Parallel Meta-heuristic Approaches to the Course Timetabling Problem

In this study, the performance of Scatter Search (SS) meta-heuristic for the post-enrolment course timetabling problems reported in recent literature was reviewed. The aim is to address the strengths and limitations of the SS structure and mechanisms; to empower more studies; to investigate the capabilities of SS; and to enhance it for solving timetabling problems as a whole. The SS is almost similar to memetic algorithms. However, it has a memory of elite solutions (which considers both high quality and diverse solutions) and combines two or more solutions explicitly based on elitism. SS contains a mechanism to strike a balance between diversification and intensification of the search. SS has five major steps: initializing a diverse collection of solutions; general solutions improvement; memorizing elite solutions, solutions combination; and improving the selected solution. Based on the outcomes of SS (tested on post-enrolment course timetabling problems), which was reported in the literature, this study concluded that the impact of SS's strategies are significant for a successful SS search performance. These strategies are: memory update, solutions selection, diversification (i.e. similarity measurement), and solutions combination. Indeed, updating the memory and solutions combination, have the greatest impact on the performance of SS. Therefore, future studies regarding the design of these two strategies for solving timetabling problems is recommended to be more carefully designed.

Exam timetabling is a computationally intractable problem, which requires heuristic techniques for producing good sub-optimal solutions within reasonable execution time. For large numbers of exams and students, sequential algorithms are likely to be time consuming. The purpose of this work is to present a parallel metaheuristic algorithm for producing good sub-optimal exam timetables in a reasonable time. Empirical results show that our proposed parallel scatter search algorithm yields good speedup. Also, they show that the parallel algorithm improves solution quality in comparison with the sequential algorithm.

The timetabling problem is well known to be an NP-complete combinatorial problem. The problem becomes even more complex when addressed to individual timetables of students. The core of dealing with the problem in this application is a timetable builder based on mixed direct-indirect encoding evolved by a genetic algorithm with a self-adaptation paradigm, where the parameters of the genetic algorithm are optimized during the same evolution cycle as the problem itself. The aim of this paper is to present an encoding for self-adaptation of genetic algorithms that is suitable for timetabling problems. Compared to previous approaches we designed the encoding for self-adaptation of not only one parameter or several ones but for all possible parameters of genetic algorithms at the same time. The proposed self-adaptive genetic algorithm is then applied for solving the real university timetabling problem and compared with a standard genetic algorithm. The main advantage of this approach is that it makes it possible to solve a wide range of timetabling and scheduling problems without setting parameters for each kind of problem in advance. Unlike common timetabling problems, the algorithm was applied to the problem in which each student has an individual timetable, so we also present and discuss the algorithm for optimized enrollment of students that minimizes the number of clashing constraints for students.

We present a parallel Delaunay refinement algorithm for generating well-shaped meshes in both two and three dimensions. Like its sequential counterparts, the parallel algorithm iteratively improves the quality of a mesh by inserting new points, the Steiner points, into the input domain while maintaining the Delaunay triangulation. The Steiner points are carefully chosen from a set of candidates that includes the circumcenters of poorly-shaped triangular elements. We introduce a notion of independence among possible Steiner points that can be inserted simultaneously during Delaunay refinements and show that such a set of independent points can be constructed efficiently and that the number of parallel iterations is O( log 2Δ), where Δ is the spread of the input — the ratio of the longest to the shortest pairwise distances among input features. In addition, we show that the parallel insertion of these set of points can be realized by sequential Delaunay refinement algorithms such as by Ruppert's algorithm in two dimensions and Shewchuk's algorithm in three dimensions. Therefore, our parallel Delaunay refinement algorithm provides the same shape quality and mesh-size guarantees as these sequential algorithms. For generating quasi-uniform meshes, such as those produced by Chew's algorithms, the number of parallel iterations is in fact O( log Δ). To the best of our knowledge, our algorithm is the first provably polylog(Δ) time parallel Delaunay-refinement algorithm that generates well-shaped meshes of size within a constant factor of the best possible.

