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Design Optimization of Battery-Electric Marine Vessels via geometric programming

IEEE ACCESS 2023年 11卷 76563-76580页

作者： Ritari, Antti Mouratidis, Panagiotis Tammi, Kari Aalto Univ Dept Mech Engn Espoo 02150 Finland

This paper proposes formulating conceptual-stage vessel design optimization problems as geometric programs, which can be transformed into convex optimization problems. Convex optimization offers significant advantages in efficiency, reliability and automation potential over the general nonlinear optimization approach typically used in naval architecture. Focusing on battery-electric vessels, geometric program compatible models are derived for lithium-ion cells, power converters, propulsion motors and propellers. Preliminary hull form development, stability calculation and structural design are also presented in the context of geometric programming. The modeling approach is applied to study optimal battery sizing for a coastal bulk carrier sailing in varying operational conditions. Using open-source software tools, the battery sizing problem is solved in less than a second on a standard desktop computer. Local sensitivity information encoded by optimal dual variables reveals that increasing the cell discharge upper bound by 1% decreases the optimal total number of cells by more than 1%. On the other hand, the sensitivities of cell volume and maximum discharging current parameters are zero, indicating that the constraints involving these parameters do not govern the solution.

关键词： INDEX TERMS Electric propulsion battery energy storage design optimization convex optimization geometric programming

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Engineering Design by geometric programming

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MATHEMATICAL PROBLEMS IN ENGINEERING 2013年第1期2013卷 1-8页

作者： Huang, Chia-Hui Natl Taipei Coll Business Dept Business Adm Taipei 100 Taiwan

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions, where all functions are of signomial form. The importance of GP comes from two relatively recent developments: (i) new methods can solve even large-scale GP extremely efficiently and reliably;(ii) a number of practical problems have recently been found to be equivalent to or approximated by GP. This study proposes an optimization approach for solving GP. Our approach is first to convert all signomial terms in GP into convex and concave terms. Then the concave terms are further treated with the proposed piecewise linearization method where only [log(2)(m - 1)] binary variables are used. It has the following features: (i) it offers more convenient and efficient means of expressing a piecewise linear function;(ii) fewer 0-1 variables are used;(iii) the computational results show that the proposed method is much more efficient and faster than the conventional one, especially when the number of break points becomes large. In addition, the engineering design problems are illustrated to evaluate the usefulness of the proposed methods.

关键词： ENGINEERING design geometric programming MATHEMATICAL optimization FUNCTIONS (Mathematics) BINARY system (Mathematics) APPROXIMATION theory

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Delay-Sensitive Task Offloading Optimization by geometric programming

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IEEE TRANSACTIONS ON CLOUD COMPUTING 2024年第3期12卷 889-896页

作者： Fathi, Mohammad Saroughi, Mohammad Zareie, Azarhedi Univ Kurdistan Fac Engn Dept Elect Engn Sanandaj *** Iran

Mobile cloud computing is an emerging technology to address the resource limitation of mobile terminals. These terminals need to satisfy the performance requirements of emerging resource-consuming applications. Among these applications, delay-sensitive applications are becoming popular with the requirements of low execution times. Satisfying the delay requirements of these applications is the main objective in the task offloading of mobile cloud computing. In this paper, considering a network of wireless and wired infrastructures, a resource allocation problem in the form of a non-convex problem is formulated to provide a fair delay for offloaded tasks by delay-sensitive applications. Both transmission and computation delays are included in the formulation of the offloading delay. To tackle the problem's complexity, the assignment of mobile terminals to radio access networks and cloud servers is done by proposing greedy assignment solutions. The derived problem which is a geometric programming problem is then solved using convex programming. The performance of the proposed solution is evaluated versus the number of mobile terminals with different values of bandwidth resources at the radio network, workloads, and demand CPU cycles at mobile terminals. Numerical results demonstrate the effectiveness of the proposed solution to decrease the offloading delay in comparison with similar schemes.

