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Order release optimisation is essential in production planning, especially in discrete manufacturing. Order release planning models with load-dependent lead times must anticipate the time-dependent work-in-process and output for any given release schedule and thus require an anticipation model that approximates the time-dependent behaviour of queueing systems. We present a generic optimisation model for order release planning in stochastic, non-stationary manufacturing systems that includes a well-defined interface for the anticipation model. We develop two stationary backlog carryover (SBC) approaches to approximate time-dependent queueing behaviour and prove their consistency with the order release model. The resulting nonlinear programming model is shown to be a special case of the well-known clearing function models. A numerical study demonstrates that the optimised order releases for different demand patterns are close to the optimum that results from simulation-based optimisation even for extreme demand and release patterns. The resulting output closely matches the simulated output with some deviations. [ABSTRACT FROM AUTHOR]

High flexibility is an important feature of seru system that has received less attention. In this paper, we discuss how to do such flexible seru system formation, especially focusing on the strategic decision phase. We formulate the flexible seru system formation problem (FSFP) as a nonlinear programming model to evaluate flexibility performance in terms of flexibility–investment cost and flexibility–loss cost. To exactly obtain the optimal solution of the FSFP, we transform the nonlinear model into a linear one and solve it with Gurobi solver. For the large-scale problem, we proposed a parallel Master–Slave adaptive genetic algorithm (PMSA-GA) by transforming it into a two-stage stochastic programming model. The adaptive selection is used to improve the quality of solutions in PMSA-GA. To reduce the computational time, multiple populations of seru formation evolve in parallel with the assistance of the Master–Slave mechanism. Extensive experiments are tested to evaluate the performance of the proposed model and algorithm, and the effect of cost parameters on the system performance is discussed. The results show that the FSFP model takes the property of dynamic demand into account and is more suitable for dynamic demand environments than the task-oriented seru formation (TOSF) strategy from the previous literature. [ABSTRACT FROM AUTHOR]

Background Purpose Methods Results Conclusion In magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming.In this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile.This study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO‐SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively.The simulation study demonstrated that the magnetic field was improved from 462  to 3.6 ppm, utilizing merely 1.2 kg of iron in a 40 cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%.The results indicated that the proposed method is expected to be effective for passive shimming. [ABSTRACT FROM AUTHOR]

The article addresses the energy consumption minimization problem in wireless powered communication networks (WPCNs) and proposes a time allocation scheme, named DaTA, which is based on the Different Target Simultaneous Wireless Information and Power Transfer (DT-SWIPT) scheme such that the wireless station can share the remaining energy after transmission to the Hybrid Access Point (HAP) to those who have not transmitted to the HAP to minimize the energy consumption of the WPCN. In addition to proposing a new frame structure, the article also considers the Signal-to-Noise (SNR) constraint to guarantee that the HAP can successfully receive data from wireless stations. In the article, the problem of minimization of energy consumption is formulated as a nonlinear programming model. We employ the SQP (Sequential Quadratic Programming) algorithm to figure out the optimal solution. Moreover, a heuristic method is proposed as well to obtain a near-optimal solution in a shorter time. The simulation results showed that the proposed scheme outperforms the related work in terms of energy consumption and energy efficiency. [ABSTRACT FROM AUTHOR]

This paper attempts to propose two adaptive nonmonotone trust-region algorithms in the multiobjective optimization (MO) case. The first proposed trust-region algorithm uses a modified maximum nonmonotone technique, which takes a convex combination of the maximum value of some preceding successful iterates and the function value in the current iterate. The second one employs the average nonmonotone technique, which takes a weighted average of the successive function values. Under some suitable assumptions, the convergence of the sequences generated by the trust-region algorithms that use the aforementioned nonmonotone techniques to a critical point is shown. Using some well-known test problems, we compare our proposed adaptive nonmonotone MO algorithms with some other MO trust-region algorithms. To conduct a thorough comparison in this regard, some performance criteria are used. These numerical results confirm a significant advantage of applying the proposed adaptive nonmonotone trust-region algorithms in solving MO problems. Finally, the proposed algorithms are implemented to optimize one of the optimization problems of the abrasive water-jet machining process. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tensor sparse principal component analysis (TSPCA) by obtaining principal components which are linear combinations of a small subset of the original features for tensorial data. The core mathematical model can be formulated as a nonsmooth nonconvex optimization problem with a polynomial objective function, and with the sparsity constraint and the unit Euclidean spherical constraint. By employing the tools in tensor analysis, along with the variational properties for the involved $ \ell _{0} $ ℓ 0 -norm, the optimality condition of TSPCA is analysed in terms of stationary points. To well resolve the problem, we reformulate the stationary conditions into the Lagrange stationary equation system via the property of the projection operator onto the sparsity constraint set. With special emphasis on the Jacobian nonsingularity of the corresponding nonlinear system, we propose the Lagrange–Newton algorithm for pursuing the stationary point, which serves as a promising approximation of the optimal solution to TSPCA. The locally quadratic convergence rate is also established under mild conditions. Numerical experiments illustrate the effectiveness of our proposed TSPCA approach in terms of the solution accuracy as well as the computation time. [ABSTRACT FROM AUTHOR]

