A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling

Rego, Marcelo Ferreira; Pinto, Julio Cesar; Cota, Luciano Perdig�ão; Souza, Marcone Jamilson Freitas

doi:10.7717/peerj-cs.844

Cited by 14 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of note, TPE successfully achieved the desired result in less than 100 iterations, establishing these algorithms as the preferred choice for addressing similar challenges. NSGA is a widely used genetic algorithm that guarantees the inclusion of individuals with extreme values of the target functionals in the set of parents (Joshi et al, 2021;Rego et al, 2022;Saravanamuthu et al, 2022). TPE, on the other hand, is a Tree-Structured Parzen Estimator algorithm typically used to optimize ML model hyperparameters (Bergstra et al, 2011;2013), and it was intriguing to find that it was also suitable for optimizing a heart valve design.…”

Section: Discussionmentioning

confidence: 99%

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Danilov,

Klyshnikov,

Onishenko

et al. 2023

Front. Bioeng. Biotechnol.

View full text Add to dashboard Cite

Majority of modern techniques for creating and optimizing the geometry of medical devices are based on a combination of computer-aided designs and the utility of the finite element method This approach, however, is limited by the number of geometries that can be investigated and by the time required for design optimization. To address this issue, we propose a generative design approach that combines machine learning (ML) methods and optimization algorithms. We evaluate eight different machine learning methods, including decision tree-based and boosting algorithms, neural networks, and ensembles. For optimal design, we investigate six state-of-the-art optimization algorithms, including Random Search, Tree-structured Parzen Estimator, CMA-ES-based algorithm, Nondominated Sorting Genetic Algorithm, Multiobjective Tree-structured Parzen Estimator, and Quasi-Monte Carlo Algorithm. In our study, we apply the proposed approach to study the generative design of a prosthetic heart valve (PHV). The design constraints of the prosthetic heart valve, including spatial requirements, materials, and manufacturing methods, are used as inputs, and the proposed approach produces a final design and a corresponding score to determine if the design is effective. Extensive testing leads to the conclusion that utilizing a combination of ensemble methods in conjunction with a Tree-structured Parzen Estimator or a Nondominated Sorting Genetic Algorithm is the most effective method in generating new designs with a relatively low error rate. Specifically, the Mean Absolute Percentage Error was found to be 11.8% and 10.2% for lumen and peak stress prediction respectively. Furthermore, it was observed that both optimization techniques result in design scores of approximately 95%. From both a scientific and applied perspective, this approach aims to select the most efficient geometry with given input parameters, which can then be prototyped and used for subsequent in vitro experiments. By proposing this approach, we believe it will replace or complement CAD-FEM-based modeling, thereby accelerating the design process and finding better designs within given constraints. The repository, which contains the essential components of the study, including curated source code, dataset, and trained models, is publicly available at https://github.com/ViacheslavDanilov/generative_design.

show abstract

Section: Discussionmentioning

confidence: 99%

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Danilov,

Klyshnikov,

Onishenko

et al. 2023

Front. Bioeng. Biotechnol.

View full text Add to dashboard Cite

show abstract

“…The NSGA-II algorithm achieves nondominated ranking by calculating the Pareto rank and crowding distance of sample points, and then generates offspring through selection, crossover, and mutation, generates new parents using the elite strategy, and then repeats this process until convergence at the Pareto front [39]. The algorithm has very good performance for two or three targets, and thus has the potential to improve the representativeness of the sampling results [40]. Moreover, the algorithm can also ensure sufficient variability among the samples of the population, guaranteeing the diversity of the sampling results [21].…”

Section: The Nsga-ii Algorithm With Constraintsmentioning

confidence: 99%

Improving the Performance of Hydrological Model Parameter Uncertainty Analysis Using a Constrained Multi-Objective Intelligent Optimization Algorithm

Liu

Kan

Ding

et al. 2023

Water

View full text Add to dashboard Cite

In the field of hydrological model parameter uncertainty analysis, sampling methods such as Differential Evolution based on Monte Carlo Markov Chain (DE-MC) and Shuffled Complex Evolution Metropolis (SCEM-UA) algorithms have been widely applied. However, there are two drawbacks which may introduce bad effects into the uncertainty analysis. The first disadvantage is that few optimization algorithms consider the physical meaning and reasonable range of the model parameters. The traditional sampling algorithms may generate non-physical parameter values and poorly simulated hydrographs when carrying out the uncertainty analysis. The second disadvantage is that the widely used sampling algorithms commonly involve only a single objective. Such sampling procedures implicitly introduce too strong an “exploitation” property into the sampling process, consequently destroying the diversity property of the sampled population, i.e., the “exploration” property is bad. Here, “exploitation” refers to using good already-existing solutions and making refinements to them, so that their fitness will improve further; meanwhile, “exploration” denotes that the algorithm searches for new solutions in new regions. With the aim of improving the performance of uncertainty analysis algorithms, in this research, a constrained multi-objective intelligent optimization algorithm is proposed that preserves the physical meaning of the model parameter using the penalty function method and maintains the population diversity using a Non-dominated Sorted Genetic Algorithm-II (NSGA-II) multi-objective optimization procedure. The representativeness of the parameter population is estimated on the basis of the mean and standard deviation of the Nash–Sutcliffe coefficient, and the diversity is evaluated on the basis of the mean Euclidean distance. The Chengcun watershed is selected as the study area, and uncertainty analysis is carried out. The numerical simulations indicate that the performance of the proposed algorithm is significantly improved, preserving the physical meaning and reasonable range of the model parameters while significantly improving the diversity and reliability of the sampled parameter population.