Solving scheduling problems enables more efficient use of production capacity. It involves defining the sequence of operations, determining the capacity of resources, and balancing workloads. Different methods, especially metaheuristics, have been used to solve these problems. This study presents the application of Scatter Search (SS), Genetic Algorithm (GA), and Greedy Randomized Adaptive Search Procedures (GRASP) for minimizing makespan in a permutation flow shop environment. In this study, the performances of these methods are compared through various test problems in the literature and a real-life problem of a company operating in the automotive sector. Study comprises 48 jobs that must be planned within a day for eight consecutive operations. In cellular manufacturing, the sequence in which each job is processed in eight operations is the same. In solving permutation flow shop scheduling problems (PFSP), one of the NP-hard problems, meta-heuristic methods are widely applied due to their successful results. From this point of view, SS, GA, and GRASP are employed in this study, and their performances are compared.

A scatter search algorithm for stacking sequence optimisation of laminate composites

In the present paper, optimization of functions with uncertainty by means of Genetic Algorithms (GA) is discussed. For such problems, there have been proposed methods of sampling fitness function several times and taking average of them for evaluation of each individual. However, important applications having uncertain fitness functions are online adaptation of real systems and complicated computer simulation using random variables. In such applications, possible number of fitness evaluation is quite limited. Hence, methods achieving optimization with less number of fitness evaluation is needed. In the present paper, the authors propose a GA for optimization of continuous fitness functions with observation noise utilizing history of search so as to reduce number of fitness evaluation. In the proposed method, value of fitness function at a novel search point is estimated not only by the sampled fitness value at that point but also by utilizing the fitness values of individuals stored in the history of search. Computer experiments using quadric fitness functions show that the proposed method outperforms the conventional GA of sampling fitness values several times at each search point in noisy environment.

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

Data partitioning algorithms aiming to minimize the execution time and the energy of computations in self-adaptable data-parallel applications on modern extreme-scale multicore platforms must address two critical challenges. First, they must take into account the new complexities inherent in these platforms such as severe resource contention and non-uniform memory access. Second, they must have low practical runtime and memory costs. The sequential data partitioning algorithms addressing the first challenge have a theoretical time complexity of O( $m * m * p * p$ ) where $m$ is the number of points in the discrete speed/energy function and $p$ is the number of available processors. They, however, exhibit high practical runtime cost and excessive memory footprint, therefore, rendering them impracticable for employment in self-adaptable applications executing on extreme-scale multicore platforms. We present, in this paper, the parallel data partitioning algorithms that address both the challenges. They take as input the functional models of performance and energy consumption against problem size and output workload distributions, which are globally optimal solutions. They have a low time complexity of O( $m * m * p$ ) thereby providing a linear speedup of O( $p$ ) and low memory complexity of O( $n$ ) where $n$ is the workload size expressed as a multiple of granularity. They employ dynamic programming approach, which also facilitates the easier integration of performance and energy models of communications. We experimentally study the practical cost of application of our algorithms in two data-parallel applications, matrix multiplication and fast Fourier transform, on a cluster in Grid’5000 platform. We demonstrate that their practical runtime and memory costs are low making them ideal for employment in self-adaptable applications. We also show that the parallel algorithms exhibit tremendous speedups over the sequential algorithms. Finally, using theoretical analysis for a forecast exascale platform, we demonstrate that the parallel algorithms have negligible execution times compared to the matrix multiplication application executing on the platform.

We present a general framework for solving a real-world multimodal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds.

