Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then consi...Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.展开更多
The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point wit...The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.展开更多
This paper introduces a new type of cutting plane for the unit commitment(UC)problem,namely“infeasibility cutting plane”.The infeasibility cutting plane refers to a type of logic constraint that eliminates the combi...This paper introduces a new type of cutting plane for the unit commitment(UC)problem,namely“infeasibility cutting plane”.The infeasibility cutting plane refers to a type of logic constraint that eliminates the combination of integer variables causing infeasibility of the UC problem while not affecting any feasible integer solutions.This paper demonstrates that under certain conditions,such a cutting plane is effective for tightening the linear programming(LP)relaxation of UC,thus achieving a valid acceleration of UC without the loss of accuracy.A theoretical and easy-to-implement criterion is provided to identify valid infeasibility cutting planes.Then,an efficient framework for constructing the infeasibility cutting planes is presented to quickly obtain multiple combinations of integer variables causing infeasibility of UC through solving a batch of relaxed LP problems.The condition that the constructed infeasibility cutting plane does not provide overlapped information is provided.Based on the test on 30 public and utility cases,the proposed cutting plane method achieves an acceleration of 1.14 to 2.41 times with full optimality guarantee.Also,results show that the proposed cutting planes also work with existing cutting plane methodologies embedded in modern solvers.展开更多
文摘Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.
文摘The generation expansion planning is one of complex mixed-integer optimization problems, which involves a large number of continuous or discrete decision variables and constraints. In this paper, an interior point with cutting plane （IP/CP） method is proposed to solve the mixed-integer optimization problem of the electrical power generation expansion planning. The IP/CP method could improve the overall efficiency of the solution and reduce the computational time. Proposed method is combined with the Bender＇s decomposition technique in order to decompose the generation expansion problem into a master investment problem and a slave operational problem. The numerical example is presented to compare with the effectiveness of the proposed algorithm.
基金supported by National Key R&D Program of China(2024YFB2409000).
文摘This paper introduces a new type of cutting plane for the unit commitment(UC)problem,namely“infeasibility cutting plane”.The infeasibility cutting plane refers to a type of logic constraint that eliminates the combination of integer variables causing infeasibility of the UC problem while not affecting any feasible integer solutions.This paper demonstrates that under certain conditions,such a cutting plane is effective for tightening the linear programming(LP)relaxation of UC,thus achieving a valid acceleration of UC without the loss of accuracy.A theoretical and easy-to-implement criterion is provided to identify valid infeasibility cutting planes.Then,an efficient framework for constructing the infeasibility cutting planes is presented to quickly obtain multiple combinations of integer variables causing infeasibility of UC through solving a batch of relaxed LP problems.The condition that the constructed infeasibility cutting plane does not provide overlapped information is provided.Based on the test on 30 public and utility cases,the proposed cutting plane method achieves an acceleration of 1.14 to 2.41 times with full optimality guarantee.Also,results show that the proposed cutting planes also work with existing cutting plane methodologies embedded in modern solvers.
