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The solution to the assembly line balancing with the hierarchical worker assignment problem (ALBHWP) provides the optimal allocation of workers and tasks to the stations that minimise the total worker cost. In the ALBHWP, tasks differ in terms of the qualification requirements of workers, and the qualification levels of workers are hierarchical. In the hierarchical workforce structure, a lower qualified worker can be replaced by higher qualified ones with higher costs, while the vice versa is not applicable. This problem has only been studied for straight assembly lines so far. In this paper, we introduce the ALBHWP for U-shaped assembly lines. We developed integer and constraint programming models for solving the ALBHWP and compared their effectiveness using an extensive set of benchmark instances. We solved the ALBHWP for straight and U-shaped assembly lines comparatively. Constraint programming models have been statistically proven to provide better quality solutions faster than integer programming models. Besides, the CP model outperforms the only available metaheuristic in the literature for the S-ALBHWP in almost all problem sizes. Another observation is that a U-shaped line design is more cost-effective than a straight line design, but solving the ALBHWP for U-shaped lines is more difficult regarding computational complexity. [ABSTRACT FROM AUTHOR]

Thermoelectric coolers (TECs) offer a promising solution for direct cooling of local hotspots and active thermal management in advanced electronic systems. However, TECs present significant trade-offs among spatial cooling, heating, and power consumption. The optimization of TECs requires extensive simulations, which are impractical for managing actual systems with multiple hotspots under spatial and temporal variations. In this study, we present a novel machine learning-assisted optimization algorithm for thermoelectric coolers that can achieve global optimal temperature by individually controlling TEC units based on real-time multi-hotspot conditions across the entire domain. We train a convolutional neural network with a combination of the inception module and multi-task learning approach to comprehend the coupled thermal-electrical physics underlying the system and attain accurate predictions for both temperature and power consumption with and without TECs. Due to the intricate interaction among passive thermal gradient, Peltier effect and Joule effect, a local optimal TEC control experiences spatial temperature trade-off which may not lead to a global optimal solution. To address this issue, we develop a backtracking-based optimization algorithm using the machine learning model to iterate all possible TEC assignments for attaining global optimal solutions. For any m × n matrix with NHS hotspots (n, m ≤ 10, 1 ≤ NHS ≤ 20), our algorithm is capable of providing 52.4% peak temperature reduction and its corresponding TEC array control within an average of 1.64 s while iterating through tens of temperature predictions behind-the-scenes. This represents a speed increase of over three orders of magnitude compared to traditional finite element method strategies which take approximately 27 min. [ABSTRACT FROM AUTHOR]

We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardiness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed. The objective function consists of three cost components: the total earliness-tardiness cost of all scheduled jobs, the cost of the common due-date, and total rejection cost. For a given number of rejected jobs and a given due-date, the problem is reduced to a non-standard linear assignment problem. Consequently, the optimal solution is shown to be obtained in polynomial time in the number of jobs. The case of a given (possibly restrictive) due-date, the extension to a setting of more than two machines, and a number of special cases, are also discussed. [ABSTRACT FROM AUTHOR]

We consider a single-machine scheduling problem with due-date assignment and stochastic processing times, where only the mean and support (i.e. an interval bounded with lower and upper values) of processing times are known to the decision maker. The objective is to jointly determine a scheduling policy and a set of due dates for all jobs, so as to minimise the total expected individually weighted costs of earliness, tardiness and due-date assignment. By identifying an upper bound with the robust optimisation approach and a lower bound, and using a linear function of them to approximate the studied objective function, we establish an approximated problem. Then, a branch-and-bound algorithm is proposed to find an optimal solution for the approximated problem. Finally, a series of computational experiments are conducted to examine the performance of problem approximation and two developed heuristic algorithms. HIGHLIGHTS Study due-date assignment scheduling problem with stochastic processing times. Apply the mean and support (interval data) to model stochastic processing times. Use a linear function of identified lower and upper bounds to make an approximation. Derive optimal due-date assignment and develop branch-and-bound algorithms. Evaluate the efficiency of branch-and-bound algorithm and heuristic algorithms. [ABSTRACT FROM AUTHOR]

A class of strong lower bounds on the solution value of a Linearised Integer Programming reformulation is introduced for the binary quadratic optimisation model to assign origin and destination nodes to strip and stack doors, resp., in a cross-dock infrastructure. The goal is to minimise the transportation cost of the commodities to be handled at the cross-dock. Strip- and stack-related decomposition submodels are developed by taking benefit of the Integer Linearisation Property that appears in the new model. A linear search heuristic is also provided for obtaining feasible solutions by exploiting the special structure of the problem. We present an extensive computational study on a testbed of 55 instances to show that the proposed joint scheme for lower bounding and feasible solution providing is very efficient. The results obtained by our proposal are similar to those obtained by CPLEX in the 50 instances taken from the literature, but usually the time is much smaller for the large instances. The comparison with CPLEX is particularly good for the new five largest instances, which make it very promising for its application in real-life cases. [ABSTRACT FROM AUTHOR]

We investigate a stochastic distributed appointment assignment and scheduling problem, which consists of assigning appointments to distributed service units and determining service sequences at each service unit. In particular, the service time duration and release time uncertainties are well-considered. The solution to this generic problem finds interesting applications in distributed production systems, healthcare systems, and post-disaster operations. We formulate the problem as a two-stage stochastic program to minimise the total transportation cost and expected makespan, idle time or overtime, and apply the sample average approximation method to make the problem tractable. We then develop a stochastic logic-based Benders decomposition method, decomposing the problem into a master problem and a subproblem. The master problem determines the appointment assignment variables, and the subproblem handles the sequence and service start time variables. Benders optimality cuts are generated from the subproblem's solution and added to the master problem. The developed stochastic logic-based method is advantageous since it can manage many scenarios in parallel. We further consider each appointment's due date, minimise the weighted earliness and tardiness, and adjust the developed method to solve this variant. Experiments on random instances demonstrate the excellent performance of the proposed model and methods. [ABSTRACT FROM AUTHOR]

