not only their completeness but also their effectiveness within a time bound. In this paper, we take a combinatorial search perspective on generating diverse solutions. We present a generic bi-level optimization framework for finding cost-sensitive diverse solutions. We propose complete methods under this framework, which guarantee finding a set of cost sensitive diverse solutions satisficing the given criteria whenever there exists such a set. We identify various aspects that affect the performance of these exhaustive algorithms and propose techniques to improve them. Experimental results show the efficacy of the proposed framework compared to an existing greedy approach.

Bounding Quality in Diverse Planning

“…where A(π) is the multi-set of actions in π. In what follows, by D ma we denote the diversity metric computed as minimum over the pairwise plan distance under stability similarity, the diversity metric implemented by multiple existing diverse planners (Nguyen et al 2012;Coman and Muñoz-Avila 2011;Vadlamudi and Kambhampati 2016).…”

“…Most diverse planners developed over the last decade are focused on addressing a particular diversity metric. For example, while the diverse planner DLAMA focuses on finding a set of plans by considering a landmark-based diversity measure (Bryce 2014), other diverse planners such as LPG-d, DIV, DFAA/DFAM, and A * AA/A * AM focus on finding a set of plans with a particular minimum action distance (Nguyen et al 2012;Coman and Muñoz-Avila 2011;Vadlamudi and Kambhampati 2016). Goldman and Kuter (2015) propose a diversity metric based on information retrieval literature.…”

“…The planners LPG-d (Nguyen et al 2012) and bFI tackle Bounded Diversity Diverse Planning (bD-k), where a set of plans, k, is a solution only if its diversity is above a certain specified bound b. Top-k planners (Katz et al 2018b;Speck, Mattmüller, and Nebel 2020) and top-quality planners , while usually are not considered diverse planners, according to the aforementioned taxonomy, return, albeit naive, solutions to the Bounded Quality Diverse Planning (bQ-k) problem, where plan set quality is required to be above a specified bound. The planners DFAA/DFAM and A * AA/A * AM (Vadlamudi and Kambhampati 2016) tackle Bounded Quality and Diversity Diverse Planning (bQbD-k), where both the quality and the diversity of plan sets is bounded.…”

“…The Thirty-Sixth AAAI Conference on Artificial Intelligence Despite these recent advances in diverse planning, the pool of existing tools is still quite limited. The planners DFAA/DFAM and A * AA/A * AM by Vadlamudi and Kambhampati (2016) are the only existing planners for bQbD-k. Topquality planners Katz and Sohrabi 2022), although technically solving bQ-k, do not tackle solution diversity. For Optimal Diversity Bounded Quality Diverse Planning (bQoptD-k), where a solution corresponds to a set of plans of best diversity among the sets of bounded quality, no planners currently exist.…”

“…To that end, we introduce a novel quality metric that reflects bounded plan costs, making a connection between the costs of plans in a set and quality of a set of plans. Focusing on the most popular diversity metric (Nguyen et al 2012;Coman and Muñoz-Avila 2011;Vadlamudi and Kambhampati 2016), for all three planners we generate a subset of all plans of bounded quality as a first step. In the second step, we select a subset of plans found in the first step that constitutes a solution to the respective computational problem.…”