Olinto César Bassi de Araújo

A fix-and-optimize heuristic for the high school timetabling problem

The high school timetabling is a classical combinatorial optimization problem that takes a large number of variables and constraints into account. Due to its combinatorial nature, solving medium and large instances to optimality is a challenging task. When resources are tight, it is often difficult to find even a feasible solution. Among the different requirements that are considered in Brazilian schools, two compactness requirements must be met on a teachers schedule: the minimization of working days and the avoidance of idle timeslots. In this paper, we present a mixed integer linear programming model and a fix-and-optimize heuristic combined with a variable neighborhood descent method. Our method uses three different types of decompositions - class, teacher and day - in order to solve the high school timetabling problem. The method is able to find new best known solutions for seven instances, including three optimal ones. A comparison with results reported in the literature shows that the proposed fix-and-optimize heuristic outperforms state-of-the-art techniques for the resolution of the problem at hand.

A multi-start random constructive heuristic for the container loading problem

This paper deals with the container loading problem which involves the selection of a subset of boxes, each box with a given volume, such that they fit in a single container and maximize its volume utilization subject to orientation and stability constraints. We propose a multi-start random constructive heuristic with a load arrangement that is based on maximal cuboids that fit in given empty spaces. Each instance is adaptively evaluated by a set of criteria, and at each step of the construction process one maximal cuboid is chosen probabilistically from a restricted list of candidates. In order to enhance the flexibility in the construction of a solution, a probabilistic reduction on such cuboids is allowed. Computational tests on several instances from the literature show that the proposed method performs better than other approaches.

Grasp with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times

This paper addresses the problem of scheduling jobs in a single machine with sequence dependent setup times in order to minimize the total tardiness with respect to job due dates. We propose variants of the GRASP metaheuristic that incorporate memory-based mechanisms for solving this problem. There are two mechanisms proposed in the literature that utilize a long-term memory composed of an elite set of high quality and sufficiently distant solutions. The first mechanism consists of extracting attributes from the elite solutions in order to influence the construction of an initial solution. The second one makes use of path relinking to connect a GRASP local minimum with a solution of the elite set, and also to connect solutions from the elite set. Reactive GRASP, which probabilistically determines the degree of randomness in the GRASP construction throughout the iterations, is also investigated. Computational tests for instances involving up to 150 jobs are reported, and the proposed method is compared with heuristic and exact methods from the literature.

Matheuristics for the capacitated p‐median problem

The improvement in the performance of computers and mathematical programming techniques has led to the development of a new class of algorithms called matheuristics. Associated with an improvement of Mixed Integer Programming (MIP) solvers, these methods have successfully solved plenty of combinatorial optimization problems. This paper presents a matheuristic approach that hybridizes local search based metaheuristics and mathematical programming techniques to solve the capacitated p-median problem. The proposal considers reduced mathematical models obtained by a heuristic elimination of variables that are unlikely to belong to a good or optimal solution. In addition, a partial optimization algorithm based on the reduction is proposed. All mathematical models are solved by an MIP solver. Computational experiments on five sets of instances confirm the good performance of our approach.

Mixed-Integer Linear Programming Formulations for the Software Clustering Problem

The clustering problem has an important application in software engineering, which usually deals with large software systems with complex structures. To facilitate the work of software maintainers, components of the system are divided into groups in such a way that the groups formed contain highly-interdependent modules and the independent modules are placed in different groups. The measure used to analyze the quality of the system partition is called Modularization Quality (MQ). Designers represent the software system as a graph where modules are represented by nodes and relationships between modules are represented by edges. This graph is referred in the literature as Module Dependency Graph (MDG). The Software Clustering Problem (SCP) consists in finding the partition of the MDG that maximizes the MQ.In this paper we present three new mathematical programming formulations for the SCP. Firstly, we formulate the SCP as a sum of linear fractional functions problem and then we apply two different linearization procedures to reformulate the problem as Mixed-Integer Linear Programming (MILP) problems. We discuss a preprocessing technique that reduces the size of the original problem and develop valid inequalities that have been shown to be very effective in tightening the formulations. We present numerical results that compare the formulations proposed and compare our results with the solutions obtained by the exhaustive algorithm supported by the freely available Bunch clustering tool, for benchmark problems.

