The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a nove...The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a novel delivery mode.Spatiotemporal collaboration,along with energy consumption with payload and wind conditions play important roles in delivery route planning.This paper introduces the traveling salesman problem with time window and onboard UAV(TSPTWOUAV)and emphasizes the consideration of real-world scenarios,focusing on time collaboration and energy consumption with wind and payload.To address this,a mixed integer linear programming(MILP)model is formulated to minimize the energy consumption costs of vehicle and UAV.Furthermore,an adaptive large neighborhood search(ALNS)algorithm is applied to identify high-quality solutions efficiently.The effectiveness of the proposed model and algorithm is validated through numerical tests on real geographic instances and sensitivity analysis of key parameters is conducted.展开更多
Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When al...Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When all weights of the patch tend to infinity,we obtain the limiting form of toric patch which is called its regular control surface.The diferent weights may induce the diferent regular control surfaces of the same toric patch.It prompts us to consider that how many regular control surfaces of a toric patch.In this paper,we study the regular decompositions of A by using integer programming method firstly,and then provide the relationship between all regular decompositions of A and corresponding state polytope.Moreover,we present that the number of regular control surfaces of a toric patch associated with A is equal to the number of regular decompositions of A.An algorithm to calculate the number of regular control surfaces of toric patch is provided.The algorithm also presents a method to construct all of the regular control surfaces of a toric patch.At last,the application of proposed result in shape deformation is demonstrated by several examples.展开更多
This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digiti...This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digitization time while considering various constraints and process dependencies. The book digitization process involves three key steps: cutting, scanning, and binding. Each step has specific requirements and limitations such as the number of pages that can be processed simultaneously and potential bottlenecks. To address these complexities, we formulate the problem as a one-machine job shop scheduling problem with additional constraints to capture the unique characteristics of book digitization. We conducted a series of experiments to evaluate the performance of our proposed approach. By comparing the optimized schedules with the baseline approach, we demonstrated significant reductions in the overall processing time. In addition, we analyzed the impact of different weighting schemes on the optimization results, highlighting the importance of identifying and prioritizing critical processes. Our findings suggest that MIP-based optimization can be a valuable tool for improving the efficiency of individual work schedules, even in seemingly simple tasks, such as book digitization. By carefully considering specific constraints and objectives, we can save time and leverage resources by carefully considering specific constraints and objectives.展开更多
Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to en...Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.展开更多
The flexible job shop scheduling problem(FJSP)is commonly encountered in practical manufacturing environments.A product is typically built by assembling multiple jobs during actual manufacturing.AGVs are normally used...The flexible job shop scheduling problem(FJSP)is commonly encountered in practical manufacturing environments.A product is typically built by assembling multiple jobs during actual manufacturing.AGVs are normally used to transport the jobs from the processing shop to the assembly shop,where they are assembled.Therefore,studying the integrated scheduling problem with its processing,transportation,and assembly stages is extremely beneficial and significant.This research studies the three-stage flexible job shop scheduling problem with assembly and AGV transportation(FJSP-T-A),which includes processing jobs,transporting them via AGVs,and assembling them.A mixed integer linear programming(MILP)model is established to obtain optimal solutions.As the MILP model is challenging for solving large-scale problems,a novel co-evolutionary algorithm(NCEA)with two different decoding methods is proposed.In NCEA,a restart operation is developed to improve the diversity of the population,and a multiple crossover strategy is designed to improve the quality of individuals.The validity of the MILP model is proven by analyzing its complexity.The effectiveness of the restart operator,multiple crossovers,and the proposed algorithm is demonstrated by calculating and analyzing the RPI values of each algorithm's results within the time limit and performing a paired t-test on the average values of each algorithm at the 95%confidence level.This paper studies FJSP-T-A by minimizing the makespan for the first time,and presents a MILP model and an NCEA with two different decoding methods.展开更多
