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Hyper Spherical Search Algorithm for Non-Linear Mixed Integer Optimization Problem

version (253 KB) by Hosein Karami
Novel optimization method to find global optimum of non-linear mixed integer objective functions


Updated 29 Aug 2016

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From a general point of view, the process of making something better is optimization. If we have a function f(x), in optimization, we want to find an argument x whose relevant cost is optimum.
Most nonlinear optimization problems that appear in different areas of engineering, science and management cannot be analytically solved. Different methods and interesting optimization techniques have widely emerged and many of their successful applications have been reported, e.g., music composition, financial forecasting, aircraft design, job-shop scheduling and drug design. Evolutionary Algorithms (EAs) are more successful than other optimization techniques. In this group, the Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Harmony Search Algorithm (HSA) are applied to solve the optimization problems within the context of expensive optimization.
A novel optimization algorithm called Hyper-Spherical Search (HSS) algorithm is proposed to solve the non-linear mixed integer optimization problems. Like other evolutionary algorithms, the proposed algorithm starts with an initial population. Population individuals are of two types: particles and hyper-sphere centers that all together form particle sets. Searching the hyper-sphere inner space made by the hyper-sphere center and its particle is the basis of the proposed evolutionary algorithm. The HSS algorithm hopefully converges to a state at which there exists only one hyper-sphere center (SC) and its particles are at the same position and have the same cost function value as the hyper-sphere center. Applying the proposed algorithm to some benchmark cost functions, shows its ability in dealing with different types of optimization problems.
This is the paper published in Neural Computing and Application Journal:
H. Karami, M. J. Sanjari, G. B. Gharehpetian, "Hyper-Spherical Search (HSS) Algorithm: A Novel Meta-heuristic Algorithm to Optimize Nonlinear Functions", Neural Computing and Applications, Vol. 25, issue: 6, pp. 1455-1465, 2014
And this is one example of its application in a problem in the field of electrical engineering:
M.J. Sanjari, H.Karami, A.H. Yatim, G.B.Gharehpetian, "Application of Hyper-Spherical Search algorithm for optimal energy resources dispatch in residential microgrids", Applied Soft Computing (Elsevier), Volume 37, pp. 15–23, 2015
All of the source codes and extra information can be found in my personal website at

Cite As

Hosein Karami (2020). Hyper Spherical Search Algorithm for Non-Linear Mixed Integer Optimization Problem (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)


Hi Hosein,
You said that this algorithm is for Mixed integer programing. Does it mean that all the variables here have to be integer?

Joey Tribyani

A very good implementation. Thank you


The help document has been added and some description in the RUN.m file has been modified.

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux