A tabu search heuristic for the Equitable Coloring Problem

The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several applications. Due to the hardness of the problem, current exact algorithms can not solve large-sized instances. Such instances must be addressed only via heuristic methods. In this paper we present a tabu search heuristic for the Equitable Coloring Problem. This algorithm is an adaptation of the dynamic TabuCol version of Galinier and Hao. In order to satisfy equity constraints, new local search criteria are given. Computational experiments are carried out in order to find the best combination of parameters involved in the dynamic tenure of the heuristic. Finally, we show the good performance of our heuristic over known benchmark instances

Creating seating plans: A practical application

© 2016 Operational Research Society Ltd. All rights reserved. 0160-5682/16. This paper examines the interesting problem of designing seating plans for large events such as weddings and gala dinners where, among other things, the aim is to construct solutions where guests are sat on the same tables as friends and family, but, perhaps more importantly, are kept away from those they dislike. This problem is seen to be N P-complete from a number of different perspectives. We describe the problem model and heuristic algorithm that is used on the commercial website www.weddingseatplanner.com. We present results on the performance of this algorithm, demonstrating the factors that can influence run time and solution quality, and also present a comparison with an equivalent IP model used in conjunction with a commercial solver

Construção de Calendários de Exames

Tese de mestrado, Estatística e Investigação Operacional (Investigação Operacional) Universidade de Lisboa, Faculdade de Ciências, 2022Todos os anos, os estabelecimentos de ensino tem de criar calendários de exames. Uma grande maioria destes estabelecimentos ainda opta pela sua criação manual, resultando numa tarefa demorada, e muitas vezes, pouco eficiente. A Faculdade de Ciências da Universidade de Lisboa não é uma exceção, utilizando um calendário de exames já criado em anos anteriores, e adaptando manualmente ao ano letivo corrente. O problema da calendarização de exames pertence a classe de problemas NP-Difícil e, como tal, para obter soluções de boa qualidade em tempos aceitáveis são necessários algoritmos heurísticos. Um dos tipos de algoritmos utilizados para este género de problemas são os algoritmos de coloração de grafos. Nesta dissertação são propostos três algoritmos, testados em dez instâncias diferentes, para a criação de um calendário de exames direcionado para a época especial, uma época de exames na qual apenas dias antes da sua realização se sabe ao certo o número de alunos para cada exame. Os primeiros algoritmos utilizados neste trabalho são de coloração de grafos e coloração equitativa, para a criação do calendário de exames, e tem como objetivo uma distribuição mais uniforme, e justa para os alunos, dos exames pelos dias da época especial. O terceiro algoritmo desenvolvido é baseado em algoritmos de caminho ótimo, para a reorganização dos dias do calendário criado para a melhoria de uma restrição soft, a garantia de que todos os alunos tenham pelo menos um dia de intervalo entre os dois exames. Os resultados obtidos foram favoráveis para todas instâncias, sendo possível concluir que a utilização de algoritmos de coloração de grafos permite atingir resultados promissores, principalmente se complementados com outro tipo de algoritmos direcionados para a melhoria das restrições soft.Every year, educational institutions have to create exam schedules. A large majority of this insti tutions still create them manually, resulting in a time-consuming and often not very efficient task. The Faculdade de Ciencias da Universidade de Lisboa is no exception, using an already existing exam schedule already created in previous years, and adapting it manually to the current academic year. The exam scheduling problem belongs to the class of NP-hard problems and, as such, to obtain good quality soluti ons in acceptable times heuristic algorithms are required. Graph coloring algorithms are one of the type of algoritmhs used for this kind of problems. In this dissertation three algorithms are proposed, tested in ten different instances, for the creation of an exam schedule aimed to the special examination period, an exam period in which only a few days before its realization it is known for sure the number of stu dents enrolled in each exam. The two first algorithms used in this work are graph coloring and equitable coloring, for the creation of the exam schedule, with the goal of a more uniform, and fairer distribution for students, of exams over the days of the special period. The third algorithm developed is based on optimal path algorithms, for the reorganization of the days of the created schedule for the improvement of the soft constraint, the guarantee that all students have at least one day between the two exams. The obtained results were favorable for all instances, and it is possible to bring to a conclusion that the use of graph coloring algorithms allows the achievement of promising results, especially if complemented with other types of algorithms, aimed at improving the soft constraints

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Planning, Scheduling, and Timetabling in a University Setting

Methods and procedures for modeling university student populations, predicting course enrollment, allocating course seats, and timetabling final examinations are studied and proposed. The university enrollment model presented uses a multi-dimensional state space based on student demographics and the Markov property, rather than longitudinal data to model student movement. The procedure for creating adaptive course prediction models uses student characteristics to identify groups of undergraduates whose specific course enrollment rates are significantly different than the rest of the university population. Historical enrollment rates and current semester information complete the model for predicting enrollment for the coming semester. The course prediction model aids in the system for reserving course seats for new students during summer registration sessions. The seat release model addresses how to estimate seat need each session, how to release seats among multiple course sections, and how to predict seat shortages and surpluses. Finally, procedures for creating reusable university final examination timetables are developed and compared. Course times, rather than individual courses, are used as the assignment elements because the demand for course times remains relatively constant despite changes in course schedules. Our heuristic procedures split the problem into two phases: a clustering phase--to minimize conflicts--and a sequencing phase--to distribute exams throughout finals week while minimizing the occurrence of consecutive exams. Results for all methods are compared using enrollment data from Clemson University