Roman Barták

Constraint satisfaction techniques in planning and scheduling

Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of finding a solution to a set of constraints. Planning is the process of finding a sequence of actions that transfer the world from some initial state to a desired state. Scheduling is the problem of assigning a set of tasks to a set of resources subject to a set of constraints. In this paper, we introduce the main definitions and techniques of constraint satisfaction, planning and scheduling from the Artificial Intelligence point of view.

Extension of O(n log n) Filtering Algorithms for the Unary Resource Constraint to Optional Activities

Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edge-finding and not-first/not-last are the most popular filtering algorithms for unary resources. In this paper we introduce new O(n log n) versions of these two filtering algorithms and one more O(n log n) filtering algorithm called detectable precedences. These algorithms use a special data structures Θ-tree and Θ-Λ-tree. These data structures are especially designed for “what-if” reasoning about a set of activities so we also propose to use them for handling so called optional activities, i.e. activities which may or may not appear on the resource. In particular, we propose new O(n log n) variants of filtering algorithms which are able to handle optional activities: overload checking, detectable precedences and not-first/not-last.

Minimal perturbation problem in course timetabling

Many real-life problems are dynamic, with changes in the problem definition occurring after a solution to the initial formulation has been reached. A minimal perturbation problem incorporates these changes, along with the initial solution, as a new problem whose solution must be as close as possible to the initial solution. A new iterative forward search algorithm is proposed to solve minimal perturbation problems. Significant improvements to the solution quality are achieved by including new conflict-based statistics in this algorithm. The proposed methods were applied to find a new solution to an existing large scale class timetabling problem at Purdue University, incorporating the initial solution and additional input changes.

Dynamic Constraint Models for Planning and Scheduling Problems

Planning and scheduling attracts an unceasing attention of computer science community. However, despite of similar character of both tasks, in most current systems planning and scheduling problems are solved independently using different methods. Recent development of Constraint Programming brings a new breeze to these areas. It allows using the same techniques for modelling planning and scheduling problems as well as exploiting successful methods developed in Artificial Intelligence and Operations Research. In the paper we analyse the problems behind planning and scheduling in complex process environments and we propose to enhance the traditional schedulers by planning capabilities to solve these problems. We argue for using dynamic models to capture such mixed planning and scheduling environment. Despite of studying the proposed framework using the complex process environment background we believe that the results are applicable in general to other (nonproduction) problem areas where mixed planning and scheduling capabilities are desirable.

New trends in constraint satisfaction, planning, and scheduling: a survey

During recent years, the development of new techniques for constraint satisfaction, planning, and scheduling has received increased attention, and substantial effort has been invested in trying to exploit such techniques to find solutions to real-life problems. In this paper, we present a survey on constraint satisfaction, planning, and scheduling from the Artificial Intelligence point of view. In particular, we present the main definitions and techniques, and discuss possible ways of integrating such techniques. We also analyze the role of constraint satisfaction in planning and scheduling, and hint at some open research issues related to planning, scheduling, and constraint satisfaction.

Limited assignments: a new cutoff strategy for incomplete depth-first search

In this paper, we propose an extension of three incomplete depth-first search techniques, namely depth-bounded backtrack search, credit search, and iterative broadening, towards producing incomplete solutions. We also propose a new cutoff strategy for incomplete depth-first search motivated by a human style of problem solving. This technique, called limited assignment number (LAN) search, is based on limiting the number of attempts tried to assign a value to the variable. A linear worst-case time complexity of LAN Search leads to promising stable time behavior in all accomplished experiments. The techniques are studied in the context of constraint satisfaction problems.

Dynamic Global Constraints in Backtracking Based Environments

Global constraints provide strong filtering algorithms to reduce the search space when solving large combinatorial problems. In this paper we propose to make the global constraints dynamic, i.e., to allow extending the set of constrained variables during search. We describe a generic dynamisation technique for an arbitrary monotonic global constraint and we compare it with the semantic-based dynamisation for the alldifferent constraint. At the end we sketch a dynamisation technique for non-monotonic global constraints. A comparison with existing methods to model dynamic problems is given as well.

Conceptual Models for Combined Planning and Scheduling

Planning and scheduling attracts an unceasing attention of computer science community. Several research areas like Artificial Intelligence, Operations Research and Constraint Programming joined their power to tackle the problems brought by real industrial life. Among them Constraint Programming plays the integrating role because it provides nice declarative capabilities for modelling and, at the same time, it can exploit directly the successful methods developed in AI and OR. In this paper we analyse the problems behind industrial planning and scheduling. In particular we give a survey of possible conceptual models for scheduling problems with some planning features. We compare their advantages and drawbacks and we explain the industrial background. These models were studied within the VisOpt project whose task is to develop a generic scheduling engine for complex production environments.

CONSTRAINT-BASED SCHEDULING: AN INTRODUCTION FOR NEWCOMERS

Abstract Constraint-based scheduling is an approach for solving real-life scheduling problems by stating constraints over the problem variables. By providing generic constraint satisfaction techniques on one side and specialised constraints on the other side, constraint programming achieves a very good generality and efficiency and thus it becomes very popular in solving real-life combinatorial (optimisation) problems. In this paper we present some constraint satisfaction techniques used in constraint-based scheduling. Our goal is to introduce the technology to newcomers rather than to provide a deep survey of the area or to describe some new results there.

Constraint satisfaction for planning and scheduling problems

The areas of planning and scheduling (from the Artificial Intelligence point of view) have seen important advances thanks to application of constraint satisfaction techniques. Currently, many important real-world problems require efficient constraint handling for planning, scheduling and resource allocation to competing goal activities over time in the presence of complex state-dependent constraints. Solutions to these problems require integration of resource allocation and plan synthesis capabilities. Hence to manage such complex problems planning, scheduling and constraint satisfaction must be interrelated. This special issue on Constraint Satisfaction for Planning and Scheduling Problems compiles a selection of papers dealing with various aspects of applying constraint satisfaction techniques in planning and scheduling. The core of submitted papers was formed by the extended versions of papers presented at COPLAS’2009: ICAPS 2009 Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems. This issue presents novel advances on planning, scheduling, constraint programming/constraint satisfaction problems (CSPs) and many other common areas that exist among them. On the whole, this issue mainly focus on managing complex problems where planning, scheduling, constraint satisfaction and search must be combined and/or interrelated, which entails an enormous potential for practical applications and future research.