As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected featu...As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features.Evolutionary computing(EC)is promising for FS owing to its powerful search capability.However,in traditional EC-based methods,feature subsets are represented via a length-fixed individual encoding.It is ineffective for high-dimensional data,because it results in a huge search space and prohibitive training time.This work proposes a length-adaptive non-dominated sorting genetic algorithm(LA-NSGA)with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective highdimensional FS.In LA-NSGA,an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths,and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively.Moreover,a dominance-based local search method is employed for further improvement.The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.展开更多
A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of...A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.展开更多
The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and ...The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and literature Instances, was divided into three stages: Stage 1, data treatment;Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II);Stage 3, analysis of the results, with a comparison of the algorithms. An optimization of 19.9% was achieved for Objective Function 1 (OF<sub>1</sub>;minimization of CO<sub>2</sub> emissions) and consequently the same percentage for the minimization of total distance, and 87.5% for Objective Function 2 (OF<sub>2</sub>;minimization of the difference in demand). Metaheuristic approaches hybrid achieved superior results for case study and instances. In this way, the procedure presented here can bring benefits to society as it considers environmental issues and also balancing work between the routes, ensuring savings and satisfaction for the users.展开更多
Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications.However,some problems cannot be modelled as a single objective optimization and neural dynamics method do...Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications.However,some problems cannot be modelled as a single objective optimization and neural dynamics method does not apply.This paper proposes the first neural dynamics model to solve bi-objective constrained quadratic program,which opens the avenue to extend the power of neural dynamics to multi-objective optimization.We rigorously prove that the designed neural dynamics is globally convergent and it converges to the optimal solution of the bi-objective optimization in Pareto sense.Illustrative examples on bi-objective geometric optimization are used to verify the correctness of the proposed method.The developed model is also tested in scientific computing with data from real industrial data with demonstrated superior to rival schemes.展开更多
This paper studies learning effect as a resource utilization technique that can model improvement in worker＇s ability as a result of repeating similar tasks. By considering learning of workers while performing setup ...This paper studies learning effect as a resource utilization technique that can model improvement in worker＇s ability as a result of repeating similar tasks. By considering learning of workers while performing setup times, a schedule can be determined to place jobs that share similar tools and fixtures next to each other. The purpose of this paper is to schedule a set of jobs in a hybrid flow shop （HFS） environment with learning effect while minimizing two objectives that are in conflict： namely maximum completion time （makespan） and total tardiness. Minimizing makespan is desirable from an internal efficiency viewpoint, but may result in individual jobs being scheduled past their due date, causing customer dissatisfaction and penalty costs. A bi-objective mixed integer programming model is developed, and the complexity of the developed bi-objective model is compared against the bi-criteria one through numerical examples. The effect of worker learning on the structure of assigned jobs to machines and their sequences is analyzed. Two solution methods based on the hybrid water flow like algorithm and non-dominated sorting and ranking concepts are proposed to solve the problem. The quality of the approximated sets of Pareto solutions is evaluated using several performance criteria. The results show that the proposed algorithms with learning effect perform well in reducing setup times and eliminate the need for setups itself through proper scheduling.展开更多
Partitioning a complex power network into a number of sub-zones can help realize a divide-and-conquer’management structure for the whole system,such as voltage and reactive power control,coherency identification,powe...Partitioning a complex power network into a number of sub-zones can help realize a divide-and-conquer’management structure for the whole system,such as voltage and reactive power control,coherency identification,power system restoration,etc.Extensive partitioning methods have been proposed by defining various distances,applying different clustering methods,or formulating varying optimization models for one specific objective.However,a power network partition may serve two or more objectives,where a trade-off among these objectives is required.This paper proposes a novel weighted consensus clustering-based approach for bi-objective power network partition.By varying the weights of different partitions for different objectives,Pareto improvement can be explored based on the node-based and subset-based consensus clustering methods.Case studies on the IEEE 300-bus test system are conducted to verify the effectiveness and superiority of our proposed method.展开更多
Traffic congestion in road transportation networks is a persistent problem in major metropolitan cities around the world.In this context,this paper deals with exploiting underutilized road capacities in a network to l...Traffic congestion in road transportation networks is a persistent problem in major metropolitan cities around the world.In this context,this paper deals with exploiting underutilized road capacities in a network to lower the congestion on overutilized links while simultaneously satisfying the system optimal flow assignment for sustainable transportation.Four congestion mitigation strategies are identified based on deviation and relative deviation of link volume from the corresponding capacity.Consequently,four biobjective mathematical programming optimal flow distribution(OFD)models are proposed.The case study results demonstrate that all the proposed models improve system performance and reduce congestion on high volume links by shifting flows to low volumeto-capacity links compared to UE and SO models.Among the models,the system optimality with minimal sum and maximum absolute relative-deviation models(SO-SAR and SO-MAR)showed superior results for different performance measures.The SO-SAR model yielded 50%and 30%fewer links at higher link utilization factors than UE and SO models,respectively.Also,it showed more than 25%improvement in path travel times compared to UE travel time for about 100 paths and resulted in the least network congestion index of1.04 compared to the other OFD and UE models.Conversely,the SO-MAR model yielded the least total distance and total system travel time,resulting in lower fuel consumption and emissions,thus contributing to sustainability.The proposed models contribute towards efficient transportation infrastructure management and will be of interest to transportation planners and traffic managers.展开更多