Fixture layout is an essential factor in intelligent manufacturing in the shipbuilding industry, affecting assembly quality and efficiency. Its optimization has become an urgent problem in the assembly process of compliant parts. Traditional fixture layout depends on workers' experience, which leads to butt clearance along the assembly interface. Thus, this article proposes a butt clearance control-oriented fixture layout optimization (BCCFLO) methodology. First, a method for calculating the part dimensional variation under the influence of fixture layout and fixture locating error is developed. Then, a constrained multi-objective integer nonlinear programming (CMINP) model is innovatively formulated to optimize the fixture layout. Furthermore, the non-dominated sorting genetic algorithm-II based on Latin hypercube sampling is designed to address the CMINP model. The case study illustrates and validates that the fixture layout achieved by the proposed method could significantly control the butt clearance for large compliant part assembly in the shipbuilding industry. [ABSTRACT FROM AUTHOR]

The optimization of process systems within the field of Chemical Engineering often confronts uncertainties that can exert significant influences on the performance and dependability of the obtained solutions. This research endeavors to investigate the application of Bayesian optimization in the realm of constrained mixed integer nonlinear problems. A comparative analysis was conducted, exploring different surrogate models, and evaluating diverse kernel functions and acquisition functions. Furthermore, a sampling strategy was devised to assess the enhancement achieved by the acquisition function. The findings of this article reveal the superior performance of sparse Gaussian processes in conjunction with computationally inexpensive acquisition functions, thereby highlighting their suitability for addressing mixed integer nonlinear programming problems characterized by noisy functions and stochastic behavior. Consequently, this article presents a computationally efficient approach to effectively tackle the challenges associated with data‐driven mixed integer nonlinear programming problems within the domain of Process System Engineering. [ABSTRACT FROM AUTHOR]

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace's production capacity and the steelmaking converter's consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods. [ABSTRACT FROM AUTHOR]

Orthogonal Nonnegative Matrix Factorization (ONMF) with orthogonality constraints on a matrix has been found to provide better clustering results over existing clustering problems. Because of the orthogonality constraint, this optimization problem is difficult to solve. Many of the existing constraint-preserving methods deal directly with the constraints using different techniques such as matrix decomposition or computing exponential matrices. Here, we propose an alternative formulation of the ONMF problem which converts the orthogonality constraints into non-convex constraints. To handle the non-convex constraints, a penalty function is applied. The penalized problem is a smooth nonlinear programming problem with quadratic (convex) constraints that can be solved by a proper optimization method. We first make use of an optimization method with two gradient projection steps and then apply a post-processing technique to construct a partition of the clustering problem. Comparative performance analysis of our proposed approach with other available clustering methods on randomly generated test problems and hard synthetic data-sets shows the outperformance of our approach, in terms of the obtained misclassification error rate and the Rand index. [ABSTRACT FROM AUTHOR]

This article presents an effective computational method based on the orthogonal collocation on finite element for nonlinear pursuit‐evasion differential game problems. The original problems are transformed into two dynamic optimization problems at first, so that the difficulty of obtaining the solution is reduced. To improve the convergence rate and the efficiency, the sensitivities describing the influence of control and interval parameters on state are derived through the discretized dynamic equations for the resulting nonlinear programming problem. The convergence speed is introduced to measure the performance in the upper level iteration. The main structure and the algorithm of the method are also given. Two demonstrative differential game problems with different scenarios from practice are studied. Compared with the approach without sensitivity information, the proposed method needs less function evaluations and saves at least 68.4% of the computational time. The research results show the effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

In this research, we present an expanded hp‐method for solving time delay optimal control (TDOC) problems, applicable to issues with both smooth and nonsmooth solutions. The method discretizes the time domain using an adaptive grid with unknown switch points. Subsequently, we use the operational integration matrix to approximate the problem's state variable derivative. Next, we approximate the state and control variables using the Legendre–Gauss–Lobatto points and Legendre spectral collocation. This formulation transforms the original problem into a nonlinear programming problem, solvable using relevant techniques. To demonstrate the efficacy of the proposed method, we solve numerical examples and compare the obtained results with those of several exiting methods. [ABSTRACT FROM AUTHOR]

With the rapid advancement of intelligent transportation systems, cooperative vehicle infrastructure systems emerge as a vital frontier for development. Real-time mutual fusion of perception data is a crucial technology for ensuring the security of ITS systems. However, the computation-intensive nature of perception data fusion poses a significant challenge in terms of computing resource allocation and scheduling. In this paper, we propose a vehicle-road cooperative network that facilitates computation offloading during the real-time perception data fusion process. We present an architecture that enables users to generate tasks and offload computations, and we formulate an integer nonlinear programming problem within this framework. Considering the dynamic, random, and time-varying characteristics of cooperative vehicle infrastructure systems, we introduced the Deep Deterministic Policy Gradient (DDPG) algorithm for perception fusion computing offloading (DDPG-PFCO). Through extensive experiments conducted on a real map, experimental results show that the proposed algorithm outperforms other comparison algorithms, exhibiting significant improvements in performance. [ABSTRACT FROM AUTHOR]