Automated high-density storage systems (AHDSS) have attracted widespread attention in recent years owing to their advantages of high throughput and space utilisation. However, owing to the characteristics of large-scale, multi-disturbance, and short-period task scenarios, a system is required to make instant and efficient decisions. To this end, this paper proposes a data-driven real-time decision-making method to solve the real-time equipment scheduling and dynamic location assignment problem in AHDSS. The proposed method comprises two phases: decision scheme learning and real-time decision-making. The operation state attribute features of the AHDSS were constructed to generate training data for equipment scheduling and location assignment scheme learning. Thereafter, a hierarchical learning and decision-making mechanism based on the deep belief network (DBN) is proposed. The integrated learning of better scheduling solutions was realised by establishing three-stage models of lift selection, shuttle selection, and location priority. Additionally, the Taguchi method was adopted to determine the best performance parameters for DBNs at different learning stages. Compared with other well-known machine learning algorithms, DBNs have a higher learning accuracy. Finally, a real-world AHDSS problem is studied, and the results demonstrate that the proposed approach outperforms existing dispatching rules. [ABSTRACT FROM AUTHOR]

In manual assembly systems, workers' differences in terms of skills, level of expertise and perceived physical effort largely affect the assembly line balancing and system performance. Traditional long-term strategic decisions may not respond to workforce changes and needs, resulting in frequent requests for line rebalancing. In this study, we propose a methodological framework and an easy-to-use Assembly Line Worker Assignment and Rebalancing Problem with different options: workers' assignment considering their performance variability, integration of worker dependent physical exertion constraints and possibility to use trainers to assist inexperienced workers. A bi-objective linear programming model is proposed aiming to minimise the cycle time and the number of reassigned tasks to respect the initial design while integrating new workers with different characteristics. The ϵ -constraint approach is used to build Pareto frontiers for this bi-objective problem. This approach is applied to three real cases. The obtained results show that the developed model can be successfully used in manufacturing companies to help the production managers to deal with workforce turnover and skills heterogeneity. [ABSTRACT FROM AUTHOR]

In order to regulate work in process (WIP) to the desired value in the job shop production control system, capacity adjustment as an effective and efficient measure, which is typically achieved by flexible staffs and working time. In this paper, instead of traditional labour-oriented approaches, we consider a machinery-based capacity adjustment via reconfigurable machine tools (RMTs) to compensate for unpredictable events. To this end, we employ model predictive control (MPC) in combination with genetic algorithm (GA) to explicitly consider complex reconfiguration strategies and address the related integer assignment optimisation problems. To further reduce energy consumption and avoid frequent and unnecessary reconfigurations while keeping a certain level of performance, we adopt an event-triggered MPC scheme with the proposed 'Double-layer event-triggering conditions'. Through extensively illustrated simulations, we demonstrate the effectiveness and plug-and-play availability of the proposed method for a six-workstation four-product job shop system and compare it to a state-of-the-art method. [ABSTRACT FROM AUTHOR]

This paper investigates an energy-efficient scheduling problem on unrelated parallel machines considering general position-based deterioration which arises from the labour-intensive textile industry. The actual processing time of a job is not only associated with the job and the machine but also with its position in the processing sequence. The objective is to minimise the total energy consumption with a bounded makespan. To address this problem, we first establish a mixed-integer linear programming (MILP) model. Afterwards, the initial model is improved by deriving lower and upper bounds on the makespan, and an upper bound on the number of jobs processed on each machine. We also develop an iterative heuristic embedded with a variable neighbourhood search procedure (IHVNS). The algorithm obtains initial solutions iteratively by solving assignment problems and then repairs and improves them with the VNS procedure. Computational results demonstrate that the improved model is up to 230 times faster than the original one. Moreover, the proposed heuristic yields excellent solutions with average gaps of less than 0.73% for large-scale instances. Especially, the results reveal that the IHVNS algorithm is more suitable than MILP models for solving large-scale problems with tight makespan restrictions. [ABSTRACT FROM AUTHOR]

Efficient fire response and the coordination of various fire vehicles are paramount for delivering optimal services and conducting effective rescue operations. This study explores the challenges of cooperative station location and vehicle assignment, focusing on the synergistic dispatch of fire vehicles from multiple stations. It highlights that the response time of the last arriving vehicle, crucial for forming a complete and effective response unit, is a critical determinant in the overall success of fire rescue operations. The primary objective of the model is to minimize the total system cost, encompassing both the capital investment in fire stations and the potential losses from fire incidents. By employing a Lagrangian relaxation technique, the model effectively simplifies the optimization challenge into more manageable sub-problems, thereby enhancing solution accuracy. The robustness and flexibility of the model were tested through simulations in a hypothetical network and a real-world scenario, using data from urban fire services. The results demonstrate the model's scalability and adaptability to different network configurations and operational constraints, showcasing its potential to substantially enhance emergency response efficiency and decision-making in urban fire management. This research makes a significant contribution to emergency response management by providing a validated framework that improves the coordination and effectiveness of fire rescue operations, thereby reducing fire damage and enhancing public safety. [ABSTRACT FROM AUTHOR]

The airline decision-making process is intended to solve complex operations planning problems sequentially. As computational power increases so do integrated approaches to solving major airline optimisation problems. In general, network carriers encounter more complex integrated problems of fleet planning, aircraft routing and increasing connectivity in the airline network. Bank optimisation problem addresses creating competitive advantage for airline network carriers, by providing better connectivity to passengers via improving their flight schedules in the airline bank structure. The aim of this study is to determine the optimal fleet to cover all flights in a flight schedule which is designed to improve connectivity in the network. The objective function takes account of the overall fleet allocation profitability on the flight schedule, the total worth of passenger connections, route profits, and the penalty cost for using excess slot. We propose a mixed integer linear programming model for the integrated bank optimisation-fleet assignment problem which can be defined as a specific flight scheduling model. To test the model, we have utilised a dataset from a Turkish carrier. The results from the integrated model show that small changes in the bank structure create more efficient schedule and fleet assignment could increase profitability at the same time. The findings imply that network and schedule planners are able to solve two major problems, simultaneously. Advances in the optimisation techniques will increase the application of the integrated models in the other parts of airline planning world, such as operations, crew planning, revenue management. [ABSTRACT FROM AUTHOR]

