An outcome space algorithm for minimizing a class of linear ratio optimization problems

This paper focuses on modelling and solving the ingredient ratio optimization problem in cement raw material blending process. A general nonlinear time-varying (G-NLTV) model is established for cement raw material blending process via considering chemical composition, feed flow fluctuation, and various craft and production constraints. Different objective functions are presented to acquire optimal ingredient ratios under various production requirements. The ingredient ratio optimization problem is transformed into discrete-time single objective or multiple objectives rolling nonlinear constraint optimization problem. A framework of grid interior point method is presented to solve the rolling nonlinear constraint optimization problem. Based on MATLAB-GUI platform, the corresponding ingredient ratio software is devised to obtain optimal ingredient ratio. Finally, several numerical examples are presented to study and solve ingredient ratio optimization problems.

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Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition

Journal of Applied Mathematics ◽

10.1155/2014/871565 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Yujian Zhou ◽

Liang Bao ◽

Yiqin Lin

Keyword(s):

Eigenvalue Problems ◽

Optimization Problems ◽

Computational Cost ◽

Image Data ◽

Subspace Analysis ◽

Left And Right ◽

Tensor Subspace ◽

Trace Ratio ◽

Ratio Optimization ◽

Projection Matrices

Tensor subspace analysis (TSA) and discriminant TSA (DTSA) are two effective two-sided projection methods for dimensionality reduction and feature extraction of face image matrices. However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA) and orthogonal DTSA (ODTSA). In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.

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Higher order duality of multiobjective constrained ratio optimization problems

Filomat ◽

10.2298/fil1907985k ◽

2019 ◽

Vol 33 (7) ◽

pp. 1985-1998

Author(s):

Arshpreet Kaur ◽

Navdeep Kailey ◽

M.K. Sharma

Keyword(s):

Generalized Convexity ◽

Feasible Solution ◽

Optimization Problems ◽

Higher Order ◽

Type I ◽

Dual Model ◽

Duality Theorems ◽

Fractional Programs ◽

Ratio Optimization ◽

Higher Order Duality

A new concept in generalized convexity, called higher order (C,?,?,?,d) type-I functions, is introduced. To show the existence of such type of functions, we identify a function lying exclusively in the class of higher order (C,?,?,?,d) type-I functions and not in the class of (C,?,?,?,d) type-I functions already existing in the literature. Based upon the higher order (C,?,?,?,d) type-I functions, the optimality conditions for a feasible solution to be an efficient solution are derived. A higher order Schaible dual has been then formulated for nondifferentiable multiobjective fractional programs. Weak, strong and strict converse duality theorems are established for higher order Schaible dual model and relevant proofs are given under the aforesaid function.

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Comparison of Meta-heuristic Algorithms on Benchmark Functions

Academic Perspective Procedia ◽

10.33793/acperpro.02.03.41 ◽

2019 ◽

Vol 2 (3) ◽

pp. 508-517

Author(s):

FerdaNur Arıcı ◽

Ersin Kaya

Keyword(s):

Heuristic Algorithms ◽

Optimization Problems ◽

Search Algorithm ◽

Optimization Algorithms ◽

Gravitational Search Algorithm ◽

Differential Evolution Algorithm ◽

Population Based ◽

Time Interval ◽

Bee Colony ◽

Different Characteristics

Optimization is a process to search the most suitable solution for a problem within an acceptable time interval. The algorithms that solve the optimization problems are called as optimization algorithms. In the literature, there are many optimization algorithms with different characteristics. The optimization algorithms can exhibit different behaviors depending on the size, characteristics and complexity of the optimization problem. In this study, six well-known population based optimization algorithms (artificial algae algorithm - AAA, artificial bee colony algorithm - ABC, differential evolution algorithm - DE, genetic algorithm - GA, gravitational search algorithm - GSA and particle swarm optimization - PSO) were used. These six algorithms were performed on the CEC&rsquo;17 test functions. According to the experimental results, the algorithms were compared and performances of the algorithms were evaluated.

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