Under the fair open-access operation mode of gas pipeline network facilities, the accurate evaluation of the remaining capacity of a gas pipeline network can help to grasp the load rate of the pipelines, and the remaining capacity can be sold to the market to increase the utilization rate of the pipelines. In this paper, the indices of the remaining capacity of injection nodes, delivery nodes, and the pipeline system are proposed, and the theoretical as well as actual remaining capacity under different gas allocation principles are analyzed. Mathematical optimization models considering the physical, legal, and gas allocation constraints are established to evaluate the remaining capacity of nodes and pipeline systems. All the mathematical optimization models established are nonlinear programming models, which are solved using the interior-point method. The indices and mathematical models proposed for the remaining capacity are verified using a gun-barrel and branch-structured pipeline system, meanwhile, the results of the theoretical and actual remaining capacity of nodes as well as pipeline systems under different gas allocation rules are compared and analyzed in detail. [ABSTRACT FROM AUTHOR]

Pressure reducing valves (PRVs) are essentially used to reduce operational pressures in water distribution systems (WDSs) to minimize water leakage. However, water age in a WDS is an important variable describing the water quality and should be kept as low as possible. Therefore, the aim of this study is to investigate the possibility and potential of simultaneously minimizing both pressure and water age by using PRVs. To determine the optimal location and setting of PRVs, a mixed-integer nonlinear programming (MINLP) problem is formulated with minimization of the sum of the weighted total water age and pressure as the objective function, where the weighting factor can be defined by the user's preference. The equality constraints consist of the hydraulic equations and water age functions to describe pressure and water age in the distribution network, while the inequality constraints ensure them in the defined operating ranges, respectively. Applying the proposed approach to two case studies, the results show that both water age and pressure can indeed be significantly reduced by the optimized position and setting of the PRVs. [ABSTRACT FROM AUTHOR]

The cross-line operation (CO) of trains in urban rail transit is an effective method to efficiently satisfy transfer passenger travel demand as well as relieve the pressure of transfer stations. The primary problem of CO is designing train services to satisfy travel demand with an uneven spatial distribution of passengers. This study constructs a nonlinear integer programming model with a novel train operation scheme, i.e., virtual coupling (VC) technology, which allows the coupling/decoupling of trains on different lines at both ends of each operation zone. This scheme makes the train capacity equitably distributed in each operation zone, thereby balancing train capacity utilization over the whole CO system. Regarding the nonlinear characteristics of the proposed model, an adaptive simulated annealing genetic algorithm (ASA-GA) was designed to quickly generate high-quality solutions. Based on real-world data from the Beijing Changping Line and Line 13, the effectiveness of the proposed model and algorithm were verified. The computation results show that in comparison to a single grouping train composition scheme without CO, a VC scheme with CO would reduce operation costs by 46.8%, with 80.6% savings of train capacity equity. Furthermore, the average passenger residence time would be reduced by 25.9%. [ABSTRACT FROM AUTHOR]

Biomass supply chain performance is heavily affected by uncertainties stemming from supply, demand, or unexpected disruptions. Unlike petrochemical plants that use crude oil, biorefineries often have to deal with the uneven spatial‐temporal distribution of feedstock supply. The modular production strategy provides more flexibility in chemical manufacturing by allowing fast capacity expansion and unit movement. However, modeling and optimizing modular biomass supply chain under uncertainties becomes challenging due to high dimensionality and the existence of discrete decisions. This work optimizes the multiperiod biomass supply chain using the rolling horizon planning and two‐stage stochastic programming framework. We then applied generalized Benders decomposition to reduce the computational complexity of the stochastic mixed integer nonlinear programming supply chain optimization. Furthermore, the solution of the stochastic programming could be used to quantitatively describe the life‐cycle assessment uncertainties of the biomass supply chain performance, demonstrating seasonality and random variability. [ABSTRACT FROM AUTHOR]

In the post-pandemic era, the complexity of the international shipping situation, such as environmental policies, port congestion, and local conflicts, poses challenges to the stability of liner shipping, which requires strict adherence to schedules. This paper addressed the issue of schedule recovery for liner ships operating under Emission Control Areas (ECAs) regulations in the face of disruptive events. It established a bi-objective nonlinear programming model based on recovery costs and delay severity and designed a bi-objective particle swarm optimization algorithm based on two traversal of voyage leg path selection and port skipping decisions of feasible solutions to solve it. The effectiveness of the algorithm was validated through a case study of a 6000 TEU liner ship, summarizing the correlation laws of operational decisions such as port skipping, voyage leg path selection, and speed adjustment, and proposing the optimal recovery strategy for liner ships under long-term ECA constraints while ensuring short-term schedule resilience. The findings demonstrate that, in compliance with emission restrictions, ships operating within ECA are required to slow down to mitigate costs. In contrast, ships operating outside of ECA regions must accelerate their pace to adhere to established shipping schedules. [ABSTRACT FROM AUTHOR]