关键词： Task analysis Delays Cloud computing Servers Resource management Optimization Computational modeling geometric programming mobile cloud computing optimization task offloading

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Control of tree water networks: A geometric programming approach

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WATER RESOURCES RESEARCH 2015年第10期51卷 8409-8430页

作者： Perelman, L. Sela Amin, S. MIT Dept Civil & Environm Engn 77 Massachusetts Ave Cambridge MA 02139 USA

This paper presents a modeling and operation approach for tree water supply systems. The network control problem is approximated as a geometric programming (GP) problem. The original nonlinear nonconvex network control problem is transformed into a convex optimization problem. The optimization model can be efficiently solved to optimality using state-of-the-art solvers. Two control schemes are presented: (1) operation of network actuators (pumps and valves) and (2) controlled demand shedding allocation between network consumers with limited resources. The dual of the network control problem is formulated and is used to perform sensitivity analysis with respect to hydraulic constraints. The approach is demonstrated on a small branched-topology network and later extended to a medium-size irrigation network. The results demonstrate an intrinsic trade-off between energy costs and demand shedding policy, providing an efficient decision support tool for active management of water systems.

关键词： water networks control geometric programming

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Copula theory approach to stochastic geometric programming

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JOURNAL OF GLOBAL OPTIMIZATION 2021年第2期81卷 435-468页

作者： Khanjani-Shiraz, Rashed Khodayifar, Salman Pardalos, Panos M. Univ Tabriz Fac Math Sci Dept Appl Math Tabriz Iran Inst Adv Studies Basic Sci IASBS Dept Math Zanjan *** Iran Univ Florida Ctr Appl Optimizat Ind & Syst Engn Gainesville FL USA

In this research, stochastic geometric programming with joint chance constraints is investigated with elliptically distributed random parameters. The constraint's random coefficient vectors are considered dependent, and the dependence of the random vectors is handled through copulas. Moreover, Archimedean copulas are used to derive the random rows distribution. A convex approximation optimization problem is proposed for this class of stochastic geometric programming problems using a standard variable transformation. Furthermore, a piecewise tangent approximation and sequential convex approximation are employed to obtain the lower and upper bounds for the convex optimization model, respectively. Finally, an illustrative optimization example on randomly generated data is presented to demonstrate the efficiency of the methods and algorithms.

关键词： geometric programming Joint chance-constraint programming Copula theory Archimedean Copulas

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Multi-objective fuzzy inventory model with three constraints: a geometric programming approach

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FUZZY SETS AND SYSTEMS 2005年第1期150卷 87-106页

作者： Mandal, NK Roy, TK Maiti, M Deemed Univ Bengal Engn Coll Dept Math Howrah 711103 W Bengal India Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India

A multi-item multi-objective inventory model with shortages and demand dependent unit cost has been formulated along with storage space, number of orders and production cost restrictions. In most of the real world situations. the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. Hence the cost parameters, the objective functions and constraints are imposed here in fuzzy environment. This model has been solved by geometric programming method. The results for the model without shortages are obtained as a particular case. The sensitivity analysis has been discussed for the change of the cost parameters. The models are illustrated with numerical examples. (C) 2004 Elsevier B.V. All rights reserved.

关键词： inventory geometric programming multi-criteria evaluation fuzzy number fuzzy goal programming

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Fuzzy geometric programming approach to a fuzzy machining economics model

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2004年第16期42卷 3253-3269页

作者： Liu, ST Vanung Univ Grad Sch Business & Management Tao Yuan 320 Taiwan

Machining economics is an important function of the process planning activity for manufacturing products with high quality and low cost. The machining economics model usually contains a highly non-linear objective function and equations that could be formulated as a geometric programming problem. The paper develops a solution method for deriving the fuzzy objective value of the fuzzy machining economics problem when some of the parameters in the problem are fuzzy numbers. A pair of geometric programs is formulated to calculate the lower and upper bounds of the unit production cost at possibility level alpha. With the ability to calculate the fuzzy objective value developed, it might help lead to a more realistic modelling effort. The developed methodology can also be applied to other engineering design problems with fuzzy numbers.

