XCSP3: An Integrated Format for Benchmarking Combinatorial Constrained Problems

Abstract

We propose a major revision of the format XCSP 2.1, called XCSP3, to build integrated representations of combinatorial constrained problems. This new format is able to deal with mono/multi optimization, many types of variables, cost functions, reification, views, annotations, variable quantification, distributed, probabilistic and qualitative reasoning. The new format is made compact, highly readable, and rather easy to parse. Interestingly, it captures the structure of the problem models, through the possibilities of declaring arrays of variables, and identifying syntactic and semantic groups of constraints. The number of constraints is kept under control by introducing a limited set of basic constraint forms, and producing almost automatically some of their variations through lifting, restriction, sliding, logical combination and relaxation mechanisms. As a result, XCSP3 encompasses practically all constraints that can be found in major constraint solvers developed by the CP community. A website, which is developed conjointly with the format, contains many models and series of instances. The user can make sophisticated queries for selecting instances from very precise criteria. The objective of XCSP3 is to ease the effort required to test and compare different algorithms by providing a common test-bed of combinatorial constrained instances. Generic Constraints Constraint intension Constraint extension Constraint smart Language-based Constraints Constraint regular Constraint grammar Constraint mdd Comparison-based Constraints Constraints allDifferent, allEqual Constraints allDistant, ordered Counting Constraints Constraints sum, count Constraints nValues, cardinality

On Using Monte-Carlo Tree Search to Solve Puzzles

“…Recently, authors in [28] present a puzzle solver based on Luddi [29], a newly proposed GDL which uses Monte-Carlo Tree search (MCTS) as its core for AI move planning. Incorporating the XCSP3 [6] solver provides a universal integrated framework for constraint problem representation, numerous Logic Puzzles are demonstrated to be effectively solved.…”

“…⌋+ ⌊ (j−1) 3 ⌋+1, 3×((i−1)%3)+(j−1)%3+1(6) Note that the first condition domain is defined for the rows variable. The second group is described as the transposed variable domain for the column variables.…”

PyCSP3: Modeling Combinatorial Constrained Problems in Python

“…< instance format = " XCSP3 " type = " CSP " > < variables > < array id = " x " note = " x [ i ] is the ith value of the sequence " size = " [6] " > 0..5 </ array > </ variables > < constraints > < cardinality note = " each value i occurs exactly x [ i ] times in the sequence " >…”

“…• XCSP 3 : an intermediate format used to represent problem instances while preserving structure of models [6] Model PyCSP 3 For modeling, as indicated above, the user can choose between two well-known languages (Python or Java), but this document is devoted to Python. As shown in Figure 1, the user who wishes to solve a combinatorial constrained problem has to:…”

“…• Using a coarse-grained XML structure permits to have compact and readable problem descriptions. Note that using JSON instead of XML for representing instances would have been possible but has some drawbacks, as explained in an appendix of XCSP 3 Specifications [6].…”