For a graph G (V , E) and ℓ ∈ ℕ , an ℓ distance coloring is a coloring f : V → { 1 , 2 , ... , t } of V with t colors such that ∀ u , v ∈ V , u ≠ v , f (u) ≠ f (v) when d (u , v) ≤ ℓ. Here d (u , v) is the distance between u and v and is equal to the minimum number of edges that connect u and v in G. The span of ℓ distance coloring of G , χ ℓ (G) , is the minimum t among all ℓ distance coloring of G. A class of channel assignment problem in cellular network can be formulated as a distance graph coloring problem in regular grid graphs. The cellular network is often modelled as an infinite hexagonal grid H , and hence determining χ ℓ (H) has relevance from practical point of view. Jacko and Jendrol [Discussiones Mathematicae Graph Theory, 2005] determined the exact value of χ ℓ (H) for any odd ℓ and for even ℓ ≥ 8 , it is conjectured that χ ℓ (H) = 3 8 (ℓ + 4 3) 2 where [ x ] is an integer, x ∈ ℝ and x − 1 2 < [ x ] ≤ x + 1 2 . For ℓ = 8 , the conjecture has been proved by Ghosh and Koley [ 2 2 nd Italian Conference on Theoretical Computer Science, 2021]. In this paper, we prove the conjecture for any even ℓ ≥ 1 0. [ABSTRACT FROM AUTHOR]

The Maximally Diverse Grouping Problem is one of the well-known combinatorial optimization problems with applications in the assignment of students to groups or courses. Due to its NP-hardness several (meta)heuristic solution approaches have been presented in the literature. Most of them include the insertion of an item of one group into another group and the swap of two items currently assigned to different groups as neighborhoods. The paper presents a new efficient implementation for both neighborhoods and compares it with the standard implementation, in which all inserts/swaps are evaluated, as well as the neighborhood decomposition approach. The results show that the newly presented approach is clearly superior for larger instances allowing for up to 160% more iterations in comparison to the standard implementation and up to 76% more iterations in comparison to the neighborhood decomposition approach. Moreover, the results can also be used for (meta)heuristic algorithms for other grouping or clustering problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a project-based organization that deals with an assignment problem in which a set of projects must be assigned to a group of project managers. This assignment is done based on the relative contributions of projects to the organizational mission and a matching score between each pair of a project and a project manager. We assume that some projects are deterministic, and the organization has signed their corresponding contracts while others are stochastic, i.e. the organization has submitted bids for these projects and may or may not win them in the future. Furthermore, we consider a finite planning horizon and presume a predetermined start time for each deterministic and stochastic project. We develop two models including a multi-stage stochastic integer programming model and a stochastic dynamic programming model to solve the problem. The latter shows better performance for small-size and less complex instances whereas the former gives better performance for more complex instances. We also developed a heuristic algorithm to solve large-size and more complex instances. Computational results indicate that the developed heuristic algorithm can reach near-optimal solutions in reasonable CPU run times and dominates the two other solution approaches particularly for large-size instances. [ABSTRACT FROM AUTHOR]

To deal with the task assignment problem of multi-AUV systems under kinematic constraints, which means steering capability constraints for underactuated AUVs or other vehicles likely, an improved task assignment algorithm is proposed combining the Dubins Path algorithm with improved SOM neural network algorithm. At first, the aimed tasks are assigned to the AUVs by the improved SOM neural network method based on workload balance and neighborhood function. When there exists kinematic constraints or obstacles which may cause failure of trajectory planning, task re-assignment will be implemented by changing the weights of SOM neurals, until the AUVs can have paths to reach all the targets. Then, the Dubins paths are generated in several limited cases. The AUV's yaw angle is limited, which results in new assignments to the targets. Computation flow is designed so that the algorithm in MATLAB and Python can realize the path planning to multiple targets. Finally, simulation results prove that the proposed algorithm can effectively accomplish the task assignment task for a multi-AUV system. [ABSTRACT FROM AUTHOR]

In this article, we investigate the higher-order nonsmooth optimality conditions for vector optimization problems with inequality, equality and set constraints in terms of the higher-order Gâteaux derivatives. First, we propose various higher-order Mangasarian–Fromovitz nonsmooth constraint qualifications for such problems. Second, we formulate higher-order KKT-type necessary optimality conditions for the local weak efficient solutions of the nonsmooth vector equilibrium problem with constraints (CVEP) and its special cases. An application of the result to the resources assignment problem with set, inequality, equality constraints is derived. Under some suitable assumptions involving a set constraint, the higher-order nonsmooth necessary optimality conditions become the higher-order sufficient optimality conditions via the higher-order directional/Gâteaux derivatives. [ABSTRACT FROM AUTHOR]

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O (n 6) time, where n is the number of jobs. [ABSTRACT FROM AUTHOR]

The placement of electric vehicle charging stations (EVCS) and battery swapping stations (BSS) is crucial to meet demand while minimizing their impact on the power system network. This article addresses the placement and scheduling of EVCS and BSS within a radial distribution network (RDN) overlaid with a road network. Electric Vehicle Routing Problem (EVRP) and Traffic Assignment Problem (TAP) is introduced to reduce EV energy consumption during trips to EVCS and BSS. A Bi-layer optimization approach is used, with the outer layer minimizing energy loss by allocating EVCS and BSS optimally, and the inner layer optimizing scheduling considering associated costs. Uncertainties related to EV is considered on a real-time trip basis and modelled using 2m-Point estimation method. The problem is solved using Differential Evolution (DE) and Prairie Dog Optimization (PDO) techniques. PDO results in a 9.6% reduction in total energy losses and a 22.5% decrease in total associated costs by optimally placing EVCS at 69, 25,114 and BSS at 19, 84,113 of the RDN compared to DE. Inclusion of 2-m PEM uncertainty increases total energy loss by 8.76% but decreases total associated costs by 6.97% compared to real-time uncertainty cases, enhancing the realism of the results. [ABSTRACT FROM AUTHOR]

