Sorry, and apologies in case my answer may sound a bit too tough : The idea "to convert a single objective optimization algorithm to a multi-objective one" only shows a lack of understanding of the essence of the multi-objective optimization. Indeed, it is just about as off the point, as trying, for instance, to convert in general partial differential equations into ordinary differential equations. Of course, one can from the start simplify grossly and brutally the multi-objective nature of the given problem, and reduce it to one single objective. However, the real and truly valuable practical issue is to avoid that, and instead, to keep the multi-objective situation alive all the time, that is, throughout the whole process of solving of the optimization problem. Now, since the late 1970s, it is known that in a multi-objective context, the role of preference type information is fast diminishing with the increase in the number of objectives. Therefore, instead of preference type information, one is obliged to use other information, such as for instance, indifference information, that is, to what extent one is indifferent between two possible outcomes. Details in this regard can be found, for instance, at arxiv:math/0506619
This forum in RG may help you.
https://www.researchgate.net/post/What_are_the_recently_invented_Evolutionary_algorithms_EAs_Optimization_method_Which_method_you_found_en_effective_method
There is not a "better" multi objective metaheuristic. It depends. With regard to Genetic Algorithms, we can highlight SPEA II, NSGA II and PESA II. There are advances in other multiobjective metaheuristics like GRASP, PSO, ACO, etc.
This is a very good paper:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.9986
As Bruno said, there is not a "better" meta-heuristic. It depends on the problem to be treated. But referring to the latest publications, The swarm intelligent algorithms are nowadays the best in performance and execution time and specially MOPSO and there different variants.
MULTIMOORA is
1) recent.
2) very simple, high school math + EXCEL, see also Brauers about Chakrovarty
3) treated matrices up to 600 elements, the only method which can do that
SEE contributions Brauers
statement (3) is incorrect - there are published methods that handle tens of thousands of dimensions - look up BORG and its derivatives
Colleague Landauer is incorrect. He considers matrices composed of elements expressed in the same unit, originally or after normalizatioon. THIS IS NOT THE POINT HERE.. Here Matrices are composed of columns all expressed in different units like €, kg, Pollution elements, surfaces, educatiion etc. with a final solution proposed.
Sorry, and apologies in case my answer may sound a bit too tough : The idea "to convert a single objective optimization algorithm to a multi-objective one" only shows a lack of understanding of the essence of the multi-objective optimization. Indeed, it is just about as off the point, as trying, for instance, to convert in general partial differential equations into ordinary differential equations. Of course, one can from the start simplify grossly and brutally the multi-objective nature of the given problem, and reduce it to one single objective. However, the real and truly valuable practical issue is to avoid that, and instead, to keep the multi-objective situation alive all the time, that is, throughout the whole process of solving of the optimization problem. Now, since the late 1970s, it is known that in a multi-objective context, the role of preference type information is fast diminishing with the increase in the number of objectives. Therefore, instead of preference type information, one is obliged to use other information, such as for instance, indifference information, that is, to what extent one is indifferent between two possible outcomes. Details in this regard can be found, for instance, at arxiv:math/0506619
We can not say which algorithm is best. Every algorithm has own advantages and disadvantages. Only way to judge is to solve the same problem with different multi-objective optimization algorithm. Try cuckoo search with levy fight. Levy flight is nothing but adopting Levy distribution for random walk to improve the exploration and exploitation for searching optimum solution in a solution space.
It is realy depends on the application and the problems you are solving. In the filed of engineering with the aid of design of experiments (DOE) and response surface modeling (RSM) and finally genetic algorithms (GA) you may consider a large variety of problems.
I was not considering dimensions as all having the same units or underlying mathematical space
up till now MULIMOORA is the best. Why?
- does not need normalization unlike all the methods with weights
- is composed of 3 independent approaches each controlling each other
Chakraborty already proved that MOORA (= 2 methods is superior to the other most used methods (see attachment TRANSFORMATIONS IN BUSSINESS AND ECONOMICS, Vilnius p.109) and since then MOORA was supplemented with a 3rd method: the Full Mulltiplicative Form, the assembly of 3 methods under the name of MULTIMOORA.
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