Proposed Solution Method Research Articles

Stochastic bifurcations and transient dynamics of probability responses with radial basis function neural networks

Stochastic noise is common in many engineering systems. Stochastic noise and nonlinearity of dynamical systems will lead to the occurrence of complex dynamic phenomena, such as stochastic bifurcations and transitions. In this paper, a radial basis function neural networks (RBF-NN) method is applied to study stochastic bifurcations and transient dynamics of probability response. A Duffing oscillator under additive and multiplicative random noise is presented to show the effectiveness of the proposed solution method. A new type of stochastic bifurcations is found with an increase of system control parameter, which is called a stochastic double P-bifurcation. It occurs when a stationary probability density function (PDF) changes from a single peak to another single one through two double peaks with their maximum exchange. It is revealed that such a double P-bifurcation is linked to two catastrophic bifurcations of its deterministic counterpart. Moreover, these different types of transient evolutions of the PDFs are observed with transitions of probability maximum peak to one, and to the other, as well as to the both of stable invariant sets from different initial PDFs. The evolutionary orientation of transient PDFs aligns with unstable invariant manifolds leading to stable invariant sets. The previous conjecture is confirmed that the noise-induced transient dynamics and bifurcations are dominated by the global topology and its sudden changes of corresponding deterministic systems without noise.

Electric Vehicle Charging Station Location-Routing Problem with Time Windows and Resource Sharing

Electric vehicles (EVs) are widely applied in logistics companies’ urban logistics distribution, as fuel prices increase and environmental awareness grows. This study introduces an EV charging station (CS) location-routing problem with time windows and resource sharing (EVCS-LRPTWRS). Resource sharing, among multiple depots within multiple service periods is proposed to adjust the transportation resource configuration for a sustainable logistics development. Solving the EVCS-LRPTWRS involves a periodic CS location selection and a multi-depot multi-period EV routing optimization. A bi-objective nonlinear programming model is proposed to formulate the EVCS-LRPTWRS with a minimum total operating cost and number of EVs. A hybrid algorithm combining the Gaussian mixture clustering algorithm (GMCA) with the improved nondominated sorting genetic algorithm-II (INSGA-II) is designed to address the EVCS-LRPTWRS. The GMCA is employed to assign customers to appropriate depots in various service periods in order to reduce the computational complexity. The INSGA-II is adopted to obtain the Pareto optimal solutions by using the CS insertion operation to select CS locations and integrating the elite retention mechanism to ensure a stable and excellent performance. The superiority of the hybrid algorithm is proven by comparison with the other three algorithms (i.e., multi-objective genetic algorithm, multi-objective particle swarm optimization, and multi-objective ant colony optimization). An empirical study of the EVCS-LRPTWRS in Chongqing City, China is conducted. Then, four types of service period divisions and three scenarios of resource sharing modes are further analyzed and discussed. The empirical results demonstrate the validity and practicability of the proposed solution method in realizing a sustainable operation in EV distribution networks.

Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension

We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries in two dimensions, focusing in this manuscript on the Poisson, modified Helmholtz, and Stokes equations. Unlike several recently proposed methods which rely on function extension, we propose a method which instead utilizes function intension, or the smooth truncation of known function values. Similar to those methods based on extension, once the inhomogeneity is truncated we may solve the PDE using any of the many simple, fast, and robust solvers that have been developed for regular grids on simple domains. Function intension is inherently stable, as are all steps in the proposed solution method, and can be used on domains which do not readily admit extensions. We pay a price in exchange for improved stability and flexibility: in addition to solving the PDE on the regular domain, we must additionally (1) solve the PDE on a small auxiliary domain that is fitted to the boundary, and (2) ensure consistency of the solution across the interface between this auxiliary domain and the rest of the physical domain. We show how these tasks may be accomplished efficiently (in both the asymptotic and practical sense), and compare convergence to two recent high-order embedded boundary schemes. Finally, to demonstrate the wide applicability of the method, we solve a nonlinear predator-prey model, achieving rapid convergence in both space and time.

