Probabilistic programming is used in some optimization problems where some or all parameters are considered as random variables, in order to deal with uncertainty, which is an inherent feature of the system. The situa...
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Probabilistic programming is used in some optimization problems where some or all parameters are considered as random variables, in order to deal with uncertainty, which is an inherent feature of the system. The situation of multiple parameters may exist in a decision making problem in our real life. The multi-choice programming can not only avoid the underestimation of parameters, but also can decide the appropriate parameter from multiple parameters. This paper deals with a probabilistic linearprogramming problem, where the right hand side parameters of probabilistic constraints are multichoice in nature and rest of the parameters are independent random variables. In this paper the probabilistic programming problem is converted to an equivalent deterministic mathematical programming model. The resulting model is then solved by standard linear or non-linear programming techniques. A numerical example is presented to illustrate the methodology.
In this paper, we examine the rationale for financial reinsurance in the casualty insurance business. As opposed to regular reinsurance, financial reinsurance refers to an investment strategy that uses the financial m...
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In this paper, we examine the rationale for financial reinsurance in the casualty insurance business. As opposed to regular reinsurance, financial reinsurance refers to an investment strategy that uses the financial markets to hedge insurance risk. The casualty insurer takes positions in derivatives on underlying assets whose prices are highly positively or negatively correlated with specific insurance risks. We formulate the asset liability management problem for a mutually owned casualty insurer, in the context of a dynamic stochastic portfolio selection model. Using numerical studies of the resulting large-scale non-linear program, we compare properties of optimal portfolios with and without the possibility of financial reinsurance. We let an alleged representative policyholder, endowed with a linear plus negative exponential utility function, evaluate the various optimal portfolios. When policyholders' utility functions exhibit reasonable levels of risk aversion, we find that portfolios reflecting financial reinsurance dominate portfolios that are not financially reinsured. (C) 2003 Elsevier B.V. All rights reserved.
The paper introduces and develops a method for investigating the application of mathematical programming to the concept of crashing in Program Evaluation and Review Technique (PERT): The main objective is the minimiza...
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Even as quantum computers continue to increase in number of qubits, high error rates limit the size of quantum circuits that can be executed. This results in low throughput and poor resource utilization on quantum com...
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ISBN:
(纸本)9798331541378
Even as quantum computers continue to increase in number of qubits, high error rates limit the size of quantum circuits that can be executed. This results in low throughput and poor resource utilization on quantum computers. To address this, recent research has focused on extending circuit optimization and compilation techniques to support simultaneous execution of quantum circuits (i.e. quantum parallelism). While much work has been spent developing parallel mapping and gate scheduling techniques, there are few approaches to the problem of parallel job scheduling on quantum computers. There are several constraints that make quantum job scheduling different from classical scheduling. We propose a scheduling algorithm, QGroup, for parallelizing circuits of different lengths and shot counts while mitigating parallel slowdowns due to measurement synchronization. QGroup achieves a better parallelism-runtime tradeoff, with significant speedup and fidelity increase over existing methods. QGroup achieves improvement in both fidelity and runtime for noise-sensitive, diverse workloads.
The bilevel fractional programming problem (BFPP), in which the follower's objective function is a linear fractional functional, is introduced and studied in this paper. The leader's and the follower's dec...
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A non-linear discrete-time mathematical program model is proposed to determining the optimal extraction policy for a single primary supplier of a durable non-renewable resource, such as gemstones or some metals. Karus...
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A non-linear discrete-time mathematical program model is proposed to determining the optimal extraction policy for a single primary supplier of a durable non-renewable resource, such as gemstones or some metals. Karush, Kuhn and Tucker conditions allow obtaining analytic solutions and general properties of them in some specific settings. Moreover, provided that the objective function (i.e., the discounted value of the incomes throughout the planning horizon) is concave, the model can be easily solved, even using standard commercial solver. However, the analysis of the solutions obtained for different assumptions of the values of the parameters show that the optimal extraction policies and the corresponding prices do not exhibit a general shape. (C) 2017 The Author. Published by Elsevier Ltd.
A primal-dual interior point algorithm for solving general nonlinearprogramming problems is presented. The algorithm solves the perturbed optimality conditions by applying a quasi-Newton method, where the Hessian of ...
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A primal-dual interior point algorithm for solving general nonlinearprogramming problems is presented. The algorithm solves the perturbed optimality conditions by applying a quasi-Newton method, where the Hessian of the Lagrangian is replaced by a positive definite approximation. An approximation of Fletcher's exact and differentiable merit function together with line-search procedures are incorporated into the algorithm. The line-search procedures are used to modify the length of the step so that the value of the merit function is always reduced. Different step-sizes are used for the primal and dual variables. The search directions are ensured to be descent for the merit function, which is thus used to guide the algorithm to an optimum solution of the constrained optimisation problem. The monotonic decrease of the merit Function at each iteration, ensures the global convergence of the algorithm. Finally, preliminary numerical results demonstrate the efficient performance of the algorithm for a variety of problems.
Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new ...
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Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.
Modular products are products that fulfill various functions through the combination of distinct modules. These detachable modules are constructed both according to the maximum physical and functional relations among ...
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Modular products are products that fulfill various functions through the combination of distinct modules. These detachable modules are constructed both according to the maximum physical and functional relations among components and maximizing the similarity of specifically modular driving forces. Accordingly, a non-linear programming is proposed to identify separable modules and simultaneously optimize the number of modules. This paper presents a systematic approach to accomplish modular product design in four major phases. Phase 1 is by means of functional and physical interaction analysis to format a component-to-component correlation matrix. Phase 2 is the exploration of design requirements to evaluate the relative importance of each modular driver. In phase 3, non-linear programming is used to formulate the objective function. In the final phase, a heuristic grouping genetic algorithm is adopted to search for the optimal or near-optimal modular architecture. This process and its application are illustrated by a real case of an electrical consumer product provided by an Original Design Manufacturer. The results demonstrate that the designer could direct a new approach to establish product modules according to the relative importance of modular drivers and the interaction among components. (C) 2004 Elsevier Ltd. All rights reserved.
We extend the Gamma-robustness approach proposed by Bertsimas and Sim for linear Programs to the case of non-linear impact of parameter variation. The seminal work considered protection from infeasibility over the wor...
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We extend the Gamma-robustness approach proposed by Bertsimas and Sim for linear Programs to the case of non-linear impact of parameter variation. The seminal work considered protection from infeasibility over the worst-case variation of coefficients in a constraint, this variation being controlled by an uncertainty budget called Gamma. When coefficients are non-linear functions of a parameter subject to uncertainty, we study a piecewise linear approximation of the function, and show that the subproblem of determining the worst-case variation can still be dualized despite the discrete structure of the piecewise linear function. We conduct numerical experiments on three different problems: Capital Budgeting, Generalized Assignment and Knapsack problems to analyze the trade-off between feasibility and objective value for the robust solution of the piecewise linear approximation compared to the nominal solution, and to a simpler binary approximation. Despite the piecewise approximation, the robust solution reveals to remain feasible over the 6800 runs performed in our experiments, with an average deterioration of the objective value of only a few percents. (C) 2018 Elsevier Ltd. All rights reserved.
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