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
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
Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical...Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.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
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
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
Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show th...Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.展开更多
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.
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National Natural Science Foundation of China(No.51405403)the Fundamental Research Funds for the Central Universities,China(No.2682014BR019)the Scientific Research Program of Education Bureau of Sichuan Province,China(No.12ZB322)
文摘Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.
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.
文摘Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.
