We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only contin...We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.展开更多
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onproces...In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onprocess synthesis problems. The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms, with the first one being developed for the deterministic case, and thesecond for the parametric case （p-MINLP）. The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker （KKT） conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution tech-niques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, twoprocess synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicitfunction of the uncertain parameters.展开更多
The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers&#...The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers' travel demand, especially on those metro lines with insufficient rolling stock. In order to cope with high passenger flow service pressure, a mixed integer nonlinear programming(MINLP) model is proposed to optimize the line plan, timetable and rolling stock circulation simultaneously, to reduce the number of rolling stocks and increase the number of full-length services. A two-step algorithm strategy is proposed. In the first stage, the train timetable is optimized under the assumption that all the train services are the full-length services. In the second stage, the rolling stock plan is optimized based on the timetable optimized in the first stage. To ensure a feasible rolling stock circulation, certain full-length services are shortened to the short-length services due to the limited number of rolling stocks. Numerical experiments are performed based on the real-life data of Shanghai Metro Line 8. Results show that the proposed method can efficiently optimize the timetable and rolling stock circulation of the whole operation day. The optimized results are beneficial for both the service and the operational costs.展开更多
Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is develope...Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is developed for the optimal design of refrigeration cycle and heat exchanger network(HEN) simultaneously. Taking the heat integration between the external heat sources/sinks and the refrigeration cycle into consideration, a superstructure with sub-coolers is developed. Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming(GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system. The GDP model is then reformulated as a Mixed Integer Nonlinear Programming(MINLP) problem with the aid of binary variables and Big-M Constraint Method. The efficacy of the process synthesis model is demonstrated by a case study of ethylene refrigeration system. The result shows that the optimization can significantly reduce the exergy loss as well as the total compression shaft work.展开更多
The optimal design of a compression refrigeration system(CRS) with multiple temperature levels is very important to chemical process industries and also represents considerable challenges in process systems engineerin...The optimal design of a compression refrigeration system(CRS) with multiple temperature levels is very important to chemical process industries and also represents considerable challenges in process systems engineering. In this paper, a general methodology for the optimal synthesis of the CRS, which simultaneously integrates CRS and Heat Exchanger Networks(HEN) to minimize the total compressor shaft work consumption based on an MINLP model, has been proposed. The major contribution of this method is in addressing the optimal design of refrigeration cycle with variable refrigeration temperature levels. The method can be used to make major decisions in the CRS design, such as the number of levels, temperature levels, and heat transfer duties. The performance of the developed methodology has been illustrated with a case study of an ethylene CRS in an industrial ethylene plant, and the optimal solution has been examined by rigorous simulations in Aspen Plus to verify its feasibility and consistency.展开更多
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integ...In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.展开更多
文摘We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金financial support from EPSRC grants (EP/M027856/1 EP/M028240/1)
文摘In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onprocess synthesis problems. The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms, with the first one being developed for the deterministic case, and thesecond for the parametric case （p-MINLP）. The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker （KKT） conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution tech-niques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, twoprocess synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicitfunction of the uncertain parameters.
基金Sponsored by the National Key R&D Program of China (Grant No.2021YFB1600100)。
文摘The rapid growth of passenger flow in urban rail transit has led to great service pressures for metro companies in organizing train services to provide higher transportation capacities in order to satisfy passengers' travel demand, especially on those metro lines with insufficient rolling stock. In order to cope with high passenger flow service pressure, a mixed integer nonlinear programming(MINLP) model is proposed to optimize the line plan, timetable and rolling stock circulation simultaneously, to reduce the number of rolling stocks and increase the number of full-length services. A two-step algorithm strategy is proposed. In the first stage, the train timetable is optimized under the assumption that all the train services are the full-length services. In the second stage, the rolling stock plan is optimized based on the timetable optimized in the first stage. To ensure a feasible rolling stock circulation, certain full-length services are shortened to the short-length services due to the limited number of rolling stocks. Numerical experiments are performed based on the real-life data of Shanghai Metro Line 8. Results show that the proposed method can efficiently optimize the timetable and rolling stock circulation of the whole operation day. The optimized results are beneficial for both the service and the operational costs.
基金Supported by the National Natural Science Foundation of China(21676183)
文摘Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is developed for the optimal design of refrigeration cycle and heat exchanger network(HEN) simultaneously. Taking the heat integration between the external heat sources/sinks and the refrigeration cycle into consideration, a superstructure with sub-coolers is developed. Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming(GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system. The GDP model is then reformulated as a Mixed Integer Nonlinear Programming(MINLP) problem with the aid of binary variables and Big-M Constraint Method. The efficacy of the process synthesis model is demonstrated by a case study of ethylene refrigeration system. The result shows that the optimization can significantly reduce the exergy loss as well as the total compression shaft work.
基金Supported by the National Natural Science Foundation of China(21676183)
文摘The optimal design of a compression refrigeration system(CRS) with multiple temperature levels is very important to chemical process industries and also represents considerable challenges in process systems engineering. In this paper, a general methodology for the optimal synthesis of the CRS, which simultaneously integrates CRS and Heat Exchanger Networks(HEN) to minimize the total compressor shaft work consumption based on an MINLP model, has been proposed. The major contribution of this method is in addressing the optimal design of refrigeration cycle with variable refrigeration temperature levels. The method can be used to make major decisions in the CRS design, such as the number of levels, temperature levels, and heat transfer duties. The performance of the developed methodology has been illustrated with a case study of an ethylene CRS in an industrial ethylene plant, and the optimal solution has been examined by rigorous simulations in Aspen Plus to verify its feasibility and consistency.
基金Supported by the National 973 Program of China (No. G2000263).
文摘In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.