In current research on task offloading and resource scheduling in vehicular networks, vehicles are commonly assumed to maintain constant speed or relatively stationary states, and the impact of speed variations on task offloading is often overlooked. It is frequently assumed that vehicles can be accurately modeled during actual motion processes. However, in vehicular dynamic environments, both the tasks generated by the vehicles and the vehicles' surroundings are constantly changing, making it difficult to achieve real-time modeling for actual dynamic vehicular network scenarios. Taking into account the actual dynamic vehicular scenarios, this paper considers the real-time non-uniform movement of vehicles and proposes a vehicular task dynamic offloading and scheduling algorithm for single-task multi-vehicle vehicular network scenarios, attempting to solve the dynamic decision-making problem in task offloading process. The optimization objective is to minimize the average task completion time, which is formulated as a multi-constrained non-linear programming problem. Due to the mobility of vehicles, a constraint model is applied in the decision-making process to dynamically determine whether the communication range is sufficient for task offloading and transmission. Finally, the proposed vehicular task dynamic offloading and scheduling algorithm based on muti-agent deep deterministic policy gradient (MADDPG) is applied to solve the optimal solution of the optimization problem. Simulation results show that the algorithm proposed in this paper is able to achieve lower latency task computation offloading. Meanwhile, the average task completion time of the proposed algorithm in this paper can be improved by 7.6% compared to the performance of the MADDPG scheme and 51.1% compared to the performance of deep deterministic policy gradient (DDPG). [ABSTRACT FROM AUTHOR]

Quadrotor technology has become increasingly important in the field of photovoltaic (PV) solar farm monitoring, but short battery life is one of the primary factors limiting its further application. To address above issue, this study proposes a linear temporal logic (LTL)-based path planning algorithm that considers the need for charging together with multiple visits to PV equipments, a single visit to communication equipment, and the avoidance of restricted regions, which enables the long-term monitoring of PV solar farms. Particularly, the location of a charging station can be determined optimally and efficiently by a heuristic algorithm based on the nonlinear programming and branch and bound (NLP-BB) algorithm. The simulation results indicate that the proposed method effectively solves the long-term monitoring path planning problem that is coupled with the optimal deployment of the charging station. [ABSTRACT FROM AUTHOR]

This paper concentrates on the divisional seru scheduling and worker assignment joint decision-making problem, and synthetically considers the difference in workers' skill sets, the diversity of workers' skill levels, the process sequence constraints, setup time, lot-splitting, etc., and then a nonlinear integer programming model is constructed to minimize the makespan. We show that it is necessary to consider the process sequence constraints, and the optimal makespan of the worker-operation allocation scheme without considering the process sequence constraints is much larger than that of considering the process sequence constraints. Moreover, as the number of workers increases, the advantage of considering sequence constraints becomes more obvious. Considering the multi-decision attributes and intractable computations of the studied problem, we turn it into bi-level programming. Then based on the combination of a hybrid genetic variable neighbourhood search algorithm (HGVNSA) and a greedy heuristic algorithm (GHA), a bi-level nested heuristic algorithm (HGVNSA-GHA) is designed. Finally, numerical experiment results show that the proposed algorithm can achieve better results and higher efficiency for the divisional seru scheduling and worker assignment model. [ABSTRACT FROM AUTHOR]

Summary: Devices in close proximity can directly communicate with each other through device‐to‐device (D2D) communication, bypassing the need for base stations. To minimize the delay for D2D active clients, we use a sequential approach to reuse cellular‐type resources. Unlike conventional methods that focus solely on uplink or downlink resource distribution, our study introduces a novel optimization technique to maximize network throughput. Our proposal incorporates a hybrid approach that combines both downlink and uplink techniques for resource allocation. We utilize random forest and game theory algorithms to ensure smooth D2D communication while reducing interference between cellular and D2D pairings. Our hybrid structure effectively addresses challenges arising from intra‐ and inter‐cell interferences resulting from spectrum reusability and deployment. This approach also improves power control and quality of service. Traditionally, NP‐hard optimization solutions are proposed for mixed‐integer nonlinear problems. In our study, the critical stages include channel assignment and energy allocation. The objective problem in resource allocation considers parameters such as the transmission power of D2D active clients, cellular users, connection distance, base stations, and quality of service constraints. Our proposed hybrid method aims to enhance overall spectrum efficiency and network throughput. Simulated results demonstrate the superiority of our modified hybrid technique compared to existing joint resource allocation methods. This comprehensive approach represents a significant advancement in addressing the complexities associated with D2D communication, offering improved efficiency and performance in contemporary network environments. [ABSTRACT FROM AUTHOR]

Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is shown to achieve fast local convergence even in the absence of a constraint qualification, generalizing the results obtained by (S.J. Wright 1998 and W.W. Hager 1999) in finite dimensions to this broader setting. [ABSTRACT FROM AUTHOR]

