Multi-objective optimization problem: evolutionary algorithms.


Multi-objective optimization problem: evolutionary algorithms.

Multi-objective Optimization problem

The multi-objective problems include multiple objective functions which are either maximized or minimized. Certain constraints are associated with every optimization problem irrespective of being single or multiple objective and these constraints are to be satisfied by any feasible solution. The general formula for multi-objective problem is stated in:



π‘šπ‘šπ‘šπ‘šπ‘šπ‘š/ min π‘“π‘“π‘šπ‘š,=1,2,3,..,π‘šπ‘š;

Subject to, 𝑔𝑔𝑖𝑖 ≥0,=1,2,3,…,𝐽𝐽 ; β„Žπ‘˜π‘˜

≥0,=1,2,3,…,𝐾𝐾; π‘₯π‘₯𝑖𝑖

𝐿𝐿 ≤ π‘₯π‘₯𝑖𝑖 ≤ π‘₯π‘₯𝑖𝑖

π‘ˆπ‘ˆ, 𝑖𝑖 = 1,2,3, … , 𝑛𝑛.








Evolutionary Algorithm

In 1960 EAs was approached. Evolutionary Algorithm can be applied for population in a surrounding with limited resources. Since it is based on the concept of survival of the fittest, the individuals compete for these resources and the ones which better adapt to the environment are the fitter candidates. These fit individuals are considered for producing the new generation through mutation and crossover. These new individuals are then evaluated and Considered as possible solutions. Evolutionary algorithm mainly stochastic and population based algorithms which involves variation parameters namely crossover and mutation through which diversity is created within and among the individuals.

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International journal of swarm intelligence and evolutionary computation