HI,

have a look at the COCO site:

http://coco.gforge.inria.fr/doku.php

Thank ivan but i need a real word problem not a benchmark function

Finding the lowest altitude of the Himalayas !

Try himmelblau function

I have tested on some benchmark function. But i don't need to benchmark function, i am looking for a real word multimodal problem.

You mean global optimization? A problem with multiple local solutions? Check out the two papers below on financial engineering applications.

The first relatew to fitting scenario trees suggesting a general purpose methodology that boils down to solving a global optimization problem with known optimal value 0.

The second relates to the optimal design of financial products.

https://www.researchgate.net/publication/259012806_Generating_multi-asset_arbitrage-free_scenario_trees_with_global_optimization

https://www.researchgate.net/publication/222796715_A_model_for_designing_callable_bonds_and_its_solution_using_tabu_search?ev=prf_pub

Article A parsimonious model for generating arbitrage-free scenario trees

Article A model for designing callable bonds and its solution using ...

Mario is right. There are several cemeteries full of interesting optimization algorithms. You could test your algorithm on a "real world problem". The problem is: is it enough to characterize the power of your algorithm?

A simple way to get a real world problem, could be:

a) Solve a parameter identification problem

- Take data from a machine learning database (http://archive.ics.uci.edu/ml/) and adapt the parameters of a system identification or classification problem, e.g. a deep layered feed forward artificial neural net should generate a multimodal problem.

- Controller design problems, depending on the goal function, tend to be multimodal. E.g. adapt the parameters for a PID-controller or a more complex controller. You can use Simulink or a similar software to simulate the control loop.

b) Topological optimization problems, e.g. optimize the material distribution in order to meet some

mechanical restrictions (minimal mass or/and stress in certain boundaries). For several problems there exist simple mathematical expressions (sorry I have no reference at hand) or you can use some FEM-simulation to evaluate the quality of the variable set.

thank you Stavros Zenios. you got it. Iván and mario thank you.

I agree with the answer of Iván Santibáñez Koref,

you can also check with the problem of real time scheduling for multitasking processes, the conventional method is to apply optimization technique to find best sampling rates.

i think this problem might be suitable to consider for your question

try problem described in "OPTIMAL PLACEMENT OF PILES IN REAL GRILLAGES: EXPERIMENTAL COMPARISON OF OPTIMIZATION ALGORITHMS", ISSN 1392 – 124X INFORMATION TECHNOLOGY AND CONTROL, 2011, Vol.40, No.2. The "black-box" program for direct problem is available there; what is interesting: the ideal solution for the problem is known in advance

You could try: "Increasing the Density of Multi-Objective Multi-Modal Solutions using Clustering and Pareto Estimation Techniques", the first author is working with RR and was motivated by a real world problem.

The minimum labelling spanning tree problem, and related modification as the minimum lablling Steiner tree problem, are examples of what you are looking for.

Here is an explanation with some references:

http://www.sergioconsoli.com/en-gb/research/minimumlabellingspanningtreeproblem.aspx

Hope this can be of any help, bye bye!

While there are some functions that can generally serve as benchmark, I believe that it is better to find something relevant to your own field of study. For water resources management problems, for Instance, you could try those appearing in: “A set of new benchmark optimization problems for water resources management”, Water Resources Management, Vol. 27 (9), pp. 3333-3348, 2013.

in term of multi-modal in optimization we have 2 different concept :

1- multi-modal function : any function that have some optimal point (local or global) but you need just 1 optimal solution and there is no different between the answers (in case of having many global optima). in this case multi-modal functions cause optimization algorithms dis-convergence or convergence to local optima that is not suitable.

2- multi-modal Optimization : in this case you have to find all global or local optima of objective function.

for case 1 there are many real world optimization problem but for case 2 I can suggest few problems like filter design or three body problem. 

you can see this paper for more information:

http://bayanbox.ir/id/8769797696875906890?download  from http://yazdani.id.ir/page/Publications 

You may try interesting analytical function(s) as used in my paper: Rajeev Kumar and PI Rockett. "Evolutionary multimodal optimization revisited". In Proc. Genetic and Evolutionary Computing Conference (GECCO-03), Chicago, IL. LNCS 2723: 1592 - 1593, July 2003. Springer.

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization

Code Codes in MATLAB for Particle Swarm Optimization

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB

https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination

Article A comparative study of metaheuristic optimization approaches...