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A substantial extent of harmful rubbish produced from manufacturing processes and health segments has posed a significant warning to the health of humans by affecting environmental concerns and the pollution of soil, air, and water resources. In this research, a multi-objective mixed-integer nonlinear programming (MINLP) model is presented for a sustainable hazardous waste location-routing problem. The position of the facilities and decisions on the routes for transferring hazardous waste as well as the waste remainder are considered to design a proper waste collection system. The proposed model tries to minimize the whole costs of the waste management system, the total hazards from the facilities and transportation, together with the CO2 emissions, simultaneously equipped with a real case study to show the applicability of the developed model. In order to show the sustainability importance, the outputs of the original model are compared with the model, not including sustainability. The outcomes illustrate that, under the lack of sustainability, total costs, transportation, and site risk along with the CO2 emissions increase, demonstrating the importance of sustainability. Besides, the extracted managerial insights support managers in making better decisions in the hazardous waste management system.

In this paper, we consider some problems that arise in connected and autonomous vehicle (CAV) systems. Their simplified variants can be formulated as scheduling problems. Therefore, scheduling solution algorithms can be used as a part of solution algorithms for real-world problems. For four variants of such problems, mathematical models and solution algorithms are presented. In particular, three polynomial algorithms and a branch and bound algorithm are developed. These CAV scheduling problems are considered in the literature for the first time. More complicated NP-hard scheduling problems related to CAVs can be considered in the future.

In this paper, an ensemble metaheuristic algorithm (denoted as LX-BBSCA) is introduced. It combines the strengths of Laplacian biogeography-based optimization (LX-BBO) and the sine cosine algorithm (SCA) to address structural engineering design optimization problems. Our primary objective is to mitigate the risk of getting stuck in local minima and accelerate the algorithm's convergence rate. We evaluate the proposed LX-BBSCA algorithm on a set of 23 benchmark functions, including both unimodal and multimodal problems of varying complexity and dimensions. Additionally, we apply LX-BBSCA to tackle five real-world structural engineering design problems, comparing the results with those obtained using other metaheuristics in terms of objective function values and convergence behavior. To ensure the statistical validity of our findings, we employ rigorous tests such as the t-test and the Wilcoxon rank test. The experimental outcomes consistently demonstrate that the ensemble LX-BBSCA algorithm outperforms not only the basic versions of BBO, SCA and LX-BBO but also other state-of-the-art metaheuristic algorithms.

This Special Issue of the journal Mathematics is dedicated to new results on the topic of discrete optimization and scheduling [...]

Abstract We use Aura Microwave Limb Sounder (MLS) trace gas measurements to investigate whether water vapor (H2O) injected into the stratosphere by the Hunga Tonga‐Hunga Ha'apai (HTHH) eruption affected the 2022 Antarctic stratospheric vortex. Other MLS‐measured long‐lived species are used to distinguish high HTHH H2O from that descending in the vortex from the upper‐stratospheric H2O peak. HTHH H2O reached high southern latitudes in June–July but was effectively excluded from the vortex by the strong transport barrier at its edge. MLS H2O, nitric acid, chlorine species, and ozone within the 2022 Antarctic polar vortex were near average; the vortex was large, strong, and long‐lived, but not exceptionally so. There is thus no clear evidence of HTHH influence on the 2022 Antarctic vortex or its composition. Substantial impacts on the stratospheric polar vortices are expected in succeeding years since the H2O injected by HTHH has spread globally.

This is the third edition of a Special Issue of Algorithms; it is of a rather different nature compared to other Special Issues in the journal, which are usually dedicated to a particular subject in the area of algorithms [...]

