Dear all,
I am working on optimization algorithms for their efficiency/inefficiency. These algorithms involve:
1. Gradient based methods: Variable Metric method, BFGS.
2. Derivative Free Methods: Hooke and Jeeves Method, Nelder-Mead Method, Multi-directional Simplex Method of V. Torczon, Frame based method of CJ Price.
3. Meta-heuristics: PSO, ABC, DE, FA, WCA, TLBO, CMA-ES
I need some suggestions in choosing some real word optimization problems for the applications of the modified approaches of the above algorithms.
Regards
Javaid Ali
Firstly, you must to do the systemic analysis of the problem you have to solve, to obtain conceptual mathematical model and later on to decompose it into interrelated subtasks. For solving every one of then you must use the must appropiate method according its characteristics. The solution of the original problem is carried out by means of the of solutions composition of the involved subtasks. If currently solving task is non lineal and the gradient can be analytically obtained, then could very useful the non lineal methods based on the gradient. If the model have implicit character, that means, it is required using numerical methods for finding the values of the objective and/or the restricted functions for it calculations, then it is required non lineal direct searching methods or metaheurístics. If the model includes discreet variables, then it is required the methods of the discreet optimization or the metaheurístics. In the attached work you can find a brief description of the needed system methodology and a diversity of tasks that are solved by a diversity of methods.
Jose Arzola
My current project: Procedural Content Generation (PCG). I think it is a good application.
You must decide what you consider a "solution" is; if you work with problem instances with known solutions you have a perfect criterion, but otherwise you need to pick some approximate stationarity condition, such that each algorithm and instance is judged in a fair way.
Also, in order to compare the convergence among several algorithms for the same problem instance database, you should utilize the excellent metric (the performance profile) provided in the paper by Dolan and Moré: 91: 201. doi:10.1007/s101070100263.
There are many applications can use the optimization approaches specially that relate with control the vibration
You can find some examples of real world problems on the publication about the CEC 2011 competition, available here on Researchgate: https://www.researchgate.net/publication/228574980_Problem_Definitions_and_Evaluation_Criteria_for_CEC_2011_Competition_on_Testing_Evolutionary_Algorithms_on_Real_World_Optimization_Problems
Article Problem Definitions and Evaluation Criteria for CEC 2011 Com...
Dear Javaid,
you choice will depend on the characteristics of your problem.
For example derivative-free methods like Nelder-Mead simplex method usually give good results when the number of unknowns is small (less than 10 in general).
On the other side, gradient based methods require the cost function to be differentiable. It is not clear this property is satisfied in your real world problem.
Meta-heuristics are perhaps more adapted but you will have to try different tuning of the method in order to compare the results of the different runs. You will not be sure to converge to a local optimum each time.
In addition in your case does efficiency mean "efficiency in converging to a local minimum" of does it mean "efficiency in converging to a low value of the cost function (not necessary a local optimum) in a short CPU time" ?
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