Value Selection Heuristics Research Articles

Efficient search procedures for solving combinatorial problems

Solving combinatorial problems is an interplay between search and inference. In this thesis, we focus on search and investigate its important aspects. We start with complete search procedures and consider binary search, which is frequently used to augment a feasibility solver to handle optimization problems. In this setting, we often observe that negative trials (i.e., showing that a certain solution quality cannot be achieved) are significantly harder than positive trials. We consider a simple cost model where negative trials cost a constant factor more than positive trials and show how binary search can be biased optimally to achieve optimal worst-case and average-case performance. Next, as a complementary approach, we turn to incomplete search procedures. We propose Hegel and Fichte’s dialectic as a local search meta-heuristic. Dialectic is an appealing mental concept for local search as it allows developing functions for search space exploration and exploitation independently. We illustrate dialectic search, its simplicity and great efficiency on problems from highly different problem domains. We then study variable and value selection heuristics, and propose a simple modification to impact-based search strategy. We present computational results on constraint satisfaction problems that show improvements in the search performance. Finally, we look at the interaction between search and inference. In particular, we investigate incrementality during tree search interleaved with constraint propagation. We first consider constraints based on context-free grammars for which we devise a time-and space-efficient filtering algorithm. We then look at constraints that enforce the same-relation for every pair of variables in binary constraint satisfaction problems. We show that achieving generalized arcconsistency in special graphs such as cliques, complete bipartite, and directed acyclic graphs is

Planning as constraint satisfaction: Solving the planning graph by compiling it into CSP

The idea of synthesizing bounded length plans by compiling planning problems into a combinatorial substrate, and solving the resulting encodings has become quite popular in recent years. Most work to-date has however concentrated on compilation to satisfiability (SAT) theories and integer linear programming (ILP). In this paper we will show that CSP is a better substrate for the compilation approach, compared to both SAT and ILP. We describe GP- CSP, a system that does planning by automatically converting Graphplan's planning graph into a CSP encoding and solving it using standard CSP solvers. Our comprehensive empirical evaluation of GP- CSP demonstrates that it is superior to both the Blackbox system, which compiles planning graphs into SAT encodings, and an ILP-based planner in a wide range of planning domains. Our results show that CSP encodings outperform SAT encodings in terms of both space and time requirements in various problems. The space reduction is particularly important as it makes GP- CSP less susceptible to the memory blow-up associated with SAT compilation methods. The paper also discusses various techniques in setting up the CSP encodings, planning specific improvements to CSP solvers, and strategies for variable and value selection heuristics for solving the CSP encodings of different types of planning problems.