This paper investigates various aspects of sufficient matrices, one of the most relevant matrix classes introduced in connection with linear complementarity problems. We summarize the most important theoretical results and properties related to sufficient matrices. Based on these, we propose different construction rules that can be used to generate new matrices that belong to this class. A nonnegative number can be assigned to each sufficient matrix, which is called its handicap and works as a measure of sufficiency. The handicap plays a crucial role in proving convergence and complexity results for interior point algorithms for linear complementarity problems. For a particular sufficient matrix, called Csizmadia's matrix, we give the exact value of the handicap, which is exponential in the size of the matrix. Another important topic that we address is deciding whether a matrix is sufficient. Tseng proved in 2000 that this decision problem is co-NP hard. We investigate three different algorithms for determining the sufficiency of a given matrix: Väliaho's algorithm, a linear programming-based algorithm, and an algorithm that facilitates nonlinear programming reformulations of the definition of sufficiency. We tested the efficiency of these methods on our recently launched benchmark data set that consists of four different sets of matrices. In this paper, we give the description and most important properties of the benchmark set, which can be used in the future to compare the performance of different interior point algorithms for linear complementarity problems. [ABSTRACT FROM AUTHOR]

The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush–Kuhn–Tucker (KKT) system at each iteration of the algorithm. When solving large-scale nonlinear problems, state-of-the art IPM solvers rely on efficient sparse linear solvers to solve the KKT system. Instead, we propose a novel reduced-space IPM algorithm that condenses the KKT system into a dense matrix whose size is proportional to the number of degrees of freedom in the problem. Depending on where the reduction occurs, we derive two variants of the reduced-space method: linearize-then-reduce and reduce-then-linearize. We adapt their workflow so that the vast majority of computations are accelerated on GPUs. We provide extensive numerical results on the optimal power flow problem, comparing our GPU-accelerated reduced-space IPM with Knitro and a hybrid full-space IPM algorithm. By evaluating the derivatives on the GPU and solving the KKT system on the CPU, the hybrid solution is already significantly faster than the CPU-only solutions. The two reduced-space algorithms go one step further by solving the KKT system entirely on the GPU. As expected, the performance of the two reduction algorithms depends critically on the number of available degrees of freedom: They underperform the full-space method when the problem has many degrees of freedom, but the two algorithms are up to three times faster than Knitro as soon as the relative number of degrees of freedom becomes smaller. [ABSTRACT FROM AUTHOR]

This work considers the trajectory optimization of a kinetic impactor spacecraft, which is sent to collide with a threatening near-Earth asteroid. It is assumed that Earth departure is done impulsively, by the upper stage of a launch vehicle, and is then followed by low-thrust electric propulsion until impact. For a given spacecraft, all of the important decision parameters, such as the date of departure, the direction of the hyperbolic departure, the thrust program, i.e. the history of the low-thrust pointing angles, and the date of impact are all chosen by the optimizer to maximize the perigee radius of the asteroid at its closest approach. Normally a trajectory optimization problem of this type would need to be described by many hundreds of decision parameters, e.g. if formulated to be solved by an optimization package (such as GPOPS) using nonlinear programming. We show that a successful and accurate optimization of the mission is possible using the heuristic method, particle swarm, and only 16 decision parameters, and present results for the deflection of 99942 Apophis at its 2029 close approach. • A particle swarm optimizer finds optimal strategies for asteroid deflection missions. • A novel method uses the system state transition matrix to increase accuracy. • The accuracy of the particle swarm solution is confirmed by using a direct transcription method. • The work shows that deflection by kinetic impact is feasible with present technology. [ABSTRACT FROM AUTHOR]

The core of operations research activity focuses on creating and using models. These models may be linear models, non-linear models, dynamic models, and others. Linear models are considered one of the most important and most widely used operations research models due to the availability of appropriate algorithms through which we can obtain the optimal solution, which prompts us to benefit from the nature of the topic under study and the information available to us about the variables in it to transform it into linear models. In classical logic, many nonlinear programming problems have been processed and transformed into linear programming problems. In this research, we present a study of the issue of planning hydroelectric systems, where the general policy for operating this system specifies two prices for selling the produced electricity, which makes this issue a non-linear programming issue. We will turn it into a linear programming problem using linear programming concepts, and then we will use Boolean concepts. Neutrosophic studies of linear programming and non-linear programming are presented to provide a neutrosophic formulation of the issue of planning hydroelectric systems, through which we obtain a neutrosophic linear model whose optimal solution fits all the conditions that the system's operating environment may experience during the operating period. During the two operating periods. [ABSTRACT FROM AUTHOR]

This work introduces and studies the important properties of a special class of new symmetry-shifted G t - olynomials (NSSG). Such polynomials have a symmetry property over the interval [−2, 0], with G n − 2 , 0 0 = − 1 n G n − 2 , 0 (− 2) . An explicit formulation of an NSSG operational matrixwas constructed, which served as a powerful tool for obtaining the desired numerical solutions. Then, a modified direct computational algorithm was suggested for solving the controlled Duffing oscillator problem. The idea behind the proposed algorithm is based on using symmetry basis functions, which are important and have real-world applications in physics and engineering. The original controlled Duffing oscillator problem was transformed into a nonlinear quadratic programming problem. Finally, numerical experiments are presented to validate our theoretical results. The numerical results emphasize that the modified proposed approach reaches the desired value of the performance index, with a few computations and with the minimum order of the NSSG basis function when compared with the other existing method, which is an important factor to consider when choosing the appropriate method in other mathematical and engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is proposed to solve the non-convex optimization problem using sequential convex programming. An approximation method was used to solve the collision avoidance constraint. An iterative approach was utilized to estimate the non-convex constraints, replacing them with their linear approximations. Through the simulation, we can see that this method allows for quadcopters to take off from a given initial position and fly to the desired final position within a specified flight time. It is guaranteed that the quadcopters will not collide with each other in different scenarios. [ABSTRACT FROM AUTHOR]