Efficient exact algorithms for continuous bi‐objective performance‐energy optimization of applications with linear energy and monotonically increasing performance profiles on heterogeneous high performance computing platforms

AbstractPerformance and energy are the two most important objectives for optimization on heterogeneous high performance computing platforms. This work studies a mathematical problem motivated by the bi‐objective optimization of data‐parallel applications on such platforms for performance and energy. First, we formulate the problem and present an exact algorithm of polynomial complexity solving the problem where all the application profiles of objective type one are continuous and strictly increasing, and all the application profiles of objective type two are linear increasing. We then apply the algorithm to develop solutions for two related optimization problems of parallel applications on heterogeneous hybrid platforms, one for performance and dynamic energy and the other for performance and total energy. Our proposed solution methods are then employed to solve the two bi‐objective optimization problems for two data‐parallel applications, matrix multiplication and gene sequencing, on a hybrid platform employing five heterogeneous processors, namely, two different Intel multicore CPUs, an Nvidia K40c GPU, an Nvidia P100 PCIe GPU, and an Intel Xeon Phi.

Probabilistic Optimal Power Flow Solution Using a Novel Hybrid Metaheuristic and Machine Learning Algorithm

This paper proposes a novel hybrid optimization technique based on a machine learning (ML) approach and transient search optimization (TSO) to solve the optimal power flow problem. First, the study aims at developing and evaluating the proposed hybrid ML-TSO algorithm. To do so, the optimization technique is implemented to solve the classical optimal power flow problem (OPF), with an objective function formulated to minimize the total generation costs. Second, the hybrid ML-TSO is adapted to solve the probabilistic OPF problem by studying the impact of the unavoidable uncertainty of renewable energy sources (solar photovoltaic and wind turbines) and time-varying load profiles on the generation costs. The evaluation of the proposed solution method is examined and validated on IEEE 57-bus and 118-bus standard systems. The simulation results and comparisons confirmed the robustness and applicability of the proposed hybrid ML-TSO algorithm in solving the classical and probabilistic OPF problems. Meanwhile, a significant reduction in the generation costs is attained upon the integration of the solar and wind sources into the investigated power systems.

Solving stochastic hydro unit commitment using benders decomposition and modified stochastic dual dynamic programming

This paper proposes a stochastic hydro unit commitment (SHUC) model for a price-taker hydropower producer in a liberalized market. The objective is to maximize the total revenue of the hydropower producer, including the immediate revenue, future revenue (i.e., opportunity cost), and startup and shutdown cost. The market price uncertainty is taken into account through the scenario tree. The solution of the model is a challenging task due to its non-convex and high-dimensional characteristics. A solution method based on the Benders Decomposition (BD) and Modified Stochastic Dual Dynamic Programming (MSDDP) is proposed to solve the problem efficiently. Firstly, the BD is applied to decompose the original problem into a Benders master problem representing the hydro unit commitment and a Benders subproblem representing the optimal operation of the hydropower plants. The Benders subproblem, which contains a large number of integer variables, is further decomposed by the period and solved by the MSDDP proposed in this paper. Finally, we verify the effectiveness of the SHUC model and the performance of the proposed solution method in case studies.

Integrated Inbound Vehicle Routing and Scheduling Under a Fixed Outbound Schedule at a Multi-Door Cross-Dock Terminal

This paper presents a newly formulated model for the integrated inbound vehicle routing and scheduling problem at a multi-door crossdocking terminal and develops a new cooperative co-evolutionary decomposition-based algorithm for its solution. The approach employs two different metaheuristic algorithms to solve the two decomposed subproblems alternatively and iteratively. For solving the routing subproblem, a hybrid of artificial bee colony (ABC) with simulated annealing (SA) is used. For solving the scheduling subproblem, a hybrid ant colony optimization (ACO) with local search is used. The proposed solution method is called SAABC-HACO. For comparison, also developed are three methods called ABCAL-HACO (ABCAL is short for ABC with adaptive limit), HABC-HACO (HABC is an ABC variant hybridized with local search), and ABC-ACO (simplified version of SAABC-HACO). All four methods were tested with 22 newly generated data sets. The test results indicate that: (i) all 4 methods are capable of finding the optimal solution identified by enumeration for a small dataset; (ii) SAABC-HACO emerges to be the best in terms of both solution quality and computational time; and (iii) both fewer number of doors and earlier outbound vehicle departure times can make it more difficult to find near-optimal solutions. Moreover, a number of issues are discussed; managerial insights are highlighted; and topics for further research are mentioned.