The eigenvalue assignment problem of second-order singular system is investigated by using acceleration–velocity–displacement feedback. The conditions are established to ensure the solvability of partial eigenvalue assignment problem of second-order singular system. The derived results are extended to complete eigenvalue assignment problem of second-order singular system. The presented solvability conditions are easily tested. Then, the methods are given to solve the eigenvalue assignment problem of second-order singular systems. Finally, several examples are given to validate our results and algorithms. [ABSTRACT FROM AUTHOR]

Geospatial data conflation involves matching and combining two maps to create a new map. It has received increased research attention in recent years due to its wide range of applications in GIS (Geographic Information System) data production and analysis. The map assignment problem (conceptualized in the 1980s) is one of the earliest conflation methods, in which GIS features from two maps are matched by minimizing their total discrepancy or distance. Recently, more flexible optimization models have been proposed. This includes conflation models based on the network flow problem and new models based on Mixed Integer Linear Programming (MILP). A natural question is: how are these models related or different, and how do they compare? In this study, an analytic review of major optimized conflation models in the literature is conducted and the structural linkages between them are identified. Moreover, a MILP model (the base-matching problem) and its bi-matching version are presented as a common basis. Our analysis shows that the assignment problem and all other optimized conflation models in the literature can be viewed or reformulated as variants of the base models. For network-flow based models, proof is presented that the base-matching problem is equivalent to the network-flow based fixed-charge-matching model. The equivalence of the MILP reformulation is also verified experimentally. For the existing MILP-based models, common notation is established and used to demonstrate that they are extensions of the base models in straight-forward ways. The contributions of this study are threefold. Firstly, it helps the analyst to understand the structural commonalities and differences of current conflation models and to choose different models. Secondly, by reformulating the network-flow models (and therefore, all current models) using MILP, the presented work eases the practical application of conflation by leveraging the many off-the-shelf MILP solvers. Thirdly, the base models can serve as a common ground for studying and writing new conflation models by allowing a modular and incremental way of model development. [ABSTRACT FROM AUTHOR]

This study addresses the challenge of selecting outstanding students at higher education institutions under multiple constraints. We propose a novel integer programming solution to manage this process, formulating it as a constrained assignment problem with a maximization objective function. This function prioritizes the fair selection of students while respecting criteria such as academic qualifications, required skills, and student preferences. The goal is to develop a decision support system that efficiently selects qualified students at higher education institutions within a reasonable time. The model was tested using real data from Moroccan preparatory classes, achieving important assignment rates across all student categories. Results demonstrate significance in execution time, fulfillment of student choices, and prioritization of outstanding students. This approach offers a flexible, efficient solution for managing academic merit-based selections, optimizing resource utilization, and enhancing fairness in the selection process. [ABSTRACT FROM AUTHOR]

Purpose: The paper aims to study the constraint solutions of the periodic coupled operator matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of constraint solutions including Hamiltonian solutions and symmetric solutions, as special cases. At the end of this paper, the new algorithm is applied to the pole assignment problem. Design/methodology/approach: When the studied periodic coupled operator matrix equations are consistent, it is proved that constraint solutions can converge to exact solutions. It is demonstrated that the solutions of the equations can be obtained by the new algorithm with any arbitrary initial matrices without rounding error in a finite number of iterative steps. In addition, the least norm-constrained solutions can also be calculated by selecting any initial matrices when the equations of the periodic coupled operator matrix are inconsistent. Findings: Numerical examples show that compared with some existing algorithms, the proposed method has higher convergence efficiency because less data are used in each iteration and the data is sufficient to complete an update. It not only has the best convergence accuracy but also requires the least running time for iteration, which greatly saves memory space. Originality/value: Compared with previous algorithms, the main feature of this algorithm is that it can synthesize these equations together to get a coupled operator matrix equation. Although the equation of this paper contains multiple submatrix equations, the algorithm in this paper only needs to use the information of one submatrix equation in the equation of this paper in each iteration so that different constraint solutions of different (coupled) matrix equations can be studied for this class of equations. However, previous articles need to iterate on a specific constraint solution of a matrix equation separately. [ABSTRACT FROM AUTHOR]

Let X be an n-element point set in the k-dimensional unit cube [ 0 , 1 ] k where k ≥ 2 . According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour) x 1 , x 2 , ... , x n through the n points, such that ∑ i = 1 n | x i - x i + 1 | k 1 / k ≤ c k , where | x - y | is the Euclidean distance between x and y, and c k is an absolute constant that depends only on k, where x n + 1 ≡ x 1 . From the other direction, for every k ≥ 2 and n ≥ 2 , there exist n points in [ 0 , 1 ] k , such that their shortest tour satisfies ∑ i = 1 n | x i - x i + 1 | k 1 / k = 2 1 / k · k . For the plane, the best constant is c 2 = 2 and this is the only exact value known. Bollobás and Meir showed that one can take c k = 9 2 3 1 / k · k for every k ≥ 3 and conjectured that the best constant is c k = 2 1 / k · k , for every k ≥ 2 . Here we significantly improve the upper bound and show that one can take c k = 3 5 2 3 1 / k · k or c k = 2.91 k (1 + o k (1)) . Our bounds are constructive. We also show that c 3 ≥ 2 7 / 6 , which disproves the conjecture for k = 3 . Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed. [ABSTRACT FROM AUTHOR]