An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each ite...An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.展开更多
Sugarcane crop occupies an area of about 23.78 million hectares in 103 countries,and an estimated production of 1.66 billion tons,adding to this volume more than 6%to 17%concerning residual biomass resulting from harv...Sugarcane crop occupies an area of about 23.78 million hectares in 103 countries,and an estimated production of 1.66 billion tons,adding to this volume more than 6%to 17%concerning residual biomass resulting from harvest.The destination of this residual biomass is a major challenge to managers of mills.There are at least two alternatives which are reduction in residue production and increased output in electricity cogeneration.These two conflicting objectives are mathematically modeled as a bi-objective problem.This study developed a bi-objective mathematical model for choosing sugarcane varieties that result in maximum revenue from electricity sales and minimum gathering cost of sugarcane harvesting residual biomass.The approach used to solve the proposed model was based on theε-constraints method.Experiments were performed using real data from sugarcane varieties and costs and showed effectiveness of model and method proposed.These experiments showed the possibility of increasing net revenue from electricity sale,i.e.,already discounted the cost increase with residual biomass gathering,in up to 98.44%.展开更多
The fluctuation of wind power brings great challenges to the secure,stable,and cost-efficient operation of the power system.Because of the time-correlation of wind speed and the wake effect of wind turbines,the layout...The fluctuation of wind power brings great challenges to the secure,stable,and cost-efficient operation of the power system.Because of the time-correlation of wind speed and the wake effect of wind turbines,the layout of wind farm has a significant impact on the wind power sequential fluctuation.In order to reduce the fluctuation of wind power and improve the operation security with lower operating cost,a bi-objective layout optimization model for multiple wind farms considering the sequential fluctuation of wind power is proposed in this paper.The goal is to determine the optimal installed capacity of wind farms and the location of wind turbines.The proposed model maximizes the energy production and minimizes the fluctuation of wind power simultaneously.To improve the accuracy of wind speed estimation and hence the power calculation,the timeshifting of wind speed between the wind tower and turbines’locations is also considered.A uniform design based two-stage genetic algorithm is developed for the solution of the proposed model.Case studies demonstrate the effectiveness of this proposed model.展开更多
We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are ...We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.展开更多
This paper illustrates a new bi-objective optimization model of real-time automatic generation control dispatch in a performance-based frequency regulation market.It attempts to simultaneously minimize the total power...This paper illustrates a new bi-objective optimization model of real-time automatic generation control dispatch in a performance-based frequency regulation market.It attempts to simultaneously minimize the total power deviation and the regulation mileage payment via optimally distributing the realtime total generation command to different regulation units.To handle this problem,an efficient non-dominated sorting genetic algorithm II is adopted to rapidly obtain a high-quality Pareto front for real-time AGC dispatch.A dynamic ideal point based decision making technique is designed to select the best compromise solution from the obtained Pareto front according to the minimization of the total regulation variation,which can effectively avoid an excessive regulation variation for each unit.Finally,two testing systems are used to verify the performance of the proposed technique.展开更多
In recent years,with strict domestic financial supervision and other policy-oriented factors,some products are becoming increasingly restricted,including nonstandard products,bank-guaranteed wealth management products...In recent years,with strict domestic financial supervision and other policy-oriented factors,some products are becoming increasingly restricted,including nonstandard products,bank-guaranteed wealth management products,and other products that can provide investors with a more stable income.Pairs trading,a type of stable strategy that has proved efficient in many financial markets worldwide,has become the focus of investors.Based on the traditional Gatev-Goetzmann-Rouwenhorst(GGR,Gatev et al.2006)strategy,this paper proposes a stock-matching strategy based on bi-objective quadratic programming with quadratic constraints(BQQ)model.Under the condition of ensuring a long-term equilibrium between pairedstock prices,the volatility of stock spreads is increased as much as possible,improving the profitability of the strategy.To verify the effectiveness of the strategy,we use the natural logs of the daily stock market indices in Shanghai.The GGR model and the BQQ model proposed in this paper are back-tested and compared.The results show that the BQQ model can achieve a higher rate of returns.展开更多
基金supported in part by the National Natural Science Foundation of China(62172065,62072060)。
文摘As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features.Evolutionary computing(EC)is promising for FS owing to its powerful search capability.However,in traditional EC-based methods,feature subsets are represented via a length-fixed individual encoding.It is ineffective for high-dimensional data,because it results in a huge search space and prohibitive training time.This work proposes a length-adaptive non-dominated sorting genetic algorithm(LA-NSGA)with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective highdimensional FS.In LA-NSGA,an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths,and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively.Moreover,a dominance-based local search method is employed for further improvement.The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.