This paper proposes a trajectory-optimization problem for spacecraft close proximity to a noncooperative target, aiming at the generation of a six-degree-of-freedom (DOF) trajectory with the fuel-optimal objective value and considering multiple constraints on the control magnitude, line-of-sight, and glide-slope. The line-of-sight and glide-slope constraints are coupled between translational and rotational motions. The dual quaternion is an effective method for establishing the translationally and rotationally coupled model, because it can represent the translation and rotation in an integrated manner. Therefore, in this study, the trajectory-optimization problem of spacecraft close proximity coupled with position and attitude is established using dual quaternions. Next, the close-proximity trajectory-optimization problem is converted into a nonlinear programming problem, which can be solved efficiently using well-developed algorithms such as convex optimization. However, the zero-order hold used in the discrete method of convex optimization is an equidistant dispersion, which cannot guarantee the satisfaction of constraints between discrete points. Therefore the pseudospectral convex method is proposed using nonequidistant collocation points to mitigate the problem of constraint violation between discrete points and improve the accuracy and computational efficiency of the algorithm. The proposed algorithm can be applied to tasks such as rendezvous and docking with noncooperative targets and close proximity. Finally, the effectiveness of the proposed method was validated via numerical simulation, and the results were compared with those of the existing approach, GPOPS. The results indicate that the proposed algorithm is superior to GPOPS in computational efficiency and objective values. [ABSTRACT FROM AUTHOR]

This paper incorporates the shortest passenger travel paths into the first train timetabling problem in urban rail transit networks. We first propose a path-based first train timetabling problem, which is formulated as a mixed-integer nonlinear programming model to reduce the travel time for passengers. To solve this model, we present a tailored branch-and-bound combined with the timetable-based Dijkstra algorithm. To further enhance the efficiency of the exact algorithm, we design a rolling time heuristic algorithm as a substitute for the branch-and-bound algorithm. Then, we proved that the rolling time heuristic combined with the timetable-based Dijkstra algorithm achieves 97.86% and 99.39% reductions in CPU time while sacrificing only 0.007% and 0.057% of optimality gap by two numerical experiments. Finally, the results based on two test networks with different structures demonstrate that the path-based first train timetabling model effectively improves passenger travel efficiency. Specifically, the travel times are reduced by 744 mins and 761 mins, while the transfer waiting times are reduced by 37.87% and 58.91% compared to the existing timetables. Moreover, the results also demonstrate that loop line networks will increase the difficulty of timetabling and lead to many passengers taking detours. To further enhance the efficiency of commuting for passengers who take the first train, URT operators may consider relaxing the limitations on the departure time of the depot stations. • A path-based first train timetabling model to minimize the total travel time in urban rail transit networks. • A tailored branch-and-bound combined with a timetable-based Dijkstra algorithm. • A rolling time heuristic algorithm to solve large-scale networks cases. [ABSTRACT FROM AUTHOR]

How to effectively utilize edge nodes with limited computing resources to ensure quality of service is a key issue for many end users in Internet of Things. To address this problem, we propose a new cloud-edge computing network architecture, which enables the system to meet the requirements of computing resource and response time. The architecture consists of a powerful cloud computing center, multiple mobile edge computing servers and users in Internet of Things. We jointly optimize the task offloading and resource allocation of end users, thereby constructing a mixed integer nonlinear programming problem in the proposed architecture. To further solve this problem, a joint optimization strategy based on binary custom fireworks algorithm is proposed. This algorithm improves the Gaussian mutation operation in traditional fireworks algorithm by introducing Gaussian mutation probability and elite selection strategy, which makes the mutation directional. Finally, simulation results verify the effectiveness of our proposed joint optimization strategy. Compared with several other newer offloading strategies, the proposed joint optimization strategy can obtain significant performance gains. [ABSTRACT FROM AUTHOR]

This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z -component the magnetic field, which is calculated by the Biot–Savart's law, with respect to the z -coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot–Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves. [ABSTRACT FROM AUTHOR]

In order to solve the problem of optimal prescribed performance control for unknown dynamic nonlinear systems, an adaptive dynamic programming method based on dynamic event-triggered control strategy is designed. By using Lyapunov stability theory, it is proved that all signals in nonlinear systems are uniformly and ultimately bounded. First, the system under consideration is transformed into an unconstrained system with the prescribed performance by the variable transformation method. Then, the integral reinforcement learning method is used to solve the optimal control problem when the system drift dynamic is unknown. In addition, a dynamic event-triggered control strategy is constructed, which can update the weight estimation and control strategy irregularly, so as to alleviate the problem of excessive data transmission burden when the designed critic neural network approximates the value function. At the same time, Zeno's behavior in the communication process is avoided. Finally, a numerical example is given to verify the validity of the proposed theory. [ABSTRACT FROM AUTHOR]