show abstract

“…The researchers studied four different variants of the problem and designed a heuristic algorithm for the general problem. Rego et al (27) proposed a novel biobjective unrelated parallel machine scheduling problem that considers TOU tariffs and sequence-dependent setup times. To tackle the problem, the researchers suggested a bi-objective mixed-integer linear programming formulation to minimize the total energy consumption and makespan.…”

Section: Introductionmentioning

confidence: 99%

“…[16] bounded power demand peak makespan/ genetic algorithm speed-scaling [18] unrelated parallel machine total energy consumption and makespan/ memetic differential evolution [19] unrelated parallel machine, sequence-dependent setup times total energy consumption and makespan/ heuristic algorithm [15] unrelated parallel machine, makespan is limited energy consumption cost/ heuristic algorithm TOU [17] uniform parallel machine number of machines employed and the total electricity cost/ heuristic algorithm [21] identical parallel machine makespan and total energy consumption/ augmented ɛconstraint method, constructive heuristic, NSGA-II [23] two-stage parallel machine total energy consumption/ Tabu Search-Greedy Insertion Hybrid algorithm [24] unrelated parallel machine, sequence-dependent setup times energy consumption costs and makespan/ the ɛ-constraint method, multiple objective simulated annealing algorithm and multiple objective particle swarm optimization algorithms [26] parallel dedicated machines, peak energy consumption at specific time intervals should not exceed a specified limit makespan/ heuristic algorithm [27] unrelated parallel machine, sequence-dependent setup times total energy consumption and makespan/ weighted sum method, NSGA-II [29] unrelated parallel machine, random job arrivals weighted combination of makespan and total energy costs/ approximate dynamic programming [30] identical parallel machine total energy consumption and makespan/ Enhanced Heuristic Scheduler [31] unrelated parallel machine, sequence-dependent setup times, bounded makespan total electricity cost/fix and relax heuristic algorithm Current paper identical parallel machine, common operation scheduling total energy consumption and total completion time/ augmented ɛ-constraint method, HNSGAII-PSO, NSGA-II Speed-scaling proposed for the problem under study in order to simultaneously minimize the total energy consumption and the total completion time. To solve small-scale instances, the augmented ɛ-constraint method (AUGMECON) is used to obtain the Pareto optimal front.…”

Section: Introductionmentioning

confidence: 99%

Energy-Conscious Common Operation Scheduling in an Identical Parallel Machine Environment

Ataei,

Ahmadizar,

Arkat

2024

IJE

View full text Add to dashboard Cite

The relentless growth of global energy consumption poses a multitude of complex challenges, including the depletion of finite energy resources and the exacerbation of greenhouse gas emissions, which contribute to climate change. In the face of these pressing environmental concerns, the manufacturing sector, a significant energy consumer, is under immense pressure to adopt sustainable practices. The critical intersection of energy consumption management and production operation scheduling emerges as a pivotal domain for addressing these challenges. The scheduling of common operations, exemplified by the cutting stock problem in industries like furniture and apparel, represents a prevalent challenge in production environments. For the first time, this paper pioneers an investigation into an identical parallel machine scheduling problem, taking into account common operations to minimize total energy consumption and total completion time concurrently. For this purpose, two bi-objective mixed integer linear programming models are presented, and an augmented εconstraint method is used to obtain the Pareto optimal front for small-scale instances. Considering the NP-hardness of this problem, a nondominated sorting genetic algorithm (NSGA-II) and a hybrid non-dominated sorting genetic algorithm with particle swarm optimization (HNSGAII-PSO) are developed to solve medium-and large-scale instances to achieve good approximate Pareto fronts. The performance of the proposed algorithms is assessed by conducting computational experiments on test problems. The results demonstrate that the proposed HNSGAII-PSO performs better than the suggested NSGA-II in solving the test problems.

show abstract

A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling

Cited by 14 publications

References 41 publications

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Perfect prosthetic heart valve: generative design with machine learning, modeling, and optimization

Improving the Performance of Hydrological Model Parameter Uncertainty Analysis Using a Constrained Multi-Objective Intelligent Optimization Algorithm

Energy-Conscious Common Operation Scheduling in an Identical Parallel Machine Environment

Contact Info

Product

Resources

About