关键词： MACHINING PRODUCTION planning MATHEMATICAL economics MANUFACTURING processes geometric programming FUZZY numbers FUZZY mathematics

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Steady-state optimization of biochemical systems through geometric programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第1期225卷 12-20页

作者： Xu, Gongxian Bohai Univ Dept Math Jinzhou 121013 Peoples R China

This paper presents an iterative strategy to address the steady-state optimization of biochemical systems. In the method we take advantage of a special class of nonlinear kinetic models known as Generalized Mass Action (GMA) models. These systems are interesting in that they allow direct merging of stoichiometric and S-system models. In most cases nonconvex steady-state optimization problems with GMA models cannot be transformed into tractable convex formulations, but an iterative strategy can be used to compute the optimal solution by solving a series of geometric programming. The presented framework is applied to several case studies and shown to the tractability and effectiveness of the method. The simulation is also studied to investigate the convergence properties of the algorithm and to give a performance comparison of our proposed and other approaches. (C) 2012 Elsevier B.V. All rights reserved.

关键词： OR in biology Optimization geometric programming Generalized mass action Biochemical systems

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ON geometric-programming AND COMPLEMENTARY SLACKNESS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第2期74卷 305-316页

作者： MCNAMARA, JR 1. College of Business and Economics Lehigh University Bethlehem Pennsylvania

When the terms in a convex primal geometric programming (GP) problem are multiplied by slack variables whose values must be at least unity, the invariance conditions may be solved as constraints in a linear programming (LP) problem in logarithmically transformed variables. The number of transformed slack variables included in the optimal LP basis equals the degree of difficulty of the GP problem, and complementary slackness conditions indicate required changes in associated GP dual variables. A simple, efficient search procedure is used to generate a sequence of improving primal feasible solutions without requiring the use of the G P dual objective function. The solution procedure appears particularly advantageous when solving very large geometric programming problems, because only the right-hand constants in a system of linear equations change at each iteration.

关键词： geometric programming LINEAR programming COMPLEMENTARY SLACKNESS LAGRANGE MULTIPLIERS

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Combining Data Reuse With Data-Level Parallelization for FPGA-Targeted Hardware Compilation: A geometric programming Framework

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2009年第3期28卷 305-315页

作者： Liu, Qiang Constantinides, George A. Masselos, Konstantinos Cheung, Peter Y. K. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2BT England Univ Peloponnese Dept Comp Sci & Technol Tripolis 22100 Greece

A nonlinear optimization framework is proposed in this paper to automate exploration of the design space consisting of data-reuse (buffering) decisions and loop-level parallelization, in the context of field-programmable-gate-array- targeted hardware compilation. Buffering frequently accessed data in on-chip memories can reduce off-chip memory accesses and open avenues for parallelization. However, the exploitation of both data reuse and parallelization is limited by the memory resources available on-chip. As a result, considering these two problems separately, e.g., first exploring data reuse and then exploring data-level parallelization, based on the data-reuse options determined in the first step, may not yield the performance-optimal designs for limited on-chip memory resources. We consider both problems at the same time, exposing the dependence between the two. We show that this combined problem can be formulated as a nonlinear program and further show that efficient solution techniques exist for this problem, based on recent advances in optimization of so-called geometric programming problems. The results from applying this framework to several real benchmarks implemented on a Xilinx device demonstrate that given different constraints on on-chip memory utilization, the corresponding performance-optimal designs are automatically determined by the framework. We have also implemented designs determined by a two-stage optimization method that first explores data reuse and then explores parallelization on the same platform, and by comparison, the performance-optimal designs proposed by our framework are faster than the designs determined by the two-stage method by up to 5.7 times.

关键词： Data-level parallelization data reuse field-programmable gate-array (FPGA) hardware compilation geometric programming optimization

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