A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

Modelo de programación entera para la asignación de materias a las aulas de la USFQ

Nowadays, the creation of the schedules is a hard and time-consuming task in the internal processes of the university. An integer programming model is used in order to solve the timetabling problem in USFQ. The model allows assigning lectures, laboratories, exercise classes, and computational laboratories. Moreover, it avoids time conflicts between subjects, professors, rooms and courses that have to be taken by the students. Furthermore, equipment and infrastructure requirements are also considered. In addition, each professor shows their schedule preferences, so they are assured to have a balanced agenda. To solve this model an heuristic is created in order to overcome the computational limitations that result of the problem complexity. The model was validated with the data of the School of Engineering and Business Administration School, allowing to solve the timetabling problem successfully. There were not conflict detected and all the specifications were achieved. Finally, it was verified that the problem solved was NP-Hard so the resolution time grows exponentially when the variables number increases.En la actualidad, la creación de horarios en la universidad es una tarea bastante compleja y que consume mucho tiempo. Se crea un modelo de programación entera para la asignación de horarios a las aulas de la USFQ, el cual es un problema que cae dentro de la categoría de NP-hard y NP-complete, lo cual significa que el tiempo de resolución crece exponencialmente conforme se incrementa el número de variables. El modelo permite asignar clases teóricas, laboratorios, ejercicios y clases de computación. Además, evita todo tipo de conflictos de horario entre clases, profesores, aulas, y entre cursos que deben ser tomados por los mismos estudiantes. También se consideran los requerimientos de cada clase en cuanto a infraestructura y equipamiento. Se tiene la opción de que los profesores indiquen las horas en las que prefieren dictar clases, y se asegura que los profesores tengan un horario balanceado. Para resolver el modelo se crea una heurística que permite superar las limitaciones computacionales producidas por la complejidad del problema. El modelo fue validado con datos de dos colegios de la USFQ permitiendo crear horarios exitosamente, sin ningún tipo de conflictos y con las características señaladas. Finalmente, con los datos obtenidos se verifica que el problema es del tipo NP-Hard por lo que su tiempo de resolución crece exponencialmente conforme aumenta el número de variables

An adaptive jellyfish search algorithm for packing items with conflict

The bin packing problem (BPP) is a classic combinatorial optimization problem with several variations. The BPP with conflicts (BPPCs) is not a well-investigated variation. In the BPPC, there are conditions that prevent packing some items together in the same bin. There are very limited efforts utilizing metaheuristic methods to address the BPPC. The current methods only pack the conflict items only and then start a new normal BPP for the non-conflict items; thus, there are two stages to address the BPPC. In this work, an adaption of the jellyfish metaheuristic has been proposed to solve the BPPC in one stage (i.e., packing the conflict and non-conflict items together) by defining the jellyfish operations in the context of the BPPC by proposing two solution representations. These representations frame the BPPC problem on two different levels: item-wise and bin-wise. In the item-wise solution representation, the adapted jellyfish metaheuristic updates the solutions through a set of item swaps without any preference for the bins. In the bin-wise solution representation, the metaheuristic method selects a set of bins, and then it performs the item swaps from these selected bins only. The proposed method was thoroughly benchmarked on a standard dataset and compared against the well-known PSO, Jaya, and heuristics. The obtained results revealed that the proposed methods outperformed the other comparison methods in terms of the number of bins and the average bin utilization. In addition, the proposed method achieved the lowest deviation rate from the lowest bound of the standard dataset relative to the other methods of comparison

The development of a general algorithmic procedure for university examination timetabling

The problem of scheduling university examinations is becoming difficult for examination officers especially when they have to construct the timetables manually. It is largely due to the increasing number of students and greater freedom in choosing the courses. Examination officers would have to spend a considerable amount of time checking for student conflicts so that no student would have to sit for more than one exam at any one time. There are also other limitations such as the number of examination rooms, the length of the examination period and others. The examination timetabling problem varies between institutions, depending on their particular needs and limited resources. Most of the existing computerised examination timetabling systems found in the literature are developed and used by particular institutions. Therefore, the aim of the research is to produce a general computerised system for timetabling examinations which can be used by most universities. The research is done in two stages; the first stage involves carrying out a survey on the university examination timetabling systems and the second stage is the construction of a university examination timetabler incorporating the common objectives and constraints found in the survey. The survey was carried out to determine the extent to which the computerised examination timetabling procedures are used, to identify the objectives and constraints which are commonly considered when constructing examination timetables and to evaluate the effectiveness of the existing examination timetabling systems in achieving the objectives and satisfying the constraints The construction of the general examination timetabling system is done in two parts. In the first part, a new algorithmic rule is developed to assign exams to the minimum number of sessions without creating conflicts for any student. The rule adopts a clique initialisation strategy as a starting point and a graph colouring approach for assigning the exams. This rule is also quite capable of scheduling exams to the sessions which are as close as to the least number of sessions possible, without having to carry out any backtracking process. The backtracking process can sometimes be time consuming if there are a lot of exams firstly to be scheduled, and secondly clashing with each other. The second part of the work involves minimising the total number of students taking two exams on the same day and scheduling large exams early in the examination period subject to a specified time limit on the overall examination period and a maximum number of students that may be examined in any session. A swapping rule was introduced where exams in one of the sessions in any day with large number of sameday exams are interchanged with exams in other sessions which will reduce the total number of same-day exams. The experimentation showed that if the swapping procedures are repeated three times, the total number of same-day exams will be reduced by 50%. The total number of same-day exams will be reduced even more if some extra sessions can be added to the initial minimum number of sessions. A simple rule was devised to schedule large exams early in the examination period

