Guided genetic algorithm for solving unrelated parallel machine scheduling problem with additional resources

This paper solved the unrelated parallel machine scheduling with additional resources (UPMR) problem. The processing time and the number of required resources for each job rely on the machine that does the processing. Each job j needed units of resources (rjm) during its time of processing on a machine m. These additional resources are limited, and this made the UPMR a difficult problem to solve. In this study, the maximum completion time of jobs makespan must be minimized. Here, we proposed genetic algorithm (GA) to solve the UPMR problem because of the robustness and the success of GA in solving many optimization problems. An enhancement of GA was also proposed in this work. Generally, the experiment involves tuning the parameters of GA. Additionally, an appropriate selection of GA operators was also experimented. The guide genetic algorithm (GGA) is not used to solve the unspecified dynamic UPMR. Besides, the utilization of parameters tuning and operators gave a balance between exploration and exploitation and thus help the search escape the local optimum. Results show that the GGA outperforms the simple genetic algorithm (SGA), but it still didn't match the results in the literature. On the other hand, GGA significantly outperforms all methods in terms of CPU time

Greedy randomized adaptive evolutionary path relinking aplicado a problemas de máquinas paralelas não relacionadas com recursos renováveis

Orientador: Prof. Dr. José Eduardo Pécora JuniorCoorientador: Prof. Dr. Maurício Guilherme de Carvalho ResendeDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa : Curitiba, 30/07/2020Inclui referências: p. 89-94Área de concentração: Programação MatemáticaResumo: Esta dissertação aborda o problema de máquinas paralelas não relacionadas, com restrição de recursos renováveis (UPMR), para minimizar o makespan. Para este problema é proposto um Greedy Randomized Adaptive Evolutionary Path-Relinking (GRAEPR) e uma abordagem híbrida com um modelo de programação por restrição (CP). Os resultados apresentam soluções competitivas com as presentes na literatura, estabelecendo alguns novos Lower e Upper Bounds. Além disso, é apresentada uma extensão para este problema. É introduzido o problema de máquinas paralelas não relacionadas, com setup dependente e restrição de recursos renováveis (UPMSR). Para este problema é apresentado um modelo de programação inteira mista (MILP), um modelo de programação por restrição e uma uma adaptação da abordagem de Fleszar e Hindi (2018). Além disso, são modificadas as abordagens do Greedy Randomized Adaptive Evolutionary Path-Relinking e híbrida desenvolvidas para o UPMR. Um conjunto de instâncias é gerada para UPMSR e os resultados evidenciam o potencial existente na abordagem GRAEPR. Palavras-chaves: Máquinas paralelas não relacionadas. Restrição de recursos Renováveis. Programação linear inteira mista. Programação por restrição. Path-relinking.Abstract: This thesis addresses the problem of unrelated parallel machines, with restriction of renewable resources (UPMR), to minimize the makespan. For this problem, a Greedy Randomized Adaptive Evolutionary Path-Relinking (GRAEPR) and a hybrid approach with a constraint programming (CP) model is proposed. The results show competitive solutions with those found in the literature, establishing some new values for Lower and Upper Bounds. In addition, an extension is presented for this problem. We introduce the problem of unrelated parallel machines, with dependent setup and restriction of renewable resources (UPMSR). For this problem, we present a mixed integer linear programming (MILP) model, a contraint programming (CP) model, and an adaptation of the approach of Fleszar and Hindi (2018). We also modify the Greedy Randomized Adaptive Evolutionary Path-Relinking and the hybrid approach developed for the UPMR. A set of instances is generated for UPMSR and the results show the potential that exists in the GRAEPR approach. Key-words: Unrelated parallel machines. Renewable resource constraint. Mixed-integer linear programming. Constraint programming. Path-relinkin

Approximation Algorithms for Modern Multi-Processor Scheduling Problems

This thesis is devoted to the design and analysis of algorithms for scheduling problems. These problems are ubiquitous in the modern world. Examples include the optimization of local transportation, managing access to concurrent resources like runways at airports and efficient execution of computing tasks on server systems. Problem instances that appear in the real world often are so large and complex that it is not possible to solve them “by hand”. This rises the need for strong algorithmic approaches, which motivates our focus of study. In this work we consider two types of scheduling problems which gained in importance due to recent technological advances. The first problem comes from the avionics industry and deals with scheduling periodically recurring tasks in a parallel computer network on a plane: Each task comes with a period p and execution time c, and needs to use a processor exclusively for c time units every p time units. The scheduling problem is to assign starting offsets for the first execution of the tasks so that no collision occurs. The second problem is a scheduling problem that arises in highly parallelized processing environments with a shared common resource, e.g., modern multi-core computer architectures. In addition to classical makespan minimization problems such as scheduling on identical machines, each job has an additional resource constraint. The scheduler must ensure that at no time, the accumulated requirement of all active jobs at that time exceeds a given limit. For both types of problems we study their algorithmic complexity in a mathematical, rigorous way by designing approximation algorithms and establishing inapproximability results. We thereby give a characterization of the approximation landscape of these problems. We also consider a more practical perspective: For an engineer from the industry, a rigorous proof that an algorithm finds a solution of certain guaranteed quality for all possible kinds of problem instances is usually not that relevant. It is rather of interest to find “good enough” or even optimal solutions for particular instances that actually appear in the real world in “reasonable” time. We show that structural insights gained in the more theoretical process of designing approximation algorithms can be highly beneficial also for obtaining practical results. In particular, we develop integer programming formulations for the avionics problem based on structural properties revealed in the design of approximation algorithms. These formulations lead to strong tools that, for the first time, enable to algorithmically solve real-world instances from our industrial partner