International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between a...International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport.In this paper,a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers.A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model.The results show that the optimal allocation scheme aligns with the principle of fairness,indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.展开更多
Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in ...Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.展开更多
As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in mult...As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.展开更多
An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be imp...An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.展开更多
Based on the analysis to the random sear ch algorithm of LUUS, a modified random directed integer search algorithm (MRDI SA) is given for first time. And a practical example is given to show that the adva ntage of th...Based on the analysis to the random sear ch algorithm of LUUS, a modified random directed integer search algorithm (MRDI SA) is given for first time. And a practical example is given to show that the adva ntage of this kind of algorithm is the reliability can’t be infuenced by the ini tial value X (0) and the start search domain R (0) . Besides, i t can be applied to solve the higher dimensional constrained nonlinear integer p rogramming problem.展开更多
In order to increase the hardware utilization and minimize the chip area a multi-transform coding architecture which includes 4 ×4 forward integer transform 4 ×4 inverse integer transform 4 ×4 Hadamard ...In order to increase the hardware utilization and minimize the chip area a multi-transform coding architecture which includes 4 ×4 forward integer transform 4 ×4 inverse integer transform 4 ×4 Hadamard transform and 2 ×2 Hadamard transform is proposed. By simplifying these transforms and exploring their similarities the proposed design merges the architectures processing individual transforms into a high-performance multi-transform coding architecture.Using a semiconductor manufacturing international corporation SMIC 0.18 μm complementary metal oxide semiconductor CMOS technology the proposed architecture achieves the maximum operating clock frequency of 200 MHz and the throughput rate of 800 ×106 pixel/s with the hardware cost of 3 704 gates.The results demonstrate that the data throughput rate per unit area DTUA of this design is at least 40.28%higher than that of the reference design.This design can meet the requirements of real-time decoding digital cinema video 4 096 ×2 048@30 Hz at 62.9 MHz which helps to reduce the power consumption.展开更多
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
A simplified integer overflow detection method based on path relaxation is described for avoiding buffer overflow triggered by integer overflow. When the integer overflow refers to the size of the buffer allocated dyn...A simplified integer overflow detection method based on path relaxation is described for avoiding buffer overflow triggered by integer overflow. When the integer overflow refers to the size of the buffer allocated dynamically, this kind of integer overflow is most likely to trigger buffer overflow. Based on this discovery, through lightly static program analysis, the solution traces the key variables referring to the size of a buffer allocated dynamically and it maintains the upper bound and lower bound of these variables. After the constraint information of these traced variables is inserted into the original program, this method tests the program with test cases through path relaxation, which means that it not only reports the errors revealed by the current runtime value of traced variables contained in the test case, but it also examines the errors possibly occurring under the same execution path with all the possible values of the traced variables. The effectiveness of this method is demonstrated in a case study. Compared with the traditional buffer overflow detection methods, this method reduces the burden of detection and improves efficiency.展开更多
基金Fundamental Research Funds for the Central Universities(2024JBZX038)National Natural Science F oundation of China(62076023)。
文摘The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a novel delivery mode.Spatiotemporal collaboration,along with energy consumption with payload and wind conditions play important roles in delivery route planning.This paper introduces the traveling salesman problem with time window and onboard UAV(TSPTWOUAV)and emphasizes the consideration of real-world scenarios,focusing on time collaboration and energy consumption with wind and payload.To address this,a mixed integer linear programming(MILP)model is formulated to minimize the energy consumption costs of vehicle and UAV.Furthermore,an adaptive large neighborhood search(ALNS)algorithm is applied to identify high-quality solutions efficiently.The effectiveness of the proposed model and algorithm is validated through numerical tests on real geographic instances and sensitivity analysis of key parameters is conducted.
