Application of Genetic Algorithm in Multi-objective Optimization

Here, is the value of individual i and is the size of the population. Before this fitness
assignment, the objective function goes through a linear transformation using the following
equation:
Here, the sign of , the scaling factor, depends on the optimization type, if it is maximization
problem, will be positive, and vice versa. The combination of this scaling and fitness assignment
ensures rapid convergence to the optimal results. Another approach to transforming the objective
function is power law scaling, mathematically:
Here, k is the problem dependent variable and can be changed to control the range of fitness
measures if required. Baker [27] suggested a rank based approach to prevent premature convergence,
where instead of using raw performance, the rank of individuals in the population is used to measure
relative fitness.
2.3.1.3. Selection:
Selection is the determination process of how many times a particular individual will participate in
reproduction. It comprises of two processes. In the first process, the raw fitness values are
converted into a real-valued expectation of an individual’s probability to be chosen for reproduction.
The second process, also known as “sampling”, selects an individual probabilistically for
reproduction based on its fitness relative to other individuals. The performance of the selection
algorithm can be determined by using three measures which are bias, spread, and efficiency. The
absolute difference between the actual and expected probability of an individual for getting selected
is defined as bias. Spread can be defined as the range of the possible number of times in which the
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