A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

Research on green single machine scheduling based on improved ant colony algorithm

This paper studies the green single-machine scheduling problem that considers the delay cost and the energy consumption of manufacturing equipment and builds its integrated optimization model. The improved ant colony scheduling algorithm based on the Pareto solution set is used to solve this problem. By setting the heuristic information, state transition rules, and other core parameters reasonably, the performance of the algorithm is improved effectively. Finally, the model and the improved algorithm are verified by the simulation experiment of 10 benchmark cases.

Single Machine Scheduling Problems With Sequence-dependent Setup Times and Precedence Delays

Sequence-dependent setup times (SDSTs) and delayed precedence (DP) occur commonly in various manufacturing settings. This study investigated the single machine scheduling problem with SDSTs and DP constraints arising in an amplifier assembly company. A mixed-integer linear programming model and a lean iterated greedy (LIG) algorithm is proposed to search for the best job sequence with minimum makespan. Based on the characteristic of delayed precedence constraints of the problem, the proposed LIG algorithm implements a straightforward but effective lean construction mechanism, which can keep the search process within the feasible solution space and quickly converge toward the (near-) global optimum. Computational results reveal that LIG significantly outperforms the state-of-the-art algorithm in terms of solution quality and computational efficiency. This study mainly contributes to providing a simple, effective, and efficient algorithm that can facilitate industrial applications and act as a new benchmark approach for future research.

Hybrid Models Incorporating Bivariate Statistics and Machine Learning Methods for Flash Flood Susceptibility Assessment Based on Remote Sensing Datasets

Flash floods are considered to be one of the most destructive natural hazards, and they are difficult to accurately model and predict. In this study, three hybrid models were proposed, evaluated, and used for flood susceptibility prediction in the Dadu River Basin. These three hybrid models integrate a bivariate statistical method of the fuzzy membership value (FMV) and three machine learning methods of support vector machine (SVM), classification and regression trees (CART), and convolutional neural network (CNN). Firstly, a geospatial database was prepared comprising nine flood conditioning factors, 485 flood locations, and 485 non-flood locations. Then, the database was used to train and test the three hybrid models. Subsequently, the receiver operating characteristic (ROC) curve, seed cell area index (SCAI), and classification accuracy were used to evaluate the performances of the models. The results reveal the following: (1) The ROC curve highlights the fact that the CNN-FMV hybrid model had the best fitting and prediction performance, and the area under the curve (AUC) values of the success rate and the prediction rate were 0.935 and 0.912, respectively. (2) Based on the results of the three model performance evaluation methods, all three hybrid models had better prediction capabilities than their respective single machine learning models. Compared with their single machine learning models, the AUC values of the SVM-FMV, CART-FMV, and CNN-FMV were 0.032, 0.005, and 0.055 higher; their SCAI values were 0.05, 0.03, and 0.02 lower; and their classification accuracies were 4.48%, 1.38%, and 5.86% higher, respectively. (3) Based on the results of the flood susceptibility indices, between 13.21% and 22.03% of the study area was characterized by high and very high flood susceptibilities. The three hybrid models proposed in this study, especially CNN-FMV, have a high potential for application in flood susceptibility assessment in specific areas in future studies.