Fuzzy Integer Linear Programming Mathematical Models for Examination Timetable Problem
This work addresses scheduling challenges in universities, but it is incremental as it applies an existing fuzzy method to a known problem with specific datasets.
The authors tackled the NP-hard Examination Timetable Problem (ETP) by developing three Fuzzy Integer Linear Programming (FILP) mathematical models to handle impreciseness, using fuzzy numbers and ranking methods, and compared them with heuristic approaches like ILP and AI-based methods on Carter benchmark datasets, showing FILP takes appreciable time but serves as a good benchmark.
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.