Minimizing a unimodal function of two integer variables

1985 ◽  
pp. 76-87 ◽  
Author(s):  
Alan J. Hoffman ◽  
Philip Wolfe
Keyword(s):  
Unimodal Function ◽  
Integer Variables

Adaptive Sampling line search for local stochastic optimization with integer variables

2021 ◽  
Author(s):  
Prasanna K. Ragavan ◽  
Susan R. Hunter ◽  
Raghu Pasupathy ◽  
Michael R. Taaffe
Keyword(s):  
Stochastic Optimization ◽  
Adaptive Sampling ◽  
Line Search ◽  
Integer Variables ◽  
Sampling Line

scholarly journals Day-ahead Market Modelling of Large-scale Highly-renewable Multi-energy Systems: Analysis of the North Sea Region Towards 2050

2020 ◽  
Author(s):  
Juan Gea Bermúdez ◽  
Kaushik Das ◽  
Hardi Koduvere ◽  
Matti Juhani Koivisto
Keyword(s):  
North Sea ◽  
Large Scale ◽  
Unit Commitment ◽  
District Heating ◽  
Energy Systems ◽  
Energy System ◽  
Computational Time ◽  
Integer Variables ◽  
The North ◽  
The North Sea

This paper proposes a mathematical model to simulate Day-ahead markets of large-scale multi-energy systems with high share of renewable energy. Furthermore, it analyses the importance of including unit commitment when performing such analysis. The results of the case study, which is performed for the North Sea region, show the influence of massive renewable penetration in the energy sector and increasing electrification of the district heating sector towards 2050, and how this impacts the role of other energy sources such as thermal and hydro. The penetration of wind and solar is likely to challenge the need for balancing in the system as well as the profitability of thermal units. The degree of influence of the unit commitment approach is found to be dependent on the configuration of the energy system. Overall, including unit commitment constraints with integer variables leads to more realistic behaviour of the units, at the cost of increasing considerably the computational time. Relaxing integer variables reduces significantly the computational time, without highly compromising the accuracy of the results. The proposed model, together with the insights from the study case, can be specially useful for system operators for optimal operational planning.

scholarly journals Integer variables estimation problems: the Bayesian approach

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Sansò ◽  
G. Venuti
Keyword(s):  
Bayesian Approach ◽  
Estimation Procedure ◽  
Least Square ◽  
Unknown Parameters ◽  
Ordinary Least Square ◽  
Integer Variables ◽  
Cycle Slips ◽  
Estimation Problems ◽  
Continuous Range ◽  
Gps Observations

In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed.

Identification of the Optimal Product Configuration and Parameters for Improving Manufacturability

1996 ◽  
Author(s):  
Deyi Xue
Keyword(s):  
Global Optimization ◽  
Optimization Methods ◽  
Product Configuration ◽  
Design System ◽  
Optimization Approach ◽  
Continuous Variables ◽  
Integer Variables ◽  
System A ◽  
Global Optimization Methods

Abstract A global optimization approach for identifying the optimal product configuration and parameters is proposed to improve manufacturability measures including feasibility, cost, and time of production. Different product configurations, including alternative design candidates and production processes, are represented by an AND/OR graph. Product parameters are described by variables including continuous variables, integer variables, Boolean variables, and discrete variables. Two global optimization methods, genetic algorithm and simulated annealing, are employed for identifying the optimal product configuration and parameters. The introduced approach serves as a key component in an integrated concurrent design system. A case study example is given to show how the proposed method is used for solving the engineering problems.

Generalized External Optimization

2005 ◽  
pp. 41-60 ◽  
Author(s):  
Fabiano Luis de Sousa ◽  
Fernando Manuel Ramos ◽  
Roberto Luiz Galski ◽  
Issamu Muraoka
Keyword(s):  
Optimization Problems ◽  
Evolutionary Model ◽  
Design Tool ◽  
Thermal Design ◽  
Extremal Optimization ◽  
Integer Variables ◽  
Constrained Problems ◽  
Self Organized ◽  
Complex Design ◽  
Self Organized Criticality

In this chapter a recently proposed meta-heuristic devised to be used in complex optimization problems is presented. Called Generalized Extremal Optimization (GEO), it was inspired by a simple co-evolutionary model, developed to show the emergence of self-organized criticality in ecosystems. The algorithm is of easy implementation, does not make use of derivatives and can be applied to unconstrained or constrained problems, non-convex or even disjoint design spaces, with any combination of continuous, discrete or integer variables. It is a global search meta-heuristic, like the Genetic Algorithm (GA) and the Simulated Annealing (SA), but with the advantage of having only one free parameter to adjust. The GEO has been shown to be competitive to the GA and the SA in tackling complex design spaces and a useful tool in real design problems. Here the algorithm is described, including a step-by-step implementation to a simple numerical example, its main characteristics highlighted, and its efficacy as a design tool illustrated with an application to satellite thermal design.

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