文摘A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.
文摘The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and literature Instances, was divided into three stages: Stage 1, data treatment;Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II);Stage 3, analysis of the results, with a comparison of the algorithms. An optimization of 19.9% was achieved for Objective Function 1 (OF<sub>1</sub>;minimization of CO<sub>2</sub> emissions) and consequently the same percentage for the minimization of total distance, and 87.5% for Objective Function 2 (OF<sub>2</sub>;minimization of the difference in demand). Metaheuristic approaches hybrid achieved superior results for case study and instances. In this way, the procedure presented here can bring benefits to society as it considers environmental issues and also balancing work between the routes, ensuring savings and satisfaction for the users.
基金supported by the National Natural Science Foundation of China(No.62466019).
文摘Neural dynamics is a powerful tool to solve online optimization problems and has been used in many applications.However,some problems cannot be modelled as a single objective optimization and neural dynamics method does not apply.This paper proposes the first neural dynamics model to solve bi-objective constrained quadratic program,which opens the avenue to extend the power of neural dynamics to multi-objective optimization.We rigorously prove that the designed neural dynamics is globally convergent and it converges to the optimal solution of the bi-objective optimization in Pareto sense.Illustrative examples on bi-objective geometric optimization are used to verify the correctness of the proposed method.The developed model is also tested in scientific computing with data from real industrial data with demonstrated superior to rival schemes.
文摘This paper studies learning effect as a resource utilization technique that can model improvement in worker＇s ability as a result of repeating similar tasks. By considering learning of workers while performing setup times, a schedule can be determined to place jobs that share similar tools and fixtures next to each other. The purpose of this paper is to schedule a set of jobs in a hybrid flow shop （HFS） environment with learning effect while minimizing two objectives that are in conflict： namely maximum completion time （makespan） and total tardiness. Minimizing makespan is desirable from an internal efficiency viewpoint, but may result in individual jobs being scheduled past their due date, causing customer dissatisfaction and penalty costs. A bi-objective mixed integer programming model is developed, and the complexity of the developed bi-objective model is compared against the bi-criteria one through numerical examples. The effect of worker learning on the structure of assigned jobs to machines and their sequences is analyzed. Two solution methods based on the hybrid water flow like algorithm and non-dominated sorting and ranking concepts are proposed to solve the problem. The quality of the approximated sets of Pareto solutions is evaluated using several performance criteria. The results show that the proposed algorithms with learning effect perform well in reducing setup times and eliminate the need for setups itself through proper scheduling.
基金supported in part by the National Key R&D Program of China(No.2016YFB0900100)the Major Smart Grid Joint Project of National Natural Science Foundation of China and State Grid(No.U1766212).
文摘Partitioning a complex power network into a number of sub-zones can help realize a divide-and-conquer’management structure for the whole system,such as voltage and reactive power control,coherency identification,power system restoration,etc.Extensive partitioning methods have been proposed by defining various distances,applying different clustering methods,or formulating varying optimization models for one specific objective.However,a power network partition may serve two or more objectives,where a trade-off among these objectives is required.This paper proposes a novel weighted consensus clustering-based approach for bi-objective power network partition.By varying the weights of different partitions for different objectives,Pareto improvement can be explored based on the node-based and subset-based consensus clustering methods.Case studies on the IEEE 300-bus test system are conducted to verify the effectiveness and superiority of our proposed method.