In work of Roman A. Polyak [R.A. Polyak, Math. Program. 92 (2002) 197–235.], the Modified Chen-Harker-Kanzow-Smale (CHKS) function was studied to relate a multiplier method and an Interior Prox method with the second order distance function. Independently, the dislocated hyperbolic penalty function (DHPF) was proposed by A.E. Xavier (1992). DHPF was rewritten and studied in [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, RAIRO:RO 57 (2023) 2941–2950.] and [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, J. Convex Anal. To appear (2024).]. Thus, this function was called the dislocated hyperbolic function (DHF). In this work, we note that DHF is a particular case of CHKS function. Then we will call the DHF function as the dislocation hyperbolic transformation function. [ABSTRACT FROM AUTHOR]

In this paper, we provide a straightforward proof of a conjecture proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241–2246.] regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in [B. Kocuk and W.-J. van Hoeve, A Computational Comparison of Optimization Methods for the Golomb Ruler Problem. (2019) 409–425.], utilizing the reformulation-linearization technique. Finally, we provide the correct outputs of the greedy heuristic proposed in [P. Duxbury, C. Lavor and L.L. de Salles-Neto, RAIRO:RO 55 (2021) 2241–2246.] and correct false conclusions stated or implied therein. [ABSTRACT FROM AUTHOR]

Background and Study Aim Linear and nonlinear programming are methods used to control intensity and volume in sports training. Despite their widespread application, there is a lack of evidence-based studies that directly compare the effects of linear versus nonlinear programming. This study aims to assess the effect of linear and nonlinear programming on improving the power, agility, and endurance of young basketball players. Material and Methods This study employs a two-group pretest-posttest experimental design. It included 40 male basketball players aged 16-18, with weights ranging from 60 to 77 kg and heights from 167 to 180 cm. Participants were divided into two groups based on their ordinal pairings. The instruments used in this study were the jump DF, lane agility, and multistage fitness tests. Data were analyzed using descriptive statistics, Wilcoxon tests, and Mann-Whitney U tests, with the assistance of SPSS 23. Results The pretest-posttest findings for both the linear and nonlinear programming groups showed significant improvements in power, speed, and endurance, with Asymptotic Significance (Asymp. sig) 2-tailed values of less than 0.05. Comparative analysis of posttest results between linear and nonlinear programming indicated significant differences: power showed an Asymp.sig value of 0.009 with a difference of 3.1; agility showed an Asymp.sig value of 0.000 with a difference of 0.35; and endurance showed an Asymp.sig value of 0.002 with a difference of 2.08. Conclusions The study demonstrates significant differences in the impacts of linear and nonlinear programming on power, agility, and endurance among young basketball players. Both programming types significantly enhance these attributes, but nonlinear programming is more effective than linear programming in improving the physical abilities of young basketball players. [ABSTRACT FROM AUTHOR]

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning. [ABSTRACT FROM AUTHOR]

Developing hydropower plants is a successful strategy for sustainable energy production in countries. On the other hand, due to the high capacity of energy production in the pumping power plant sector, the strategy of saving and continuous exploitation of these power plants is one of the successful policies of governments. Therefore, in this research, the optimization of energy production and maintenance costs in one of the large storage pump power plants in Iran has been discussed and investigated based on the optimization mathematical model strategy. Therefore, a Mixed Integer Nonlinear Programming mathematical model was developed in this field. Due to the uncertainty in the presented mathematical model, the fuzzification strategy was used in the mathematical model. On the other hand, in order to achieve the optimal production plan, an energy production cost optimization policy has been presented to reduce the difference in supply and demand in the energy production network. In order to evaluate the presented mathematical model, four meta-heuristic algorithms of Multi-objective Keshtel Algorithm, Multi-objective Simulated Annealing, Non-dominated Ranking Genetic Algorithm and Non-dominated Sorting Genetic Algorithm II were used with binary coding. The results of this research have shown that the solution of the meta-heuristic NRGA algorithm has been done despite the approximation of the optimal solutions in a suitable period of time, and the results of the research indicate the applicability of the presented model in the studied power plant. Therefore, according to the level of optimization performed in the case study, it has caused the improvement of planning by 7% to 12% and effective optimization processes. [ABSTRACT FROM AUTHOR]

The energy hub provides a comprehensive solution uniting energy producers, consumers, and storage systems, thereby optimizing energy utilization efficiency. The single integrated energy system's limitations restrict renewable absorption and resource allocation, while uncoordinated demand responses create load peaks, and global warming challenges sustainable multi-energy system operations. Therefore, our work aims to enhance multi-energy flexibility by coordinating various energy hubs within a hydrogen-based integrated system. This study focuses on a cost-effective, ecologically sound, and flexible tertiary hub (producer, prosumer, and consumer) with integrated demand response programs, demonstrating a 17.30% reduction in operation costs and a 13.14% decrease in emissions. Power-to-gas technology enhances coupling efficiency among gas turbines, boilers, heat pumps, and chillers. A mixed-integer nonlinear programming model using a GAMS BARON solver will achieve the optimal results of this study. The proposed model's simulation results show reduced energy market costs, total emissions, and daily operation expenses. [ABSTRACT FROM AUTHOR]

