Amnon Meisels

A Graph-Based Hyper-Heuristic for Educational Timetabling Problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-theart approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems. � 2005 Elsevier B.V. All rights reserved.

Asynchronous Forward-checking for DisCSPs

A new search algorithm for solving distributed constraint satisfaction problems (DisCSPs) is presented. Agents assign variables sequentially, but perform forward checking asynchronously. The asynchronous forward-checking algorithm (AFC) is a distributed search algorithm that keeps one consistent partial assignment at all times. Forward checking is performed by sending copies of the partial assignment to all unassigned agents concurrently. The algorithm is described in detail and its correctness proven. The sequential assignment method of AFC leads naturally to dynamic ordering of agents during search. Several ordering heuristics are presented. The three best heuristics are evaluated and shown to improve the performance of AFC with static order by a large factor. An experimental comparison of AFC to asynchronous backtracking (ABT) on randomly generated DisCSPs is also presented. AFC with ordering heuristics outperforms ABT by a large factor on the harder instances of random DisCSPs. These results hold for two measures of performance: number of non-concurrent constraints checks and number of messages sent.

Modelling and Solving Employee Timetabling Problems

Employee timetabling is the operation of assigning employees to tasks in a set of shifts during a fixed period of time, typically a week. We present a general definition of employee timetabling problems (ETPs) that captures many real-world problem formulations and includes complex constraints. The proposed model of ETPs can be represented in a tabular form that is both intuitive and efficient for constraint representation and processing. The constraint networks of ETPs include non-binary constraints and are difficult to formulate in terms of simple constraint solvers. We investigate the use of local search techniques for solving ETPs. In particular, we propose several versions of hill-climbing that make use of a novel search space that includes also partial assignments. We show that, on large and difficult instances of real world ETPs, where systematic search fails, local search methods perform well and solve the hardest instances. According to our experimental results on various techniques, a simple version of hill climbing based on random moves is the best method for solving large ETP instances.

Inter-agent cooperation and communication for agent-based robust dynamic scheduling in steel production

This paper describes a negotiation protocol proposed for inter-agent cooperation in a multi-agent system that we developed for optimisation and dynamic integrated scheduling within steel production. The negotiation protocol is a two-level bidding mechanism based on the Contract Net Protocol. The purpose of this protocol is to allow the agents to cooperate and coordinate their local schedules in order to find globally near-optimal robust schedules, whilst minimising the disruption caused by the occurrence of unexpected real-time events. We conduct several experiments to investigate the performance of this negotiation protocol to coordinate the agents in generating good quality robust schedules. This performance is evaluated in terms of stability and utility measures used to evaluate the robustness of the steel production processes in the presence of real-time events.

Asynchronous forward bounding for distributed COPs

A new search algorithm for solving distributed constraint optimization problems (DisCOPs) is presented. Agents assign variables sequentially and compute bounds on partial assignments asynchronously. The asynchronous bounds computation is based on the propagation of partial assignments. The asynchronous forward-bounding algorithm (AFB) is a distributed optimization search algorithm that keeps one consistent partial assignment at all times. The algorithm is described in detail and its correctness proven. Experimental evaluation shows that AFB outperforms synchronous branch and bound by many orders of magnitude, and produces a phase transition as the tightness of the problem increases. This is an analogous effect to the phase transition that has been observed when local consistency maintenance is applied to MaxCSPs. The AFB algorithm is further enhanced by the addition of a backjumping mechanism, resulting in the AFB-BJ algorithm. Distributed backjumping is based on accumulated information on bounds of all values and on processing concurrently a queue of candidate goals for the next move back. The AFB-BJ algorithm is compared experimentally to other DisCOP algorithms (ADOPT, DPOP, OptAPO) and is shown to be a very efficient algorithm for DisCOPs.

Message delay and DisCSP search algorithms

Distributed constraint satisfaction problems (DisCSPs) are composed of agents, each holding its own variables, that are connected by constraints to variables of other agents. Due to the distributed nature of the problem, message delay can have unexpected effects on the behavior of distributed search algorithms on DisCSPs. This has been recently shown in experimental studies of asynchronous backtracking algorithms (Bejar et al., Artif. Intell., 161:117–148, 2005; Silaghi and Faltings, Artif. Intell., 161:25–54, 2005). To evaluate the impact of message delay on the run of DisCSP search algorithms, a model for distributed performance measures is presented. The model counts the number of non concurrent constraints checks, to arrive at a solution, as a non concurrent measure of distributed computation. A simpler version measures distributed computation cost by the non-concurrent number of steps of computation. An algorithm for computing these distributed measures of computational effort is described. The realization of the model for measuring performance of distributed search algorithms is a simulator which includes the cost of message delays. Two families of distributed search algorithms on DisCSPs are investigated. Algorithms that run a single search process, and multiple search processes algorithms. The two families of algorithms are described and associated with existing algorithms. The performance of three representative algorithms of these two families is measured on randomly generated instances of DisCSPs with delayed messages. The delay of messages is found to have a strong negative effect on single search process algorithms, whether synchronous or asynchronous. Multi search process algorithms, on the other hand, are affected very lightly by message delay.

Modeling and solving distributed constraint satisfaction problems (DCSPs)

Constraint satisfaction problems (CSP) are part of many real world domains, such as computer vision and scheduling problems. Often, CSPs are solved in real life by several agents, each of them working on a part of the problem [3, 4]. A distributed CSP can be viewed as a set of constraint networks(CN), each CN being solved by a different agent, where the CNs are connected by constraints. A major assumption of the present paper is that checking constraints inside the distributed components has a much lower cost than checking constraints across different components. The latter check involves some kind of message passing that the solving algorithm would like to minimize. The processing of CNs have been studied extensively in the last decade [1, 2], usually within the standard model which is sequential. Several at tempts have been made at studying the processing of CNs in parallel The most relevant study of distributed CSPs has been made by Yokoo [5]. The basic difference between our approach and Yokoos approach is that our algorithms try to take advantage of the differences between the DCSPs components. The model of a DCSP of the present paper uses agents that are connected by a communication network (i.e., no common memory, just message passing). The number of agents is equal or larger by a small constant, to the number of subproblems in the given division of the DCSP. Based on this we state the following goals for our multi-agent algorithms:

Dynamic Ordering for Asynchronous Backtracking on DisCSPs

An algorithm that performs asynchronous backtracking on distributed

Solving Employee Timetabling Problems by Generalized Local Search

CSPs