文摘Traffic congestion in road transportation networks is a persistent problem in major metropolitan cities around the world.In this context,this paper deals with exploiting underutilized road capacities in a network to lower the congestion on overutilized links while simultaneously satisfying the system optimal flow assignment for sustainable transportation.Four congestion mitigation strategies are identified based on deviation and relative deviation of link volume from the corresponding capacity.Consequently,four biobjective mathematical programming optimal flow distribution(OFD)models are proposed.The case study results demonstrate that all the proposed models improve system performance and reduce congestion on high volume links by shifting flows to low volumeto-capacity links compared to UE and SO models.Among the models,the system optimality with minimal sum and maximum absolute relative-deviation models(SO-SAR and SO-MAR)showed superior results for different performance measures.The SO-SAR model yielded 50%and 30%fewer links at higher link utilization factors than UE and SO models,respectively.Also,it showed more than 25%improvement in path travel times compared to UE travel time for about 100 paths and resulted in the least network congestion index of1.04 compared to the other OFD and UE models.Conversely,the SO-MAR model yielded the least total distance and total system travel time,resulting in lower fuel consumption and emissions,thus contributing to sustainability.The proposed models contribute towards efficient transportation infrastructure management and will be of interest to transportation planners and traffic managers.
文摘An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
文摘Sugarcane crop occupies an area of about 23.78 million hectares in 103 countries,and an estimated production of 1.66 billion tons,adding to this volume more than 6%to 17%concerning residual biomass resulting from harvest.The destination of this residual biomass is a major challenge to managers of mills.There are at least two alternatives which are reduction in residue production and increased output in electricity cogeneration.These two conflicting objectives are mathematically modeled as a bi-objective problem.This study developed a bi-objective mathematical model for choosing sugarcane varieties that result in maximum revenue from electricity sales and minimum gathering cost of sugarcane harvesting residual biomass.The approach used to solve the proposed model was based on theε-constraints method.Experiments were performed using real data from sugarcane varieties and costs and showed effectiveness of model and method proposed.These experiments showed the possibility of increasing net revenue from electricity sale,i.e.,already discounted the cost increase with residual biomass gathering,in up to 98.44%.
基金supported by the National Natural Science Foundation of China(No.51377178,51607051)Anhui Provincial Natural Science Foundation(No.1908085QE237,2108085UD08)Visiting Scholarship of State Key Laboratory of Power Transmission Equipment&System Security and New Technology(Chongqing University)(2007DA105127).
文摘The fluctuation of wind power brings great challenges to the secure,stable,and cost-efficient operation of the power system.Because of the time-correlation of wind speed and the wake effect of wind turbines,the layout of wind farm has a significant impact on the wind power sequential fluctuation.In order to reduce the fluctuation of wind power and improve the operation security with lower operating cost,a bi-objective layout optimization model for multiple wind farms considering the sequential fluctuation of wind power is proposed in this paper.The goal is to determine the optimal installed capacity of wind farms and the location of wind turbines.The proposed model maximizes the energy production and minimizes the fluctuation of wind power simultaneously.To improve the accuracy of wind speed estimation and hence the power calculation,the timeshifting of wind speed between the wind tower and turbines’locations is also considered.A uniform design based two-stage genetic algorithm is developed for the solution of the proposed model.Case studies demonstrate the effectiveness of this proposed model.
基金supported by the National Natural Science Foundation of China(Nos.11871362)。
文摘We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.
基金supported by National Natural Science Foundation of China(51907112,61963020)Natural Science Foundation of Guangdong Province of China(2019A1515011671).
文摘This paper illustrates a new bi-objective optimization model of real-time automatic generation control dispatch in a performance-based frequency regulation market.It attempts to simultaneously minimize the total power deviation and the regulation mileage payment via optimally distributing the realtime total generation command to different regulation units.To handle this problem,an efficient non-dominated sorting genetic algorithm II is adopted to rapidly obtain a high-quality Pareto front for real-time AGC dispatch.A dynamic ideal point based decision making technique is designed to select the best compromise solution from the obtained Pareto front according to the minimization of the total regulation variation,which can effectively avoid an excessive regulation variation for each unit.Finally,two testing systems are used to verify the performance of the proposed technique.
基金The research is supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(No.19XNH089).
文摘In recent years,with strict domestic financial supervision and other policy-oriented factors,some products are becoming increasingly restricted,including nonstandard products,bank-guaranteed wealth management products,and other products that can provide investors with a more stable income.Pairs trading,a type of stable strategy that has proved efficient in many financial markets worldwide,has become the focus of investors.Based on the traditional Gatev-Goetzmann-Rouwenhorst(GGR,Gatev et al.2006)strategy,this paper proposes a stock-matching strategy based on bi-objective quadratic programming with quadratic constraints(BQQ)model.Under the condition of ensuring a long-term equilibrium between pairedstock prices,the volatility of stock spreads is increased as much as possible,improving the profitability of the strategy.To verify the effectiveness of the strategy,we use the natural logs of the daily stock market indices in Shanghai.The GGR model and the BQQ model proposed in this paper are back-tested and compared.The results show that the BQQ model can achieve a higher rate of returns.