A column generation approach to high school timetabling modeled as a multicommodity flow problem

School timetabling is a classic optimization problem that has been extensively studied due to its practical and theoretical importance. It consists in scheduling a set of class-teacher meetings in a predetermined period of time, satisfying requirements of different types. Given the combinatorial nature of this problem, solving medium and large instances of timetabling to optimality is a challenging task. When resources are tight, often it is difficult to find even a feasible solution. Several techniques have been developed in the literature to tackle the high school timetabling problem. Since the use of exact methods, as mathematical programming techniques, are considered impracticable to solve large real world instances, metaheuristics and hybrid metaheuristics are the most used solution approaches. In this paper we propose a multicommodity flow model for the high school timetabling problem. In addition, we apply Dantzig–Wolfe decomposition to the proposed model, propose a column generation algorithm, and present experimental results on well known instances of the problem. The results show that the lower bounds obtained through our approach are tight and can be generated faster than previous approaches reported in the literature.

Exact Algorithms for the Imbalanced Time Minimizing Assignment Problem

This paper studies the imbalanced time minimizing assignment problem (ITMAP) dealing with the allocation of n jobs to m (< n) machines. There are few works about this problem in the literature. In fact, only one lexi-shearch algorithm was found for the ITMAP, but it contain an slight error that was corrected here. Other algorithm by dynamic programming was found for the R∣Cmax problem and adapted for the ITMAP. A new approach through a linear model for this problem is introduced in this paper achieving considerables better results.

Conception and design of a lighting system based on Light Emitting Diodes for spectrum simulation

This work aims to develop an electronic system based on Light Emitting Diodes (LEDs) to emulate a reference light spectrum. Light Emitting Diodes are used due to their well-known advantages over other light sources. As an example of application, this work focuses on the design and implementation of a solid-state solar simulator whose spectrum resembles the natural daylight to support research on photosynthetic organisms. The system design and a spectrum optimization process are presented. Mixed Integer Programming (MIP) is adopted to set the optimal amount of LEDs that result in the most accurate response. The study of the LED spectrum, power converters for LED driving and control are discussed.

Binary integer programming applied to fault section estimation in power systems

This paper proposes a novel methodology for fault section estimation in electrical power systems based on binary integer programming (BIP). The operators of control centers are sometimes overloaded by the number of alarm messages produced when protection operate to clear faults. The main motivation for this work is the development of an alarm processing tool to support the operator decisions after disturbances in order to enhance the service reliability and reduce the power restoration time. The BIP model classifies SCADA alarms to estimate the faulted section and also to identify the malfunctioned protective devices. Possible fault scenarios were considered in part of a real Brazilian power system to validate the methodology. The results show that the proposed approach can find the optimal solution even in case of multiple faults or in case of protection devices failures.

Modelling and symmetry breaking in scheduling problems on batch processing machines

Problems of scheduling batch-processing machines to minimise the makespan are widely exploited in the literature, mainly motivated by real-world applications, such as burn-in tests in the semiconductor industry. These problems consist of grouping jobs in batches and scheduling them on machines. We consider problems where jobs have non-identical sizes and processing times, and the total size of each batch cannot exceed the machine capacity. The processing time of a batch is defined as the longest processing time among all jobs assigned to it. Jobs can also have non-identical release times, and in this case, a batch can only be processed when all jobs assigned to it are available. This paper discusses four different versions of batch scheduling problems, considering a single processing machine or parallel processing machines and considering jobs with or without release times. New mixed integer linear programming formulations are proposed as enhancements of formulations proposed in the literature, and symmetry breaking constraints are investigated to reduce the size of the feasible sets. Computational results show that the proposed formulations have a better performance than other models in the literature, being able to solve to optimality instances only considered before to be solved by heuristic procedures.