Heart disease is a global health concern of paramount importance, causing a significant number of fatalities and disabilities. Precise and timely diagnosis of heart disease is pivotal in preventing adverse outcomes and improving patient well-being, thereby creating a growing demand for intelligent approaches to predict heart disease effectively. This paper introduces an ensemble heuristic–metaheuristic feature fusion learning (EHMFFL) algorithm for heart disease diagnosis using tabular data. Within the EHMFFL algorithm, a diverse ensemble learning model is crafted, featuring different feature subsets for each heterogeneous base learner, including support vector machine, K-nearest neighbors, logistic regression, random forest, naive bayes, decision tree, and XGBoost techniques. The primary objective is to identify the most pertinent features for each base learner, leveraging a combined heuristic–metaheuristic approach that integrates the heuristic knowledge of the Pearson correlation coefficient with the metaheuristic-driven grey wolf optimizer. The second objective is to aggregate the decision outcomes of the various base learners through ensemble learning. The performance of the EHMFFL algorithm is rigorously assessed using the Cleveland and Statlog datasets, yielding remarkable results with an accuracy of 91.8% and 88.9%, respectively, surpassing state-of-the-art techniques in heart disease diagnosis. These findings underscore the potential of the EHMFFL algorithm in enhancing diagnostic accuracy for heart disease and providing valuable support to clinicians in making more informed decisions regarding patient care.

This special issue of Algorithms is dedicated to recent developments of scheduling algorithms and new applications [...]

University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which differ in terms of efficiency, performance, and optimization speed. Accordingly, this research aims to apply an exact optimization method to provide an optimal solution to the course scheduling problem. In other words, in this research, an integer programming model is presented to solve the USC problem. In this model, the constraints include the facilities of classrooms, courses of different levels and compression of students’ curriculum, courses outside the faculty and planning for them, and the limited time allocated to the professors. The objective is to maximize the weighted sum of allocating available times to professors based on their preferences in all periods. To evaluate the presented model’s feasibility, it is implemented using the GAMS software. Finally, the presented model is solved in a larger dimension using a real data set from a college in China and compared with the current program in the same college. The obtained results show that considering the mathematical model’s constraints and objective function, the faculty courses’ timetable is reduced from 4 days a week to 3 working days. Moreover, master courses are planned in two days, and the courses in the educational groups do not interfere with each other. Furthermore, by implementing the proposed model for the real case study, the maximum teaching hours of the professors are significantly reduced. The results demonstrate the efficiency of the proposed model and solution method in terms of optimization speed and solution accuracy.

Symbolic pole/zero analysis is a crucial step in designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. This study presents a mathematical model combined with a heuristic–metaheuristic solution method for symbolic pole/zero simplification in operational transconductance amplifiers. First, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is used for the simplification of the derived symbolic roots. The developed method is tested on three operational transconductance amplifiers. The obtained results show the effectiveness of the proposed method in achieving accurate simplified symbolic pole/zero expressions with the least complexity.

Phosphorus (P) is the most important substance in inorganic fertilizers used in the agriculture industry. In this study, a multi-product and multi-objective model is presented considering economic and environmental concerns to design a renewable and sustainable P-fertilizer supply chain management (PFSCM) strategy. To handle the complexities of the model, an ensemble heuristic–metaheuristic algorithm utilizing the heuristic information available in the model, the whale optimization algorithm, and a variable neighborhood search (named H-WOA-VNS) is proposed. First, a problem-dependent heuristic is designed to generate a set of near-optimal feasible solutions. These solutions are fed into a population-based whale optimization algorithm which benefits from exploration and exploitation strategies. Finally, the single-solution variable neighborhood search is applied to further improve the quality of the solution using local search operators. The objective function of the algorithm is formulated as a weighted average function to minimize total economic cost while increasing crop yield and P use efficiency. The experimental results for a real case study of the P-fertilizer supply chain confirm the effectiveness of the proposed method in improving the crop yield and P use efficiency by 33% and 27.8%, respectively. The results demonstrate that the proposed H-WOA-VNS algorithm outperforms the Heuristic, WOA, and VNS models in reducing the total objective function value of the PFSCM model by 9.8%, 2.9%, and 4%, respectively.

This article explores the impact of social media (SM) on the marketing goals of organizations in Iran during the COVID-19 pandemic. We examine the extent to which firms utilize social media marketing to promote their products in Iran compared to the pre-COVID-19 era. The validity and reliability of the 279 survey results are confirmed using internal and external validity and Cronbach’s alpha. The results show that there is a significant positive relationship between the use of SM and the distraction level. Moreover, the gender of the marketer has an impact on the perceived usefulness and application of SM. Finally, a positive effect of working hours per day on the SM usage and the marketing performance is observed. Despite a negative distraction effect, there is no evidence of reduced marketing performance. This research could help organizations to influence the purchasing processes of customers more effectively and at a lower cost.