In this paper, the minimum norm partial eigenstructure assignment problems (PESAPs) in vibration system with time delay is studied via acceleration‐velocity‐displacement active control. A new explicit solution is given for solving PESAPs using orthogonality relations of symmetric vibration system. A new constructive technique is presented to solve the PESAPs in vibration system with time delay by singular value decomposition method. An optimization algorithm is proposed to solve the minimum norm PESAPs by a quasi‐Newton optimization method. The proposed algorithm works without using the knowledge of receptance matrices and without solving the Sylvester equation. The effectiveness of the proposed algorithm is verified by the results of two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we take a mechanism design approach to optimal assignment problems with asymmetrically informed buyers. In addition, the surplus generated by an assignment of a buyer to a seller may be adversely affected by externalities generated by other assignments. The problem is complicated by several factors. Buyers know their own valuations and externality costs but do not know this same information for other buyers. Buyers also receive private signals correlated with the state and, consequently, the implementation problem exhibits interdependent valuations. This precludes a naive application of the VCG mechanism and to overcome this interdependency problem, we construct a two-stage mechanism. In the first stage, we exploit correlation in the firms signals about the state to induce truthful reporting of observed signals. Given that buyers are honest in stage 1, we then use a VCG-like mechanism in stage 2 that induces honest reporting of valuation and externality functions. [ABSTRACT FROM AUTHOR]

The subarray partition of reconfigurable intelligent surface (RIS) can reduce the complexity and hardware cost of the RIS architecture while achieving satisfactory performance, which has great practical significance. However, existing RIS subarray partition methods do not consider the scenario with eavesdropper and are not suitable for such scenario. Therefore, this paper discusses the joint optimization design of subarray partition and reflection coefficients to maximize the system secrecy rate in the multi-antenna eavesdropper scenario. Since this problem is a nonconvex combinatorial optimization problem, we solve it by alternating optimization, and propose RIS-assisted MIMO secure communication schemes based on fixed and dynamic subarray partition respectively. In fixed subarray partition scheme, the closed expressions of the optimal transmit covariance matrix and the optimal reflection coefficients are obtained through theoretical analysis, where the reflection coefficients are optimized by coordinate descent method. The fixed subarray partition scheme is not limited by the subarray structure and the number of subarray units. In dynamic subarray partition scheme, we transform the subarray partition optimization problem into a task assignment problem, and propose an improved discrete particle swarm optimization (DPSO) algorithm to solve it. Simulations and analyses show that compared with the without partition scheme, two proposed schemes can achieve a satisfactory secrecy rate while reducing system complexity and hardware cost. In addition, the dynamic subarray partition scheme has better secrecy rate performance and better stability than fixed subarray partition scheme, but its implementation is more complex. [ABSTRACT FROM AUTHOR]

This paper studies an optimal assignment problem of heterogenous students to schools with a particular kind of preference complementarity: peer effects, defined by the average ability of those in the same school. The tractability of the problem allows us to characterize the optimal assignment mechanism, which has a simple "(stochastic) pass-fail" structure. Its shape is mainly determined by the convexity/concavity of the attainment function, interpreted as the preference for/against having diverse-ability students in different schools. We also provide comparative statics as to when more or less mixture of heterogenous ability types would be desirable. [ABSTRACT FROM AUTHOR]

Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time. [ABSTRACT FROM AUTHOR]

We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. This problem is closely related to the theory of recognizing and learning signed determinantal point processes in machine learning, as kernels of these point processes are magnitude-symmetric matrices. In this work, we prove a number of properties regarding sparse and generic magnitude-symmetric matrices. We show that principal minors of order at most ℓ , for some invariant ℓ depending only on principal minors of order at most two, uniquely determine principal minors of all orders. In addition, we produce a polynomial-time algorithm that, given access to principal minors, recovers a matrix with those principal minors using only a quadratic number of queries. Furthermore, when principal minors are known only approximately, we present an algorithm that approximately recovers a matrix, and show that the approximation guarantee of this algorithm cannot be improved in general. [ABSTRACT FROM AUTHOR]

We consider one variant of stable assignment problems in a bipartite graph endowed with nonnegative capacities on the edges and quotas on the vertices. It can be viewed as a generalization of the stable allocation problem introduced by Baïou and Balinsky, which arises when strong linear orders of preferences on the vertices in the latter are replaced by weak ones. At the same time, our stability problem can be stated in the framework of a theory by Alkan and Gale on stable schedule matchings generated by choice functions of a wide scope. In our case, the choice functions are of a special, so-called mixed , type. The main content of this paper is devoted to a study of rotations in our mixed model, functions on the edges determining "elementary" transformations between close stable assignments. These look more sophisticated compared with rotations in the stable allocation problem (which are generated by simple cycles). We efficiently construct a poset of rotations and show that the stable assignments are in bijection with the so-called closed functions for this poset; this gives rise to a "compact" affine representation for the lattice of stable assignments and leads to an efficient method to find a stable assignment of minimum cost. [ABSTRACT FROM AUTHOR]

In the era of Industry 5.0, there is a significant gap in addressing ergonomic risks and imprecise task times in manufacturing systems. This study aims to fill this gap by extending the ergonomic assembly line balancing problem with worker assignment. It employs a novel two-phase framework combining a constructive heuristic for feasibility with a unique ergonomic assessment method developed through a fuzzy expert system. Validated using 96 synthesized numerical instances, the proposed method addresses the scarcity of fuzzy and ergonomic-oriented data in benchmarks. Then, computational results are thoroughly analyzed to evaluate the method’s performance and identify potential areas for further research. The proposed optimization method provided high-quality solutions with a majority demonstrating low ergonomic risk and high worker safety, contributing to an overall improvement in ergonomic conditions. The integration of fuzzy expert system and advanced optimization techniques yields a robust framework for achieving a safer and more efficient manufacturing environment. [ABSTRACT FROM AUTHOR]

Due to the dynamic complexities of the multi-unmanned vessel target assignment problem at sea, especially when addressing moving targets, traditional optimization algorithms often fail to quickly find an adequate solution. To overcome this, we have developed a multi-agent reinforcement learning algorithm. This approach involves defining a state space, employing preferential experience replay, and integrating self-attention mechanisms, which are applied to a novel offshore unmanned vessel model designed for dynamic target allocation. We have conducted a thorough analysis of strike positions and times, establishing robust mathematical models. Additionally, we designed several experiments to test the effectiveness of the algorithm. The proposed algorithm improves the quality of the solution by at least 30% in larger scale scenarios compared to the genetic algorithm (GA), and the average solution speed is less than 10% of the GA, demonstrating the feasibility of the algorithm in solving the problem. [ABSTRACT FROM AUTHOR]