Blok Zincir Ekonomisinde Yeni Uygulamalar: E-Fatura Üzerine Bir İnceleme

Blockchain and smart contracts have begun to find their place in many ways of doing business. While the blockchain technology is sometimes used for the purpose of not changing the data, sometimes it is aimed at reducing the investment expenditures of the use of central software. Business processes in the field of accounting are increasingly benefiting from the benefits of digitalization. However, the solutions related to accounting are in the form of solutions belonging to the central software architecture. It is a requirement that the invoices created in the accounting processes are kept for a certain period of time due to legal obligations and that these invoices are not changed and guaranteed. At this point, processes are managed thanks to smart contracts provided by Blockchain technology. In addition, decentralized storage technologies are used as a solution for data storage. In this study, a solution proposal has been presented on how to process and store e-invoice with decentralized applications and has been implemented as an application. The proposed solution method helps to carry the approval processes needed in accounting processes to triple approval level, to reveal the processes of e-invoice in a decentralized application architecture, and to manage data security through blockchain technology.

Truck routing and platooning optimization considering drivers’ mandatory breaks

Truck platooning has been touted as one of the most promising technologies to improve fuel efficiency thanks to the reduced air drag of the digitally connected truck’s slipstream in a trainlike convoy. The benefits of truck platooning lie in the reduced fuel consumption and labor cost, and the enhanced driving experience. However, these benefits cannot be realized without an appropriate routing, scheduling, and platooning plan of trucks subject to practical constraints, especially the drivers’ break requirement for long-haul journeys. This study addresses the truck routing and platooning problem considering drivers’ mandatory breaks as well as other characteristics such as the state-and-position-dependent fuel-saving rates of platooning, trucks’ designated intermediate relays, and platoon size limit. The problem is to route the trucks to their respective destinations on time using the least amount of fuel by maximizing the formations of fuel-saving platoons over entire trips while satisfying the break time requirement of drivers. A mixed-integer linear programming (MILP) model is first developed for the proposed problem. A hybrid algorithm integrating the partial-MILP approach and iterated neighborhood search with tailored search operators is proposed to address the problem. Various randomly generated networks are used in numerical experiments to examine the effectiveness and efficiency of our proposed model and solution method. An extensive sensitivity analysis is also conducted to explore the impacts of several major influential factors, i.e., the drivers’ mandatory break times, the fuel reduction rate of the leading truck of platoons, as well as the width of the service time window, on the system performance and derive the managerial insights.

Fractional approach for mathematical model of phytoplankton–toxic phytoplankton–zooplankton system with Mittag-Leffler kernel

The solution for phytoplankton–toxic phytoplankton–zooplankton system with q-homotopy analysis transform method (q-HATM) is discussed. The projected system exemplifies three components (namely, zooplankton, toxic–phytoplankton as well as phytoplankton) and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton. The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana–Baleanu (AB) operator. The equilibrium points and stability have been discussed with the assistance of the Routh–Hurwitz rule in this work within the frame of generalized calculus. The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model, and we consider five different initial conditions for the projected system. Further, the physical nature of the achieved solution has been captured for fractional order, external force and diverse mass. The achieved consequences explicate that the proposed solution method is highly methodical, easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology.

A Discrete-Continuous PSO for the Optimal Integration of D-STATCOMs into Electrical Distribution Systems by Considering Annual Power Loss and Investment Costs