This Special Issue of Algorithms is dedicated to the 1st Online Conference on Algorithms (IOCA 2021), which was held completely online from 27 September to 10 October 2021 [...]

One of the recently proposed strategies in health systems is providing services to patients at home and improving the service quality in addition to reducing the health system costs. In the real world, some services, such as biological tests or blood sampling, force the nurses to start or end his/her route from/at the laboratory instead of the depot, changing the whole optimal planning. The effect of these special service requirements and features has not been considered so far. In this study, a new mathematical model is suggested considering the flexibility of starting/ending places of each nurse’s route according to the specific characteristics of each service. Then, several sets of problems in various sizes are solved using the proposed model, where the results confirm the efficiency of the proposed approach. In addition, some sensitivity analyses are performed on the parameters of the required features of the services, followed by some managerial insights and directions for future studies.

This is the second edition of a special issue of Algorithms that is of a rather different nature compared to other Special Issues in the journal, which are usually dedicated to a particular subject in the area of algorithms [...]

This Special Issue of Mathematics is dedicated to the application of Operations Research methods to a wide range of problems [...]

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (“branch less and cut more”). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is O(γm2nlogn), where γ can be either n or the maximum job delivery time qmax. This complexity can even be reduced further by using a smaller number κ

This Special Issue of Algorithms is of a different nature than other Special Issue in the journal, which are usually dedicated to a particular subjects in the area of algorithms [...]

Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure.

Discrete optimization is an important area of applied mathematics which is at the intersection of several disciplines and covers both theoretical and practical aspects [...]

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.

Graph theory is an important area of Applied Mathematics with a broad spectrum of applications in many fields [...]

This special issue of Algorithms is a follow-up issue of an earlier one, entitled ‘Algorithms for Scheduling Problems’. In particular, the new issue is devoted to the development of exact and heuristic scheduling algorithms. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. In the Call for Papers, we mentioned topics such as single-criterion and multi-criteria scheduling problems with additional constraints including setup times (costs), precedence constraints, batching (lot sizing), resource constraints as well as scheduling problems arising in emerging applications.

Discrete optimization is an important area of applied mathematics that is at the intersection of several disciplines and covers both theoretical and practical aspects [...]

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polynomial dynamic programming algorithm of the complexity O ( n 5 ) and a heuristic procedure of the complexity O ( n 3 ) . This settles the complexity status of the problem under consideration which was open before and extends earlier work for the two-station single-track railway scheduling problem. We also present computational results of the comparison of both algorithms. For the 30,000 instances with up to 30 jobs considered, the average relative error of the heuristic is less than 1 % . In our tests, the practical running time of the dynamic programming algorithm was even bounded by O ( n 4 ) .

The authors have found two errors in the paper published in Materials [...]

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-section, as well as the packing algorithms are investigated. Five patterns of channel shapes are detected to represent any irregular porous structures. A novel heuristic packing algorithm for monosized spheres and different irregularities is proposed. It begins with an initial configuration based on an fcc unit cell and the subsequent densification of the obtained structure by shaking and gravity procedures. A verification of the algorithm was carried out for nine sinusoidal axisymmetric channels with different Dmin/Dmax ratio by MATLAB® simulations, reaching a packing fraction of at least 0.67 (for sphere diameters of 5%Dmin or less), superior to a random close packing density. The maximum packing fraction was 73.01% for a channel with a ratio of Dmin/Dmax = 0.1 and a sphere size of 5%Dmin. For sphere diameters of 50%Dmin or larger, it was possible to increase the packing factor after applying shaking and gravity movements.

This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main topics include sequencing and scheduling with additional constraints (setup times or costs, precedence constraints, resource constraints, and batch production environment) and production planning and scheduling problems arising in real-world applications.