The School Bus Routing Problem (SBRP) is a challenging optimization problem that has received increasing attention in recent years. The problem is composed of three sub-problems: facility location selection, assignment problem, and vehicle routing problem, which can be solved in a single stage or across multiple stages. In this study, we propose a novel two-stage approach to solve the SBRP that combines Fuzzy C Means (FCM) and K-means clustering algorithms with a Genetic Algorithm (GA). In the first stage, we used FCM and K-means to identify the optimal bus stop locations and assigned students to the nearest stop based on the distance metric. This two-stage approach reduces the search space and improves the efficiency of the GA in the second stage. In the second stage, we employed the GA to generate the optimal vehicle route that minimizes the total distance traveled by all vehicles. We compared our results with those in the literature and found that the K Means-GA approach outperformed the previous results. However, the FCM-GA approach yielded significantly inferior results, indicating that the choice of clustering algorithm plays a crucial role in the performance of the overall system. Our study provides insights into the importance of selecting appropriate clustering algorithms for solving the SBRP and proposes a two-stage solution that can be easily implemented in real-world scenarios. Our approach reduces the computational time and provides an effective solution for reducing the total distance traveled by school buses. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel cloud-edge collaborative task assignment model for smart farms that consists of a cloud server, m edge servers, and n sensors. The edge servers rely solely on solar-generated energy, which is limited, whereas the cloud server has access to a limitless amount of energy supplied by the smart grid. Each entire task from a sensor is processed by either an edge server or the cloud server. We consider the task to be unsplittable. Building on the algorithm for the multimachine job scheduling problem, we develop a corresponding approximation algorithm. In addition, we propose a new discrete heuristic based on the dwarf mongoose optimization algorithmm, named the discrete dwarf mongoose optimization algorithm, and we utilize the proposed approximation algorithm to improve the convergence speed of this heuristic while yielding better solutions. In this study, we consider task sets with heavy tasks independently, where a heavy task is a task that requires many computing resources to process. If such tasks are assigned as ordinary tasks, the assignment results may be poor. Therefore, we propose a new method to solve this kind of problem. [ABSTRACT FROM AUTHOR]

Safefy-critical domains often employ autonomous agents which follow a sequential decision-making setup, whereby the agent follows a policy to dictate the appropriate action at each step. AI-practitioners often employ reinforcement learning algorithms to allow an agent to find the best policy. However, sequential systems often lack clear and immediate signs of wrong actions, with consequences visible only in hindsight, making it difficult to humans to understand system failure. In reinforcement learning, this is referred to as the credit assignment problem. To effectively collaborate with an autonomous system, particularly in a safety-critical setting, explanations should enable a user to better understand the policy of the agent and predict system behavior so that users are cognizant of potential failures and these failures can be diagnosed and mitigated. However, humans are diverse and have innate biases or preferences which may enhance or impair the utility of a policy explanation of a sequential agent. Therefore, in this paper, we designed and conducted human-subjects experiment to identify the factors which influence the perceived usability with the objective usefulness of policy explanations for reinforcement learning agents in a sequential setting. Our study had two factors: the modality of policy explanation shown to the user (Tree, Text, Modified Text, and Programs) and the "first impression" of the agent, i.e., whether the user saw the agent succeed or fail in the introductory calibration video. Our findings characterize a preference-performance tradeoff wherein participants perceived languagebased policy explanations to be significantly more useable; however, participants were better able to objectively predict the agent's behavior when provided an explanation in the form of a decision tree. Our results demonstrate that user-specific factors, such as computer science experience (p < 0.05), and situational factors, such as watching agent crash (p < 0.05), can significantly impact the perception and usefulness of the explanation. This research provides key insights to alleviate prevalent issues regarding innappropriate compliance and reliance, which are exponentially more detrimental in safety-critical settings, providing a path forward for XAI developers for future work on policy-explanations. [ABSTRACT FROM AUTHOR]

In this paper, we present a column generation-based algorithm for the bi-objective gate assignment problem (GAP) to generate gate schedules that minimize squared slack time at the gates while satisfying passenger expectations by minimizing their walking distance. While most of the literature focuses on heuristic or metaheuristic solutions for the bi-objective GAP, we propose flow-based and column-based models that lead to exact or near optimal solution approaches. The developed algorithm calculates a set of solutions to approximate the Pareto front. The algorithm is applied to the over-constrained GAP where gates are a limited resource and it is not possible to serve every flight using a gate. Our test cases are based on real data from an international airport and include various instances with flight-to-gate ratios between 23.9 and 34.7. Numerical results reveal that a set of solutions representing a compromise between the passenger-oriented and robustness-oriented objectives may be obtained with a tight optimality gap and within reasonable computational time even for these difficult problems. [ABSTRACT FROM AUTHOR]

Ride-hailing services have grown rapidly, presenting challenges such as increased traffic congestion, inefficient driver workload distribution, and environmental concerns like higher fuel consumption and emissions. This study develops a non-linear ride-hailing assignment model addressing these issues by considering service level, driver workload, and fuel consumption. A piecewise linear method was employed to handle a non-linear programming model, and the method was modified to function autonomously without operator intervention. The model's performance was evaluated using a publicly accessible dataset of taxi trips in Manhattan, focusing on indicators such as passenger waiting time, driver workload distribution, and fuel consumption. Numerical simulations demonstrated significant improvements: a 15% reduction in average passenger waiting time, a 20% improvement in balancing driver workloads, and a 10% decrease in overall fuel consumption, contributing to reduced emissions and environmental impact. The modified piecewise linear method proved effective in optimizing ride-hailing assignments, providing a more efficient and sustainable solution. The model also showed robustness in handling large datasets, ensuring scalability and applicability to various urban settings. These findings highlight the model's potential to enhance operational efficiency and promote sustainability in ride-hailing services. By integrating considerations for service level, driver workload, and fuel consumption, the model offers a holistic approach to addressing the key challenges faced by the ride-hailing industry. This study provides valuable insights for future ride-hailing development and implementations of ride-hailing systems, promoting practices that are both efficient and environmentally friendly. [ABSTRACT FROM AUTHOR]