基金Supported by the National Natural Science Foundation of China(12001327,12071057)。
文摘Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When all weights of the patch tend to infinity,we obtain the limiting form of toric patch which is called its regular control surface.The diferent weights may induce the diferent regular control surfaces of the same toric patch.It prompts us to consider that how many regular control surfaces of a toric patch.In this paper,we study the regular decompositions of A by using integer programming method firstly,and then provide the relationship between all regular decompositions of A and corresponding state polytope.Moreover,we present that the number of regular control surfaces of a toric patch associated with A is equal to the number of regular decompositions of A.An algorithm to calculate the number of regular control surfaces of toric patch is provided.The algorithm also presents a method to construct all of the regular control surfaces of a toric patch.At last,the application of proposed result in shape deformation is demonstrated by several examples.
文摘This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digitization time while considering various constraints and process dependencies. The book digitization process involves three key steps: cutting, scanning, and binding. Each step has specific requirements and limitations such as the number of pages that can be processed simultaneously and potential bottlenecks. To address these complexities, we formulate the problem as a one-machine job shop scheduling problem with additional constraints to capture the unique characteristics of book digitization. We conducted a series of experiments to evaluate the performance of our proposed approach. By comparing the optimized schedules with the baseline approach, we demonstrated significant reductions in the overall processing time. In addition, we analyzed the impact of different weighting schemes on the optimization results, highlighting the importance of identifying and prioritizing critical processes. Our findings suggest that MIP-based optimization can be a valuable tool for improving the efficiency of individual work schedules, even in seemingly simple tasks, such as book digitization. By carefully considering specific constraints and objectives, we can save time and leverage resources by carefully considering specific constraints and objectives.
基金supported by the National Natural Science Foundation of China(No.92371206)the Postgraduate Scientific Research Innovation Project of Hunan Province,China(No.CX2023063).
文摘Satellite Component Layout Optimization(SCLO) is crucial in satellite system design.This paper proposes a novel Satellite Three-Dimensional Component Assignment and Layout Optimization(3D-SCALO) problem tailored to engineering requirements, aiming to optimize satellite heat dissipation while considering constraints on static stability, 3D geometric relationships between components, and special component positions. The 3D-SCALO problem is a challenging bilevel combinatorial optimization task, involving the optimization of discrete component assignment variables in the outer layer and continuous component position variables in the inner layer,with both influencing each other. To address this issue, first, a Mixed Integer Programming(MIP) model is proposed, which reformulates the original bilevel problem into a single-level optimization problem, enabling the exploration of a more comprehensive optimization space while avoiding iterative nested optimization. Then, to model the 3D geometric relationships between components within the MIP framework, a linearized 3D Phi-function method is proposed, which handles non-overlapping and safety distance constraints between cuboid components in an explicit and effective way. Subsequently, the Finite-Rectangle Method(FRM) is proposed to manage 3D geometric constraints for complex-shaped components by approximating them with a finite set of cuboids, extending the applicability of the geometric modeling approach. Finally, the feasibility and effectiveness of the proposed MIP model are demonstrated through two numerical examples"and a real-world engineering case, which confirms its suitability for complex-shaped components and real engineering applications.
基金Supported by National Natural Science Foundation of China(Grant Nos.52205529 and 62303204)the Youth Innovation Team Program of Shandong Higher Education Institution(Grant No.2023KJ206)the Guangyue Youth Scholar Innovation Talent Program support received from Liaocheng University(Grant No.LCUGYTD2022-03)。
文摘The flexible job shop scheduling problem(FJSP)is commonly encountered in practical manufacturing environments.A product is typically built by assembling multiple jobs during actual manufacturing.AGVs are normally used to transport the jobs from the processing shop to the assembly shop,where they are assembled.Therefore,studying the integrated scheduling problem with its processing,transportation,and assembly stages is extremely beneficial and significant.This research studies the three-stage flexible job shop scheduling problem with assembly and AGV transportation(FJSP-T-A),which includes processing jobs,transporting them via AGVs,and assembling them.A mixed integer linear programming(MILP)model is established to obtain optimal solutions.As the MILP model is challenging for solving large-scale problems,a novel co-evolutionary algorithm(NCEA)with two different decoding methods is proposed.In NCEA,a restart operation is developed to improve the diversity of the population,and a multiple crossover strategy is designed to improve the quality of individuals.The validity of the MILP model is proven by analyzing its complexity.The effectiveness of the restart operator,multiple crossovers,and the proposed algorithm is demonstrated by calculating and analyzing the RPI values of each algorithm's results within the time limit and performing a paired t-test on the average values of each algorithm at the 95%confidence level.This paper studies FJSP-T-A by minimizing the makespan for the first time,and presents a MILP model and an NCEA with two different decoding methods.
