A matheuristic for customized multi-level multi-criteria university timetabling

Course timetables are the organizational foundation of a university’s educational program. While students and lecturers perceive timetable quality individually according to their preferences, there are also collective criteria derived normatively such as balanced workloads or idle time avoidance. A recent challenge and opportunity in curriculum-based timetabling consists of customizing timetables with respect to individual student preferences and with respect to integrating online courses as part of modern course programs or in reaction to flexibility requirements as posed in pandemic situations. Curricula consisting of (large) lectures and (small) tutorials further open the possibility for optimizing not only the lecture and tutorial plan for all students but also the assignments of individual students to tutorial slots. In this paper, we develop a multi-level planning process for university timetabling: On the tactical level, a lecture and tutorial plan is determined for a set of study programs; on the operational level, individual timetables are generated for each student interlacing the lecture plan through a selection of tutorials from the tutorial plan favoring individual preferences. We utilize this mathematical-programming-based planning process as part of a matheuristic which implements a genetic algorithm in order to improve lecture plans, tutorial plans, and individual timetables so as to find an overall university program with well-balanced timetable performance criteria. Since the evaluation of the fitness function amounts to invoking the entire planning process, we additionally provide a proxy in the form of an artificial neural network metamodel. Computational results exhibit the procedure’s capability of generating high quality schedules

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Learning-Based Approaches for Graph Problems: A Survey

Over the years, many graph problems specifically those in NP-complete are studied by a wide range of researchers. Some famous examples include graph colouring, travelling salesman problem and subgraph isomorphism. Most of these problems are typically addressed by exact algorithms, approximate algorithms and heuristics. There are however some drawback for each of these methods. Recent studies have employed learning-based frameworks such as machine learning techniques in solving these problems, given that they are useful in discovering new patterns in structured data that can be represented using graphs. This research direction has successfully attracted a considerable amount of attention. In this survey, we provide a systematic review mainly on classic graph problems in which learning-based approaches have been proposed in addressing the problems. We discuss the overview of each framework, and provide analyses based on the design and performance of the framework. Some potential research questions are also suggested. Ultimately, this survey gives a clearer insight and can be used as a stepping stone to the research community in studying problems in this field.Comment: v1: 41 pages; v2: 40 page