Amrudee Sukpan

Managing dynamic CSPs with preferences

We present a new framework, managing Constraint Satisfaction Problems (CSPs) with preferences in a dynamic environment. Unlike the existing CSP models managing one form of preferences, ours supports four types, namely: unary and binary constraint preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of dynamic constraint applications under preferences and where the possible changes are known and available a priori. Conditional preferences allow some preference functions to be added dynamically to the problem, during the resolution process, if a given condition on some variables is true. A composite preference is a higher level of preference among the choices of a composite variable. Composite variables are variables whose possible values are CSP variables. In other words, this allows us to represent disjunctive CSP variables. The preferences are viewed as a set of soft constraints using the fuzzy CSP framework. Solving constraint problems with preferences consists in finding a solution satisfying all the constraints while optimizing the global preference value. This is handled by four variants of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency in practice. In order to evaluate and compare the performance of these four strategies, we conducted an experimental study on randomly generated dynamic CSPs with quantitative preferences. The results are reported and discussed in the paper.

Managing Temporal Constraints with Preferences

Abstract Preferences in temporal problems are common but significant in many real world applications. In this paper, we extend our temporal reasoning framework, managing numeric and symbolic information, in order to handle preferences. Unlike the existing models managing single temporal preferences, ours supports four types of preferences, namely: numeric and symbolic temporal preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of temporal constraint problems. The preferences are considered here as a set of soft constraints using a c-semiring structure with combination and projection operators. Solving temporal constraint problems with preferences consists in finding a solution satisfying all the temporal constraints while optimizing the preference values. This is handled by a variant of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency. Experimental tests, we conducted on randomly generated temporal constraint problems with preferences, favor a variant of MAC as the constraint propagation strategy that should be used within the branch and bound algorithm.

Conditional and composite (temporal) csps

Constraint Satisfaction Problems (CSPs) have been widely used to solve combinatorial problems. In order to deal with dynamic CSPs where the information regarding any possible change is known a priori and can thus be enumerated beforehand, conditional constraints and composite variables have been studied in the past decade. Indeed, these two concepts allow the addition of variables and their related constraints in a dynamic manner during the resolution process. More precisely, a conditional constraint restricts the participation of a variable in a feasible scenario while a composite variable allows us to express a disjunction of variables where only one will be added to the problem to solve. In order to deal with a wide variety of real life applications under temporal constraints, we present in this paper a unique temporal CSP framework including numeric and symbolic temporal information, conditional constraints and composite variables. We call this model, a Conditional and Composite Temporal CSP (or CCTCSP). To solve the CCTCSP we propose two methods respectively based on Stochastic Local Search (SLS) and constraint propagation. In order to assess the efficiency in time of the solving methods we propose, experimental tests have been conducted on randomly generated CCTCSPs. The results demonstrate the superiority of a variant of the Maintaining Arc Consistency (MAC) technique (that we call MAX+) over the other constraint propagation strategies, Forward Checking (FC) and its variants, for both consistent and inconsistent problems. It has also been shown that, in the case of consistent problems, MAC+ outperforms the SLS method Min Conflict Random Walk (MCRW) for highly constrained CCTCSPs while both methods have comparable time performance for under and middle constrained problems. MCRW is, however, the method of choice for highly constrained CCTCSPs if we decide to trade search time for the quality of the solution returned (number of solved constraints).

A new temporal CSP framework handling composite variables and activity constraints

A well known approach to managing the numeric and the symbolic aspects of time is to view them as constraint satisfaction problems (CSPs). Our aim is to extend the temporal CSP formalism in order to include activity constraints and composite variables. Indeed, in many real life applications the set of variables involved by the temporal constraint problem to solve is not known in advance. More precisely, while some temporal variables (called events) are available in the initial problem, others are added dynamically to the problem during the resolution process via activity constraints and composite variables. Activity constraints allow some variables to be activated (added to the problem) when activity conditions are true. Composite variables are defined on finite domains of events. We propose in this paper two methods based respectively on constraint propagation and stochastic local search (SLS) for solving temporal constraint problems with activity constraints and composite variables. We call these problems conditional and composite temporal constraint satisfaction problems (CCTCSPs). Experimental study we conducted on randomly generated CCTCSPs demonstrates the efficiency of our exact method based on constraint propagation in the case of middle constrained and over constrained problems while the SLS based method is the technique of choice for under constrained problems and also in case we want to trade search time for the quality of the solution returned (number of solved constraints)