Currently, with the quick increase in global population, the energetic crisis, the environmental problematic, and the development of the power electronic devices generated the need to include new technologies for supporting and potentiating electrical distributions systems; Distribution Static Compensators (D-STATCOMs) are highly used for this task due to the advantages that this technology presents: reduction in power loss, operation costs, and chargeability of branches, among others. The possibility to include this kind of technology within the electrical system has shown the need to develop efficient methodologies from the point of view of quality solution, repeatability and processing times by considering operation and investment costs as well as the technical conditions of the electrical grids under a scenario of variable power demand and then representing the real operation of the electrical grid. With the aim to propose a solution for this requirement, this paper presents a new Discrete-Continuous Particle Swarm Optimization (DCPSO) algorithm to solve the problem of the optimal integration of D-STATCOMs into Electrical Distribution Systems (EDSs). In this case, the objective function is the minimization of annual operating costs by using a weighted mono-objective function composed of the annual power loss and the investment cost and by including all constraints associated with the operation of an EDS in a distributed reactive compensation environmentinside the mathematical formulation. In order to evaluate the effectiveness and robustness of the proposed solution method, this study implemented two tests systems (i.e., 33- and 69-bus), as well as four comparison methods, and different considerations related to the inclusion of D-STATCOMs in the EDSs. Furthermore, for evaluating the repeatability of the solution obtained by each solution methods used, each algorithm was executed 100 times in Matlab software. The results obtained demonstrated that the proposed DCPSO/HSA methodology achieved the best trade-off between solution quality and processing time, with low standard deviation values for EDSs of any size.

Robust design of service systems with immobile servers, general arrival and service patterns, and demand uncertainty

This paper addresses the problem of robustly designing a service system consisting of immobile servers, each modelled as a G/G/1 queuing system, when the arrival rates are not known with certainty. The problem involves locating service centers, determining their capacities and assigning customers to them to minimize the total cost, which includes the setup, access and waiting costs. Besides the nominal problem, two robust problems with budget and ball uncertainty sets are considered. A piecewise-linear approximation is applied to handle the nonlinear waiting cost, which enables all the problems to be tightly approximated as mixed-integer quadratic programs. We also propose a Lagrangian approach that is capable of finding high-quality solutions and strong bounds for instances of practical sizes. Numerical experiments were conducted to validate the proposed models and solution methods and to study the effect of the problem parameters, the uncertainty set size and the objective function approximations on the optimal solution.

Multi-period hub location problem: a review

In hub-and-spoke systems, due to the changes in the input parameters affecting the system over time, transportation system providers should make the right and timely decisions about hub facilities. For this reason, multi-period hub location problems are especially important. This paper presents a comprehensive review of multi-period hub location problems from 1990 up to the most recent published studies. First, we study the developed models based on some characteristics: type of planning horizon (continuous-time and discrete-time), capacity constraints (uncapacitated, capacitated, and modular), type of problem (median and covering), type of services (single-level and hierarchical), number of commodities and modes, type of hub facility (mobile and virtual), type of assignment (single and multiple), and type of parameters (deterministic and uncertain). Also, practical applications of the models are investigated. Then, we survey the proposed solution methods and real-life case studies. Finally, future suggestions are presented for researchers.

Integrated aircraft tail assignment and cargo routing problem with through cargo consideration

Traditionally, freight airlines assign individual aircraft to each flight and sequentially determine the cargo itineraries for each order. This may limit the option of cargo itineraries, and lead to mismatches between cargo demands and freighter capacities. To overcome this limitation, we introduce the concepts of through cargo connection and short through cargo connection. A through cargo connection requires cargoes to stay on the same aircraft between two connected flights, and a short through cargo connection is a through connection that needs less time than the standard cargo transshipment time. By considering the through cargo connections and short through cargo connections, we can generate the complete set of all possible cargo itineraries, so as to improve the overall schedule efficiency and robustness, and reduce the cargo ground handling cost. In this paper, two mathematical models (the connection- and string-based models) are proposed to solve the aircraft tail assignment problem (TAP) and cargo routing problem (CRP) simultaneously with through cargo considerations. We developed a column generation framework to solve the LP relaxation of the string-based model, and a diving heuristic with reoptimization strategy to find a good IP solution in a reasonable time. The proposed solution methods are tested using industrial cases from the largest freight airline in China. The computational experiments revealed that the integrated models could bring up to 5.04%∼10.31% profit growth, and the through cargo savings are tripled compared with the baseline solutions. By analyzing the computational performance of two models, we recommend that airlines can apply connection-based model only if the problems are not very large and the computational time is sufficient; otherwise, the string-based model is more robust in terms of problem scales and computational time.