Far-range rendezvous problem of geosynchronous orbit is studied based on the linear equation of near-circular deviation, and a two-layer nonlinear programming model is established based on the in-plane 3-pulse manuveur strategy. In the outer layer, the particle swarm optimization algorithm is used to optimize the arugment angle of the first and second pulses, which improves the traditional method of fixing at apogee or perigee. After determining the arugment angle of the first pulse and the second pulse, the inner layer uses the near-circular deviation linear equation to solve the arugment angle of the third pulse and the speed increment of the three pulses quickly. Simulation results show that the proposed planning method can reach the designated terminal in the specified time with less fuel cost, and has engineering application value. [ABSTRACT FROM AUTHOR]

In response to the European Union (EU)'s sanctions on Russian oil products, tanker shipping firms may adopt two strategies to reoptimize their shipping networks. The first strategy is to switch the flag states of tankers that are not eligible to operate on certain routes. The second strategy is to reposition tankers based on their flag states, i.e., moving those tankers that are eligible from other groups to specified routes. To help tanker shipping firms minimize the total operating cost during the planning horizon in the context of EU oil sanctions, including costs of fleet repositioning, flag switching, and fuel, this study investigates an integrated problem of fleet repositioning, flag switching, transportation scheduling, and speed optimization considering the dynamic relationships among fuel consumption, speed, and load. By formulating the problem as a nonlinear integer programming model and applying various linearization techniques to convert the nonlinear model into a linear optimization model solvable by off-the-shelf linear optimization solvers, this study demonstrates the practical application potential of the proposed model, with the longest solution time of less than two hours for a numerical instance with seven routes. Furthermore, through sensitivity analyses on important factors including unit fuel prices, crude oil transportation demand, and the tanker repositioning cost, this study provides managerial insights into the operations management of tanker shipping firms. [ABSTRACT FROM AUTHOR]

There is considered the possibility of solving the problem of choosing the optimal width of curved emergency corridors, both sides of which are parts of an ellipse to further minimize the mixing of human flows (and, accordingly, to prevent congestion in people's movement) during evacuation in case of fire or other emergencies. The issue of changing the corridor width along its length is considered in two ways: one-dimensional unconditional optimization and the classical Kuhn-Tucker theorem. A sequence of steps is proposed to implement the task of finding the optimal corridor width.

Nonlinear optimal control problems governed by variable-order fractional integro-differential equations constitute an important subgroup of optimal control problems. This group of problems is often difficult or impossible to solve analytically because of the variable-order fractional derivatives and fractional integrals. In this article, we utilized the expansion of Lagrange polynomials in terms of Chebyshev polynomials and the power series of Chebyshev polynomials to find an approximate solution with high accuracy. Subsequently, by employing collocation points, the problem was transformed into a nonlinear programming problem. In addition, variable-order fractional derivatives in the Caputo sense were represented by a new operational matrix, and an operational matrix represented fractional integrals. As a result, the mentioned integro-differential optimal control problem becomes a nonlinear programming problem that can be easily solved with the repetitive optimization method. In the end, the proposed method is illustrated by numerical examples that demonstrate its efficiency and accuracy.

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. [ABSTRACT FROM AUTHOR]

This note comments on the study of [Diri Kenger, Zülal, Çağrı Koç, and Eren Özceylan. 2020. "Integrated Disassembly Line Balancing and Routing Problem." International Journal of Production Research 58 (23): 7250–7268.] which studies an integrated disassembly line balancing and routing problem and develops two mixed integer linear programming (MILP) models and three mixed integer nonlinear programming (MINLP) models to handle five different scenarios, respectively. The purpose is twofold. First, we demonstrate that the two MILP models can be separated into two parallel subproblems whose optimal solutions can be combined to obtain the optimal solution of the original models. Second, we show that the three MINLP models can be linearised and propose two different linearisation techniques to reformulate them as equivalent MILP models. Computational results indicate that the linearised model outperforms the original nonlinear model in most cases. [ABSTRACT FROM AUTHOR]

Repetitive group inspection of production lots is considered to develop the failure censored plan with minimal expected sampling effort using prior information. Optimal reliability test plans are derived for the family of log-location-scale lifetime distributions, whereas a limited beta distribution is assumed to model the proportion nonconforming, p. A highly efficient and quick step-by-step algorithm is proposed to solve the underlying mixed nonlinear programming problem. Conventional repetitive group plans are often very effective in reducing the average sample number with respect to other inspection schemes, but sample sizes may increase under certain conditions such as high censoring. The inclusion of previous knowledge from past empirical results contributes to drastically reduce the amount of sampling required in life testing. Moreover, the use of expected sampling risks significantly improves the assessment of the actual producer and consumer sampling risks. Several tables and figures are presented to analyse the effect of the available prior evidence about p. The results show that the proposed lot inspection scheme clearly outperforms the standard repetitive group plans obtained under the traditional approach based on conventional risks. Finally, an application to the manufacture of integrated circuits is included for illustrative purposes. [ABSTRACT FROM AUTHOR]