基金supported by the National Natural Science Foundation of Chinathe Civil Aviation Administration of China (U2333206).
文摘International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport.In this paper,a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers.A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model.The results show that the optimal allocation scheme aligns with the principle of fairness,indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275260 and 11905211)the Fundamental Research Funds for the Central Universities(Grant No.202364008)the Young Talents Project of Ocean University of China。
文摘Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.
文摘As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.
文摘An improved method based on the Tikhonov regularization principle and the precisely known reference station coordinate is proposed to design the regularized matrix. The ill-conditioning of the normal matrix can be improved by the regularized matrix. The relative floating ambiguity can be computed only by using the data of several epochs. Combined with the LAMBDA method, the new approach can correctly and quickly fix the integer ambiguity and the success rate is 100% in experiments. Through using measured data sets from four mediumlong baselines, the new method can obtain exact ambiguities only by the Ll-frequency data of three epochs. Compared with the existing methods, the improved method can solve the ambiguities of the medium-long baseline GPS network RTK only using L1-frequency GPS data.
文摘Based on the analysis to the random sear ch algorithm of LUUS, a modified random directed integer search algorithm (MRDI SA) is given for first time. And a practical example is given to show that the adva ntage of this kind of algorithm is the reliability can’t be infuenced by the ini tial value X (0) and the start search domain R (0) . Besides, i t can be applied to solve the higher dimensional constrained nonlinear integer p rogramming problem.
基金The National Key Technology R&D Program of China during the 12th Five Year Plan Period(No.2013BAJ05B03)
文摘In order to increase the hardware utilization and minimize the chip area a multi-transform coding architecture which includes 4 ×4 forward integer transform 4 ×4 inverse integer transform 4 ×4 Hadamard transform and 2 ×2 Hadamard transform is proposed. By simplifying these transforms and exploring their similarities the proposed design merges the architectures processing individual transforms into a high-performance multi-transform coding architecture.Using a semiconductor manufacturing international corporation SMIC 0.18 μm complementary metal oxide semiconductor CMOS technology the proposed architecture achieves the maximum operating clock frequency of 200 MHz and the throughput rate of 800 ×106 pixel/s with the hardware cost of 3 704 gates.The results demonstrate that the data throughput rate per unit area DTUA of this design is at least 40.28%higher than that of the reference design.This design can meet the requirements of real-time decoding digital cinema video 4 096 ×2 048@30 Hz at 62.9 MHz which helps to reduce the power consumption.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
基金The National Natural Science Foundation of China (No.60873050,60703086)the Opening Foundation of State Key Laboratory of Software Engineering in Wuhan University (No.SKLSE20080717)
文摘A simplified integer overflow detection method based on path relaxation is described for avoiding buffer overflow triggered by integer overflow. When the integer overflow refers to the size of the buffer allocated dynamically, this kind of integer overflow is most likely to trigger buffer overflow. Based on this discovery, through lightly static program analysis, the solution traces the key variables referring to the size of a buffer allocated dynamically and it maintains the upper bound and lower bound of these variables. After the constraint information of these traced variables is inserted into the original program, this method tests the program with test cases through path relaxation, which means that it not only reports the errors revealed by the current runtime value of traced variables contained in the test case, but it also examines the errors possibly occurring under the same execution path with all the possible values of the traced variables. The effectiveness of this method is demonstrated in a case study. Compared with the traditional buffer overflow detection methods, this method reduces the burden of detection and improves efficiency.
