"The Crossword puzzle (CP) is a simple problem to illustrate the formalization process of a problem into a CSP. The problem is to place words of a dictionary in a given structure satisfying certain constraints. The variables are the rows and columns in the crossword, and their values are the words in a dictionary."
– Marc Torrens. An Application using the JCL: The Air Travel Planning System. Diploma Thesis, 1997, Chapter 1, Section 1.2.1.
ETP is NP Hard combinatorial optimization problem. It has received tremendous research attention during the past few years given its wide use in universities. In this Paper, we develop three mathematical models for NSOU, Kolkata, India using FILP technique. To deal with impreciseness and vagueness we model various allocation variables through fuzzy numbers. The solution to the problem is obtained using Fuzzy number ranking method. Each feasible solution has fuzzy number obtained by Fuzzy objective function. The different FILP technique performance are demonstrated by experimental data generated through extensive simulation from NSOU, Kolkata, India in terms of its execution times. The proposed FILP models are compared with commonly used heuristic viz. ILP approach on experimental data which gives an idea about quality of heuristic. The techniques are also compared with different Artificial Intelligence based heuristics for ETP with respect to best and mean cost as well as execution time measures on Carter benchmark datasets to illustrate its effectiveness. FILP takes an appreciable amount of time to generate satisfactory solution in comparison to other heuristics. The formulation thus serves as good benchmark for other heuristics. The experimental study presented here focuses on producing a methodology that generalizes well over spectrum of techniques that generates significant results for one or more datasets. The performance of FILP model is finally compared to the best results cited in literature for Carter benchmarks to assess its potential. The problem can be further reduced by formulating with lesser number of allocation variables it without affecting optimality of solution obtained. FLIP model for ETP can also be adapted to solve other ETP as well as combinatorial optimization problems.
We present a tutorial introduction to the area of preference handling - one of the core issues in the design of any system that automates or supports decision making. The main goal of this tutorial is to provide a framework, or perspective, within which current work on preference handling -representation, reasoning, and elicitation - can be understood. Our intention is not to provide a technical description of the diverse methods used, but rather, to provide a general perspective on the problem and its varied solutions and to highlight central ideas and techniques.
Although timetabling has long been studied through constraint satisfaction based techniques, along with many alternatives, only recently work has been reported where distributed timetabling problems (DisTTPs) was studied as distributed constraint satisfaction problems (DisCSPs). We present an alternative method for solving DisTTPs based on multiply sectioned constraint networks (MSCNs). The proposed solution has several distinguishing features: Unlike the existing algorithms for DisCSPs whose worst-case time complexities are exponential, the algorithm suite based on MSCNs is efficient when the network topology is sparse. Unlike the existing DisTTP algorithm where a central agent is needed, there is no need for a central agent in the proposed solution. Unlike the existing DisTTP algorithm where partial timetables of other agents must be disclosed to the central agent, the proposed method keeps partial timetables of all agents private. We report our preliminary experimental result on distributed university timetabling problems (DisUTTPs). Multiagent system, Multiply Sectioned Constraint Networks, Distributed Constraint Satisfaction, Distributed University Timetabling.
Artificial Intelligence (AI) is a field of both great breadth and depth. Thus, determining undergraduate material for an AI course can be problematic. Fortunately, AI is continually searching for new perspectives on problem solving that eventually propagate into the Computer Science mainstream. An approach is proposed for undergraduate AI education that utilizes these aspects of exploration and propagation. The approach introduces important individual techniques early in the computer science curriculum to form a foundation for the upper-level AI course focusing on research methods.
In most schools and colleges, producing a timetable is a task that is dreaded by those charged with annually creating it. In schools in particular, it can be difficult to produce any solution at all because teaching resources are usually stretched to the limit. This situation is made more difficult by the fact that the person making up the timetable must not only produce a valid solution but one that is of good quality. A large number of judgmental factors are involved in producing a good-quality timetable. Some of these are educational (for example, it is undesirable for a group of pupils to have a Spanish lesson immediately following a German one), others pertain to the work conditions of the staff (for example, the teaching load should be distributed evenly through the day so that no teacher has a long, contiguous block of lessons), and others are political (for example, a senior teacher should not end up with fewer free periods than a more junior one).