A double layer neural network for solving mixed-integer quadratic optimization problems

2016 ◽  
Author(s):  
Shamshul Bahar Yaakob ◽  
Mohd Zamri Hasan ◽  
Amran Ahmed
Keyword(s):  
Neural Network ◽  
Double Layer ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Mixed Integer

scholarly journals Robust Linear Neural Network for Constrained Quadratic Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Zixin Liu ◽  
Yuanan Liu ◽  
Lianglin Xiong
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Perturbation Theory ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Analysis Method ◽  
Linear Neural Network ◽  
Constrained Quadratic Optimization

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper.

A Mixed-Integer Fractional Optimization Approach to Best Subset Selection

2021 ◽  
Author(s):  
Andrés Gómez ◽  
Oleg A. Prokopyev
Keyword(s):  
Optimization Problems ◽  
Subset Selection ◽  
Quadratic Optimization ◽  
Data Partitioning ◽  
Information Criteria ◽  
Computational Experiments ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Fractional Optimization ◽  
Recent Advances

We consider the best subset selection problem in linear regression—that is, finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We are primarily concerned with alternatives to cross-validation methods that do not require data partitioning and involve a range of information criteria extensively studied in the statistical literature. We show that the problem of interest can be modeled using fractional mixed-integer optimization, which can be tackled by leveraging recent advances in modern optimization solvers. The proposed algorithms involve solving a sequence of mixed-integer quadratic optimization problems (or their convexifications) and can be implemented with off-the-shelf solvers. We report encouraging results in our computational experiments, with respect to both the optimization and statistical performance. Summary of Contribution: This paper considers feature selection problems with information criteria. We show that by adopting a fractional optimization perspective (a well-known field in nonlinear optimization and operations research), it is possible to leverage recent advances in mixed-integer quadratic optimization technology to tackle traditional statistical problems long considered intractable. We present extensive computational experiments, with both synthetic and real data, illustrating that the new fractional optimization approach is orders of magnitude faster than existing approaches in the literature.

scholarly journals A Multi-Objective Approach toward Optimal Design of Sustainable Integrated Biodiesel/Diesel Supply Chain Based on First- and Second-Generation Feedstock with Solid Waste Use

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2261
Author(s):  
Evgeniy Ganev ◽  
Boyan Ivanov ◽  
Natasha Vaklieva-Bancheva ◽  
Elisaveta Kirilova ◽  
Yunzile Dzhelil
Keyword(s):  
Supply Chain ◽  
Optimal Design ◽  
Solid Waste ◽  
Second Generation ◽  
Agricultural Land ◽  
Optimization Problems ◽  
Biodiesel Production ◽  
Mixed Integer ◽  
Economic Criterion ◽  
Multi Objective

This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and second-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.

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