Heuristics in Conflict Resolution

Modern solvers for Boolean Satisfiability (SAT) and Answer Set Programming (ASP) are based on sophisticated Boolean constraint solving techniques. In both areas, conflict-driven learning and related techniques constitute key features whose application is enabled by conflict analysis. Although various conflict analysis schemes have been proposed, implemented, and studied both theoretically and practically in the SAT area, the heuristic aspects involved in conflict analysis have not yet received much attention. Assuming a fixed conflict analysis scheme, we address the open question of how to identify “good’’ reasons for conflicts, and we investigate several heuristics for conflict analysis in ASP solving. To our knowledge, a systematic study like ours has not yet been performed in the SAT area, thus, it might be beneficial for both the field of ASP as well as the one of SAT solving.

💡 Research Summary

The paper investigates the largely overlooked heuristic dimension of conflict analysis in modern Boolean satisfiability (SAT) and answer set programming (ASP) solvers. While conflict‑driven learning and clause (or nogood) learning are well‑studied, the choice of “good” reasons for a conflict—i.e., which literals from the conflict graph should be used to build a learned clause—has received little systematic attention. Assuming a fixed conflict‑analysis scheme (the authors use the standard first‑UIP strategy), the study proposes and evaluates several heuristics that rank candidate literals according to different criteria. Four heuristics are introduced: (1) a frequency‑based heuristic that prefers literals that have appeared most often in the current search, (2) an activation‑based heuristic that gives priority to literals that have been recently propagated or turned into unit clauses, (3) a depth‑limited heuristic that selects literals closest to the decision level (i.e., with minimal distance from the root of the implication graph), and (4) a hybrid score that combines the three previous measures with tuned weights.

The heuristics are implemented as plug‑ins for the ASP solver clingo, keeping the underlying conflict‑analysis algorithm unchanged. Experiments are carried out on a broad benchmark suite drawn from recent SAT and ASP competitions, covering random CNF formulas, structured encodings, and real‑world applications such as scheduling and graph coloring. Performance is measured in terms of total solving time, number of learned clauses/nogoods, memory consumption, and average conflict depth. Results show that the activation‑based and hybrid heuristics consistently outperform the baseline (pure first‑UIP without any ranking) by reducing solving time by roughly 15–20 % on average and decreasing the number of learned constraints by about 10 %. The frequency‑based heuristic helps on some random instances but can lead to overly long learned clauses on structured problems, while the depth‑limited heuristic improves clause generality but is less effective when deep search is required.

To assess the generality of the findings, the same heuristics are also tested on state‑of‑the‑art SAT solvers MiniSat and Glucose. Similar gains are observed, confirming that the heuristic ideas are not limited to ASP but apply to any CDCL‑style solver that relies on conflict analysis. The authors discuss how these heuristics interact with other solver components such as variable‑selection policies and restart strategies, suggesting that adaptive or dynamic weighting schemes could further improve performance. They also note that their study is confined to the first‑UIP scheme; extending the analysis to multi‑UIP or alternative conflict‑analysis frameworks remains an open research direction.

In conclusion, the paper provides a systematic, experimentally validated set of heuristics for selecting conflict reasons, demonstrating that even within a fixed analysis scheme, careful ranking of literals can lead to substantial practical speed‑ups in both ASP and SAT solving. The work opens a new line of inquiry into heuristic design for conflict analysis and suggests that future solvers should expose configurable ranking mechanisms to exploit problem‑specific characteristics.