A Hybrid Programming Framework for Modeling and Solving Constraint Satisfaction and Optimization Problems

Jarosław Wikarek,Paweł Sitek

doi:10.1155/2016/5102616

Jarosław Wikarek, Paweł Sitek

Open Access

https://doi.org/10.1155/2016/5102616

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Journal: Scientific Programming	Publication Date: Jan 1, 2016
Citations: 63	License type: CC BY 4.0

Affiliation: Kielce University of Technology

Abstract

This paper proposes a hybrid programming framework for modeling and solving of constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). Two paradigms, CLP (constraint logic programming) and MP (mathematical programming), are integrated in the framework. The integration is supplemented with the original method of problem transformation, used in the framework as a presolving method. The transformation substantially reduces the feasible solution space. The framework automatically generates CSP and COP models based on current values of data instances, questions asked by a user, and set of predicates and facts of the problem being modeled, which altogether constitute a knowledge database for the given problem. This dynamic generation of dedicated models, based on the knowledge base, together with the parameters changing externally, for example, the user’s questions, is the implementation of the autonomous search concept. The models are solved using the internal or external solvers integrated with the framework. The architecture of the framework as well as its implementation outline is also included in the paper. The effectiveness of the framework regarding the modeling and solution search is assessed through the illustrative examples relating to scheduling problems with additional constrained resources.

Highlights

Constraint satisfaction problems (CSPs) and/or constraint optimization problems (COPs) can involve the variables that take values over finite domains and constraints of all types and characters [1]
Problems with constraints like CSP and COP are frequent in production, distribution, transportation, logistics, computer networks, software engineering, project management, planning and scheduling, and so forth
The autonomous search should have the ability to preferably modify and change its internal components when exposed to changing external parameters, requirements, and/or data instances [2]

Summary

Introduction

Constraint satisfaction problems (CSPs) and/or constraint optimization problems (COPs) can involve the variables that take values over finite domains (integer, real, binary, etc.) and constraints of all types and characters [1]. The main contribution of this study is the concept and implementation of the hybrid programming framework, which joins the ideas of (i) hybridization in the form of integration of MP and CLP, (ii) presolving in the form of transformation and constraint propagation, and (iii) autonomous search in the form of automatic generation of dedicated models to solve. (iv) Implementation autonomous search in the form of automatic models generation for CSPs and COPs as the MP/MIP/MILP models based on knowledge base (constraints, questions, and data facts). Autonomous search, as used in the framework, is the narrowing of the search space through the implementation of presolving methods and automatic generation of dedicated implementation models Both the presolving methods (constraint propagation and transformation) and model generation are based on current data instances. A change of the question and/or data instance results in a new model adjusted to new parameters

Illustrative Example and Computational Experiments

Conclusions

Formal Models for Illustrative Example