Managing Conditional and Composite CSPs

Conditional CSPsand Composite CSPshave been known in the CSP discipline for fifteen years, especially in scheduling, planning, diagnosis and configuration domains. Basically a conditional constraintrestricts the participation of a variable in a feasible scenario while a composite variable allows us to express a disjunction of variables or sub CSPs where only one will be added to the problem to solve. In this paper we combine the features of Conditional CSPsand Composite CSPsin a unique framework that we call Conditional and Composite CSPs (CCCSPs). Our framework allows the representation of dynamic constraint problems where all the information corresponding to any possible change are available a priori. Indeed these latter information are added to the problem to solve in a dynamic manner, during the resolution process, via conditional (or activity) constraints and composite variables. A composite variable is a variable whose possible values are CSP variables. In other words this allows us to represent disjunctive variables where only one will be added to the problem to solve. An activity constraint activates a non active variable (this latter variable will be added to the problem to solve) if a given condition holds on some other active variables. In order to solve the CCCSP, we propose two methods that are respectively based on constraint propagation and Stochastic Local Search (SLS). The experimental study, we conducted on randomly generated CCCSPs demonstrates the efficiency of a variant of the MAC strategy (that we call MAC+) over the other constraint propagation techniques. We will also show that MAC+ outperforms the SLS method MCRW for highly consistent CCCSPs. MCRW is however the procedure of choice for under constrained and middle constrained problems and also for highly constrained problems if we trade search time for the quality of the solution returned (number of solved constraints).

Solving conditional and composite temporal constraints

One of the main challenges when designing constraint based systems in general and those involving temporal constraints in particular, is the ability to deal with conditional constraints and composite variables. Indeed, in this particular case the set of variables involved by the constraint problem to be solved is not known in advance. More precisely, while some variables (called initial variables) are available in the initial problem, others are added dynamically to the problem during the resolution process via activity constraints and composite variables. Activity constraints allow some variables to be activated (added to the problem) when activity conditions are true. Composite variables are variables whose values are the possible variables each composite variable can take. We propose a method based on constraint propagation for solving efficiently constraint problems involving numeric and symbolic temporal constraints, composite variables and activity constraints. We call these latter problems conditional and composite temporal constraint satisfaction problems (CCTCSPs). Experimental evaluation conducted on randomly generated CCTCSPs demonstrates the efficiency of our method to solve these problems especially when using the forward check strategy during the search.

Solving conditional and composite constraint satisfaction problems

Constraint Satisfaction Problems (CSPs) have been widely used to solve combinatorial problems. In order to deal with dynamic CSPs where the information regarding any possible change is known a priori and can thus be enumerated beforehand, conditional constraints and composite variables have been studied in the past decade. Indeed, these two concepts allow the addition of variables and their related constraints in a dynamic manner during the resolution process. More precisely, a conditional constraint restricts the participation of a variable in a feasible scenario while a composite variable allows us to express a disjunction of variables where only one will be added to the problem to solve.n In this paper we introduce a unique CSP framework including conditional constraints and composite variables. We call this model, a Conditional and Composite CSP (or CCCSP). In order to solve a CCCSP, we propose two methods respectively based on Stochastic Local Search (SLS) and backtrack search with constraint propagation. The experimental comparison of these two methods, on randomly generated consistent CCCSPs, demonstrates the efficiency of the exact method based on constraint propagation in the case of middle and under constrained problems while the SLS based method is the technique of choice for highly constrained problems and also in case we want to trade search time for the quality of the solution returned (number of solved constraints).

Conditional and Composite Temporal Constraints with Preferences

Preferences in temporal problems are common but significant in many real world applications. In this paper, we extend our temporal reasoning framework, managing numeric and symbolic information, in order to handle preferences. Unlike the existing models managing single temporal preferences, ours supports four types of preferences, namely: numeric and symbolic temporal preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of temporal constraint problems. The preferences are considered here as a set of soft constraints using a c-semiring structure with combination and projection operators. Solving temporal constraint problems with preferences consists of finding a solution satisfying all the temporal constraints while optimizing the preference values. This is handled by a variant of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency. Preliminary tests, we conducted on randomly generated temporal constraint problems with preferences, favor the forward checking principle as a constraint propagation strategy