Collaborative multicenter reverse logistics network design with dynamic customer demands

The vehicle routing problem for waste recycling has been created to improve resource utilization and reduce environmental pollution as a result of the rapid consumption of natural resources and the negative impact of waste on the environment. This study investigates a collaborative multicenter vehicle routing problem with time windows and dynamic customer demands. The collaboration among logistics facilities is an effective mechanism to reduce the number of vehicles and improve resource utilization in a multicenter reverse logistics network. A multi-objective mathematical programming model is proposed to coordinate static and dynamic customer demands while minimizing the total operating cost, the number of vehicles, and the total waiting time. A hybrid heuristic algorithm comprising an improved k-medoids clustering algorithm and an extended reference point-based non-dominated genetic algorithm- III, is designed to solve the multi-objective optimization model. The clustering algorithm is implemented to reduce the network complexity. The extended reference point-based non-dominated genetic algorithm- III with a dynamic insertion strategy is proposed to adjust service routes for dynamic customer demands and find the Pareto optimal solution for the multi-objective optimization model. The performance of the proposed algorithm is evaluated, and results suggest that the extended reference point-based non-dominated genetic algorithm- III has superior solutions in solving the collaborative multicenter vehicle routing problem with time windows and dynamic customer demands compared with other algorithms. The cost savings resulting from optimization are fairly distributed among participants in a collaborative alliance via the minimum cost remaining savings and principle of strictly monotonic path selection. The proposed methods are applied in a case study of a realistic reverse logistics network in Chongqing City, China. Different service periods and optimization strategies are discussed and compared to verify the effectiveness of the proposed solution methods. The optimization results indicate that the collaborative mechanism and dynamic insertion strategy can improve resource utilization and transportation efficiency and contribute to a sustainable urban logistics transportation system.

Stochastic scheduling of ground movement problem integrated with taxiway routing and gate/stand allocation

The authors propose a new scheduling model and solution method for Ground Movement Problem (GMP) which is designed to manage the movements of flights on the surface of airport air-side in an effective manner. Since the arrival time for arrival flights and off-block time for departure flights are usually uncertain parameters for GMP, the proposed scheduling model is stochastic and integrates the three-dimensional (3-D) taxiway routes’ assignment (with variable taxiing speed for flights) and the gates/stands allocation for the flights, with fully capturing multiple constraints related to taxiways, gates/stands and aircraft performance limits. The solution method also provides a stochastic quantification scheme concerning both uncertainties by the arrival time and off-block time information. The schedule results can realize the immunity of the above time uncertainties within a tolerable risk probability. We finally provide numerical analysis to verify the stochastic scheduling model with mixed integer and linear programming (MILP) basics and illustrate the effectiveness of proposed solution method by a test case on Hangzhou international airport in China.

A comprehensive risk assessment view on interval type-2 fuzzy controller for a time-dependent HazMat routing problem

Hazardous material transportation is an integral part of industries that pose significant risks. Hazardous material transportation risk of is proportional to the volume of materials transferred, the length of the link, and the population density, which varies over time. By modeling the effects of time on population density, this paper presents a multi-objective time-dependent hazardous materials routing problem for efficiently managing hazardous material transportation. The proposed model's objectives include the reduction of transportation risks and travel costs. Given the uncertainty associated with hazardous materials routing, an interval type-2 fuzzy logic controller is used to estimate risk; its inputs include population density, vehicle load, link length, and time of day. A type-2 fuzzy multi-objective evolutionary algorithm based on decomposition is used to optimize the proposed model and an adaptive large neighborhood search to enhance the local neighbor search mechanism. Additionally, by utilizing the nadir reference point, the distribution of Pareto front approximation is improved. Furthermore, a new metric is introduced to evaluate the dispersion of Pareto front approximation. The proposed method is compared to three other state-of-the-art evolutionary algorithms using eleven different performance metrics for validation. Then, using the multiple-criteria decision-making approach, the meta-heuristics algorithms are evaluated. The obtained results demonstrate the proposed solution method algorithm's competitiveness and superiority over the other three evolutionary algorithms.

Scheduling Diagnostic Testing Kit Deliveries with the Mothership and Drone Routing Problem.