Emploi du Temps : Problème mathématique ou problème pour Ia Programmation en Logique avec Contraintes ?

This technical report is a bibliographic study, an analysis and a synthesis of needs. This work is realized as part of a thesis about the subject"Constraint Logic Programming's application to the Timetable problems", within the department of Constraint Logic Programming (PLA :"Programmation en Logique et Applications") and the CNET's division SLC of Lannion-A. The subsidies come on the one hand from the Brittany's local committee, on the other hand from the national center of telecommunications studies (CNET).The Timetable problem is difficult and can give many days of work to one or two persons. A Timetable is very important due to the fact that it deals with the good management of time for different people who have their own activities. In big institutions (secondary schools, colleges of tlniversity ; CNET ...), many difficulties arise : big volume of data, fuzzy criterion of optimization, combinatorial problem, very varied constraints, inopportune changes. Then, many applications have grown either from mathematic models assisted by graph theory, or from other techniques such as operational research or artificial intelligence.This paper draws the requirements to solve this problem and proposes a model of resolution by the approach of Constraint Logic Programming.Cette note technique est le résultat d'une étude bibliographique, d'une analyse et d'une synthèse des besoins, réalisées dans le cadre d'une thèse dont le sujet est "Application de la Programmation en Logique avec Contraintes aux problèmes d'Emploi du Temps", au sein de l'équipe Programmation en Logique avec Contraintes (PLA) dans la division SLC au CNET-Lannion A. Cette thèse est subventionnée d'une part par le Conseil Régional de Bretagne et d'autre part par le CNET.Le problème d'Emploi du Temps est un problème difficile qui peut donner plusieurs jours de travail à une ou deux personnes. L'importance d'un Emploi du Temps est évidente puisqu'il s'agit de gérer le temps de différentes personnes possédant leurs propres activités et ceci d'une manière satisfaisante pour chacune d'elle. Dans de grands établissements (lycées, grandes écoles ;CNET ; IRET ; ...), on se trouve confronté à de multiples difficultés : volume important d'informations, critère d'optimisation flou, combinatoire, contraintes très diverses, changements intempestifs. De ce fait, plusieurs recherches et essais de résolutions se sont développés, que ce soit par des modélisations mathématiques aidées de la théorie des graphes ou que ce soit par d'autres techniques issues de la Recherche Opérationnelle ou de l’IntelligenceArtificielle.Ce document conclut en dégageant les besoins pour informatiser et résoudre ce problème et propose une modélisation de résolution fondée sur I'approche Programmation en Logique avec Contraintes

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

Planeación de evaluaciones de recuperación en la Universidad Autónoma Metropolitana

En la División de Ciencias Básicas e Ingeniería de la Universidad Autónoma Metropolitana, Unidad Azcapotzalco se calendarizan dos tipos de evaluaciones: evaluaciones globales y evaluaciones de recuperación. Esta tesis estará enfocada en el problema de planeación de evaluaciones de recuperación, el cual es un problema que combina aspectos de los problemas de planeación de cursos y de evaluaciones, pues las evaluaciones de recuperación deben planearse antes de la inscripción de los alumnos, pero pueden compartir salón. En la práctica, la planeación de evaluaciones de recuperación debe tomar en cuenta muchos aspectos distintos y es casi un hecho que no puedan encontrarse planeaciones perfectas. Por ejemplo, minimizar el número de salones y el número de horarios por día aumenta la probabilidad de generar empalmes entre evaluaciones que el alumno quiera inscribir al mismo tiempo, mientras que minimizar el número de días de evaluación posiblemente requiera usar más horarios por día. El problema puede verse como un problema multi-objetivo, pero en esta tesis se propone usar métodos de programación matemática para encontrar mejores planeaciones. En este caso, se propone usar la técnica usual de convertir un problema multiobjetivo en un problema mono-objetivo optimizando una suma ponderada de los objetivos múltiples.Investigación realizada con el apoyo del Programa Nacional de Posgrados de Calidad del Consejo Nacional de Ciencia y Tecnología (CONACYT)