A large number of studies have been conducted in the area of semiconductor final test scheduling (SFTS) problems. As a specific example of the simultaneous multiple resources scheduling problem, intelligent manufacturing planning and scheduling based on meta-heuristic methods, such as the genetic algorithm (GA), simulated annealing, and particle swarm optimization, have become common tools for finding satisfactory solutions within reasonable computational times in real settings. However, only a few studies have analyzed the effects of interdependent relations during group decision-making activities. Moreover, for complex and large problems, local constraints and objectives from each managerial entity and their contributions toward global objectives cannot be effectively represented in a single model. This paper proposes a novel cooperative estimation of distribution algorithm (CEDA) to overcome these challenges. The CEDA extends a co-evolutionary framework incorporating a divide-and-conquer strategy. Numerous experiments have been conducted, and the results confirmed that CEDA outperforms hybrid GAs for several SFTS problems.

Logistics Equipment Scheduling (LES) problem in iron and steel industry is to select appropriate raw material piles and equipments for logistics equipment schedule with the objective of minimizing the operation cost of raw material yard, maximizing the utilization and the equilibrium ratio of reclaimers in the production process. Different from previous literatures, according to the characteristics of raw material yard, the LES problem is divided into two phases: the first one is how to select raw material piles, the other one is a reclaimer scheduling problem. The LES problem is formulated as a multi-targets mixed integer programming model by considering the practical requirements. The complexity of the model motivates us to develop a scatter search-based strategy algorithm to solve the problem approximately. Problem-oriented coding scheme and solution combination method are proposed in scatter search. The computational results on real data show that the cost is decreased by 25.85% in average compared with manual schedule.

Three diagnostic rapid test kits (Chembio HIV-1/2 Stat-Pak, Alere DetermineTM HIV-1/2, and Core HIV-1/2) for human immunodeficiency virus types 1 and 2 (HIV-1/2) antibodies detection were evaluated against a gold standard fourth generation ELISA (Dia-Pro). Hundred and seventy two serum samples were collected from Lulubriggs Health Center, University of Port Harcourt, Rivers State. All samples were tested for HIV-1/2 using the three rapid test (parallel algorithm and serial algorithm), and retested using the 4th generation ELISA. The results obtained were compared with those from the ELISA. The DetermineTM rapid strips had sensitivity of 66.7%, specificity of 100%, positive predictive value 100%, negative predictive value 89.4% and total agreement of 91.3%. Stat-pak and Core HIV-1/2 rapid strips both had sensitivity of 71.7%, specificity of 100%, positive predictive value 100%, and negative predictive value 90.7% and total agreement of 92.4%. Determine was mostly used by the participant laboratories 18 of 30 (60%). The performance evaluation of the testing algorithm showed that parallel algorithm is more accurate in comparison to serial algorithm. The result of this study reveals that most rapid test are less sensitive and the accuracy of serial testing algorithm is low, this implies that most acute HIV infection will be missed with rapid assay and false negative results will be reported as actual negative with serial algorithm.

Operating room (OR) planning and scheduling is a highly complex combinatorial optimization problem that involves patient assignment, OR allocation, and surgical sequencing within a constrained planning horizon. This study addresses the OR scheduling problem by incorporating downstream bed availability in both hospital wards and intensive care units (ICUs), aiming to improve operational efficiency and patient outcomes. A mixed-integer programming (MIP) model is developed to minimize the total completion time across all operating rooms during the planning period. Given the NP-hard nature of the problem, a novel Genetic Engineering Algorithm (GEA) is proposed as an advanced extension of the traditional Genetic Algorithm (GA). The GEA incorporates three innovative search strategies inspired by genetic engineering principles, refining the crossover and mutation operators to improve solution quality and convergence speed. To evaluate the effectiveness of the proposed algorithm, GEA and its variants are tested on 18 benchmark instances of varying problem sizes for the proposed OR planning and scheduling problem. A real-world case study from a hospital in Pakistan illustrates the practical applicability of the proposed approach using different real-world criteria. The results demonstrate that GEA consistently outperforms state-of-the-art metaheuristic algorithms. Its robustness and accuracy are further validated using 10 standard mathematical benchmark functions. The results confirm the GEA’s effectiveness and efficiency in addressing complex OR planning and scheduling problems and underscore its potential for advancing metaheuristic algorithm design in combinatorial optimization.

Parallel and sequential transformations on digital images