A critical component in the public health response to pandemics is the ability to determine the spread of diseases via diagnostic testing kits. Currently, diagnostic testing kits, treatments, and vaccines for the COVID-19 pandemic have been developed and are being distributed to communities worldwide, but the spread of the disease persists. In conjunction, a strong level of social distancing has been established as one of the most basic and reliable ways to mitigate disease spread. If home testing kits are safely and quickly delivered to a patient, this has the potential to significantly reduce human contact and reduce disease spread before, during, and after diagnosis. This paper proposes a diagnostic testing kit delivery scheduling approach using the Mothership and Drone Routing Problem (MDRP) with one truck and multiple drones. Due to the complexity of solving the MDRP, the problem is decomposed into 1) truck scheduling to carry the drones and 2) drone scheduling for actual delivery. The truck schedule (TS) is optimized first to minimize the total travel distance to cover patients. Then, the drone flight schedule is optimized to minimize the total delivery time. These two steps are repeated until it reaches a solution minimizing the total delivery time for all patients. Heuristic algorithms are developed to further improve the computational time of the proposed model. Experiments are made to show the benefits of the proposed approach compared to the commonly performed face-to-face diagnosis via the drive-through testing sites. The proposed solution method significantly reduced the computation time for solving the optimization model (less than 50 minutes) compared to the exact solution method that took more than 10 hours to reach a 20% optimality gap. A modified basic reproduction rate (i.e., mR0) is used to compare the performance of the drone-based testing kit delivery method to the face-to-face diagnostic method in reducing disease spread. The results show that our proposed method (mR0= 0.002) outperformed the face-to-face diagnostic method (mR0= 0.0153) by reducing mR0 by 7.5 times.

A hybrid column-generation and genetic algorithm approach for solving large-scale multimission selective maintenance problems in serial K-out-of-n:G systems

This paper introduces a solution method for the multimission selective maintenance problem (SMP) that combines column-generation (CG) and genetic algorithms (GAs). The multimission SMP is an optimisation problem that arises when a system performs a sequence of missions separated by breaks of finite duration. During these finite breaks, only a subset of possible maintenance actions can be performed due to resource limitations. The problem is in deciding what actions to perform during each break duration such that the system meets or exceeds a minimum target reliability for all missions. The resulting optimisation problems are usually modelled as mixed integer nonlinear mathematical programmes, which are hard to solve. They are usually solved using metaheuristics. We propose a solution method based on CG framework in which the subproblems are solved using a GA. By integrating the GA within the classical CG framework, high-quality solutions can be obtained very quickly. The proposed solution method is capable of solving systems composed of both parallel and k-out-of-n:G subsystems. This hybrid CG algorithm is shown to obtain near optimal solutions and outperform other metaheuristic solution methods; it is also shown to be capable of solving large-scale systems composed of many subsystems and hundreds of components in a reasonable amount of time.

Two-sided disassembly line balancing problem with sequence-dependent setup time: A constraint programming model and artificial bee colony algorithm

The large-size products can allow workers to perform tasks on both sides of the line. Hence, a two-sided disassembly line is preferred to ensure several advantages, such as a shorter line. The two-sided disassembly line balancing problem (TDLBP) is relatively new in the literature. This study considers the two-sided disassembly line balancing problem with sequence-dependent setup time (TDLBP-SDST) to reflect the real practice better, as sequence-dependent setup times may exist between tasks in many real-life applications. To the authors’ best knowledge, sequence-dependent setup time has not been considered for the TDLBP in the current literature. The proposed problem creates a more complicated problem. Therefore, proposing effective solution techniques is more critical for obtaining better results. This study proposes two new mixed-integer linear programming models and a novel constraint programming (CP) model to define and solve the TDLBP-SDST. A genetic algorithm, an artificial bee colony algorithm, and the improved versions of these two algorithms are also developed to solve the large-size problems due to the NP-hardness of the TDLBP-SDST. Furthermore, a novel CP model is proposed for the standard TDLBP without considering sequence-dependent setup times. Initially, we compare the performance of the proposed CP model to those of the previous state-of-the-art methods in the literature for the TDLBP without sequence-dependent setup time. The computational results show that the proposed CP model outperforms all the other solution methods and reports the best-known results for all existing benchmark instances for the TDLBP. Then, we present the computational results of the proposed models and algorithms for the TDLBP-SDST. Computational study on a comprehensive set of generated instances indicates that the proposed solution methods effectively solve the TDLBP-SDST.