Bat Algorithm (BA) is a nature-inspired metaheuristic search algorithm designed to efficiently explore complex problem spaces and find near-optimal solutions. The algorithm is inspired by the echolocation behavior of bats, which acts as a signal system to estimate the distance and hunt prey. Although the BA has proven effective for various optimization problems, it exhibits limited exploration ability and susceptibility to local optima. The algorithm updates velocities and positions based on the current global best solution, causing all agents to converge toward a specific location, potentially leading to local optima issues in optimization problems. On this premise, this paper proposes the Modified Bat Algorithm (MBA) as an enhancement to address the local optima limitation observed in the original BA. MBA incorporates the frequency and velocity of the current best solution, enhancing convergence speed to the optimal solution and preventing local optima entrapment. While the original BA faces diversity issues, both the original BA and MBA are introduced. To assess MBA's performance, three sets of test functions (classical benchmark functions, CEC2005, and CEC2019) are employed, with results compared to those of the original BA, Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Dragonfly Algorithm (DA). The outcomes demonstrate the MBA's significant superiority over other algorithms. In addition, MBA successfully addresses a real-world assignment problem (call center problem), traditionally solved using linear programming methods, with satisfactory results. [ABSTRACT FROM AUTHOR]

Internal audit is an independent function that provides objective assurance and advisory services to business partners in the form of projects. As the skilled human resources, internal auditors play a significant role in ensuring audit quality and thus should be managed properly. However, there are only very few studies on auditor-project assignment problems at the operational level. Also, many studies on general team formation problems neglect the real-life implications of simplifying mathematical models to enable practitioners to understand and implement. To bridge these gaps, this study presents a new integrated two-phase approach to assign internal auditors to multiple projects. In the designed decision support model, a harmonious level index is firstly proposed, measuring the suitability between auditor capability and project characteristics using a simplified fuzzy filter ranking method. Then, Min–Max multi-choice goal programming (MMCGP) model provides the assignment solution that balances internal auditors' multi-dimensional fit to the projects and their preferences, and thus optimizes the productivity of internal audit projects and staff's job satisfaction. A real case study is presented to illustrate the effectiveness of the proposed model and its solution. The comparison results further show that the proposed model outperforms the manual operations and the exiting approaches in the literature. This research extends the existing literature on auditor assignment problem by developing a flexible decision support tool and a practical classification of auditor competency. The MMCGP approach also provides an ideal staff assignment solution by setting multiple aspiration levels for each goal and balancing the unwanted deviations among goals. [ABSTRACT FROM AUTHOR]

In the online facility assignment problem OFA (k , { c i } i = 1 k) , there exist k servers s 1 , ... , s k on a metric space where each s i has an integer capacity c i and a request arrives one-by-one. The task of an online algorithm is to irrevocably match a current request with one of the servers with vacancies before the next request arrives. As special cases for OFA (k , { c i } i = 1 k) , we consider OFA (k , { c i } i = 1 k) on a line , which is denoted by OFAL (k , { c i } i = 1 k) and OFAL eq (k , { c i } i = 1 k) , where the latter is the case of OFAL (k , { c i } i = 1 k) with equidistant servers. In this paper, we perform the competitive analysis for the above problems. As a natural generalization of the greedy algorithm grdy, we introduce a class of algorithms called MPFS (Most Preferred Free Servers) and show that any MPFS algorithm has the capacity-insensitive property, i.e., for any MPFS algorithm alg for OFA (k , { c i } i = 1 k) , if alg is c -competitive when c 1 = ⋯ = c k = 1 , then alg is c -competitive for general { c i } i = 1 k . By applying the capacity-insensitive property of the greedy algorithm grdy, we derive the matching upper and lower bounds 4 k − 5 on the competitive ratio of grdy for OFAL eq (k , { c i } i = 1 k). To investigate the capability of MPFS algorithms, we show that the competitive ratio of any MPFS algorithm alg for OFAL eq (k , { c i } i = 1 k) is at least 2 k − 1. Then, we propose a new MPFS algorithm idas (Interior Division for Adjacent Servers) for OFAL (k , { c i } i = 1 k) and show that the competitive ratio of idas for OFAL eq (k , { c i } i = 1 k) is at most 2 k − 1 , i.e., idas for OFAL eq (k , { c i } i = 1 k) is best possible in all the MPFS algorithms. We also give numerical experiments to investigate the performance of idas and grdy and show that idas performs better than grdy for distribution of request sequences with locality. [ABSTRACT FROM AUTHOR]

Imbalances between limited police resource allocations and the timely handling of road traffic crashes are prevalent. To optimize resource allocations and route choices for traffic police routine patrol vehicle (RPV) assignments, a dynamic crash handling response model was developed. This approach was characterized by two objective functions: the minimum waiting time and the minimum number of RPVs. In particular, an adaptive large neighborhood search (ALNS) was designed to solve the model. Then, the proposed ALNS-based approach was examined using comprehensive traffic and crash data from Ningbo, China. Finally, a sensitivity analysis was conducted to evaluate the bi-objective of the proposed model and simultaneously demonstrate the efficiency of the obtained solutions. Two resolution methods, the global static resolution mode, and real-time dynamic resolution mode, were applied to explore the optimal solution. The results show that the optimal allocation scheme for traffic police is 13 RPVs based on the global static resolution mode. Specifically, the average waiting time for traffic crash handling can be reduced to 5.5 min, with 53.8% less than 5.0 min and 90.0% less than 10.0 min. [ABSTRACT FROM AUTHOR]

Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eigenvalue assignment problems to reassign partial undesired eigenvalues accurately. Since it is difficult to achieve robust control by assigning desired eigenvalues to precise positions with rank-one control, we assigned eigenvalues within specified regions to provide the necessary freedom. According to the sensitivity analysis theories, we derived the sensitivity of closed-loop eigenvalues to parameter perturbations to measure robustness and proposed a numerical algorithm for solving robust regional eigenvalue assignment problems so that the closed-loop eigenvalues were insensitive to parameter perturbations. Numerical experiments demonstrated the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a scenario in which protected and unprotected services coexist in an elastic optical network under dynamic traffic. In the investigated scenario, unprotected services can reuse the reserved idle bandwidth to provide protection to the protected services. Under this scenario, we propose a new heuristic algorithm that enables such reuse as well as define and introduce a new assignment problem in elastic optical networks, named a Transmission Spectrum Assignment (T-SA) problem. In this paper, we consider a scenario in which services may be routed using the multipath routing approach. Additionally, protection using bandwidth squeezing is also considered. We assess our proposal through simulations on three different network topologies and compare our proposal against the classical protection approach, in which bandwidth reuse is not allowed. For the simulated range of network loads, the maximum (minimum) blocking probability reduction obtained by our proposal is approximately 48% (10%) in the European topology, 46% (7%) in the NSFNET topology, and 32% (6%) in the German topology. [ABSTRACT FROM AUTHOR]

Background: Accurate tomographic reconstructions require the knowledge of the actual acquisition geometry. Many mobile C‐arm CT scanners have poorly reproducible acquisition geometries and thus need acquisition‐specific calibration procedures. Most of geometric self‐calibration methods based on projection data either need prior information or are limited to the estimation of a low number of geometric calibration parameters. Other self‐calibration methods generally use a calibration pattern with known geometry and are hardly implementable in practice for clinical applications. Purpose: We present a three‐step marker based self‐calibration method which does not require the prior knowledge of the calibration pattern and thus enables the use of calibration patterns with arbitrary markers positions. Methods: The first step of the method aims at detecting the set of markers of the calibration pattern in each projection of the CT scan and is performed using the YOLO (You Only Look Once) Convolutional Neural Network. The projected marker trajectories are then estimated by a sequential projection‐wise marker association scheme based on the Linear Assignment Problem which uses Kalman filters to predict the markers 2D positions in the projections. The acquisition geometry is finally estimated from the marker trajectories using the Bundle‐adjustment algorithm. Results: The calibration method has been tested on realistic simulated images of the ICRP (International Commission on Radiological Protection) phantom, using calibration patterns with 10 and 20 markers. The backprojection error was used to evaluate the self‐calibration method and exhibited sub‐millimeter errors. Real images of two human knees with 10 and 30 markers calibration patterns were then used to perform a qualitative evaluation of the method, which showed a remarkable artifacts reduction and bone structures visibility improvement. Conclusions: The proposed calibration method gave promising results that pave the way to patient‐specific geometric self‐calibrations in clinics. [ABSTRACT FROM AUTHOR]

Summary: The spectral efficiency of a cellular network can be increased significantly by allowing spatial reuse of its spectrum by an underlay device‐to‐device (D2D) network. In an underlay D2D network, devices in close vicinity are allowed to establish low‐power direct links with little to no involvement of the base station. In order to increase the spectral efficiency and the number of devices with channel access, multiple D2D pairs may transmit in each cellular channel. Additionally, each pair can be allowed to utilize multiple channels to transmit so as to maximize the D2D network capacity. This multiple‐pair multiple‐channel (MPMC) strategy is quite appealing but is limited by the resultant additional aggregate interference and the inherent complexity, hence necessitating the need for a fast and reliable channel allocation scheme. This work proposes a polynomial‐time iterative Hungarian assignment with feedback (IHAF) algorithm for multiple channel allocations amongst multiple D2D pairs that increases the D2D network capacity manifold while maintaining the desired minimum capacity for each cellular user. [ABSTRACT FROM AUTHOR]

The advent of new technologies and their implementation in manufacturing is accelerating the progress of Industry 4.0 (I4.0). Among the enabling technologies of I4.0, collaborative robots (cobots) push factory reconfiguration and prompt for worker empowerment by exploiting the respective assets of both humans and robots. Indeed, human has superior dexterity, flexibility, problem-solving ability. Robot excels in strength, endurance, accuracy and is expendable for risky activities. Therefore, task assignment problem in a production line with coexisting humans and robots cannot limit to the workload balancing among workers but should make the most of everyone respective abilities. The outcomes should not be only an increased productivity, but also improved production quality, human safety and well-being. Task assignment strategy should rely on a comprehensive assessment of the tasks from the viewpoint of suitability to humans or robots. As there are several conflicting evaluation criteria, often qualitative, the study defines the set of criteria, their metrics and proposes a method for task classification relying on Fuzzy Inference System to map each task onto a set of collaboration classes. The outcome of the study is the formal description of a set of evaluation criteria with their metrics. Another outcome is a Fuzzy Classification procedure that support production managers to properly consider all the criteria in the assignment of the tasks. The proposed methodology was tested on a case study derived from a manual manufacturing process to demonstrate its application during the process planning. [ABSTRACT FROM AUTHOR]

This paper presents two novel algorithmic frameworks to address the logit-based stochastic user equilibrium traffic assignment problem (SUE-TAP). Following the different variant of the gradient projection (termed as GP2) algorithm, we propose an improved GP2 algorithm (IGP) for the SUE-TAP. This study initially presents a smart approach for determining the allocation of more or less effort to specific origin–destination (OD) pairs. Subsequently, the TAP can be decomposed by different OD pairs, whereas the proposed IGP algorithm is designed based on the serial scheme (i.e., the Gauss–Seidel method). Therefore, a new parallel algorithm P-IGP is proposed, which integrates the block coordinate descent (BCD) method and the IGP algorithm. In specific, the independent OD pairs can be separated into several blocks, and the OD-based restricted subproblems within each block can be solved in parallel. Then, we outline the entire process of implementing the P-IGP algorithm to address the SUE-TAP. Several numerical experiments are conducted to verify the proposed algorithms. The results reveal that the proposed IGP algorithm demonstrates significantly speeder convergence in comparison to the traditional GP2 algorithm, achieving a remarkable acceleration of approximately 12%. Furthermore, the performance of the P-IGP algorithm surpasses that of the proposed IGP algorithm, and it can further achieve a notable 4–5-fold enhancement in convergence efficiency. [ABSTRACT FROM AUTHOR]