# gamultiobj(): what are Fitness, Score and Rank?

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e_frog il 14 Dic 2021
Risposto: Jaynik il 1 Mar 2024
Hi, I need some help understanding the differences between the fitness, score and rank of individuals in the genetic algorithm. How do those three aspects get calculated for each individual? The documentation seems to be a little bit vague on that (or maybe I just don’t understand it correctly...). Thanks in advance!
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### Risposte (1)

Jaynik il 1 Mar 2024
Hi,
Based on the documentation and the references present at the end, fitness refers to the raw values of the objective functions for each individual in the population that is the value of the fitness function for all the solutions in the result matrix. In multi-objective optimization, each individual has multiple objective function values, one for each objective. The fitness values are used to determine how well an individual performs relative to the optimization goals.
The scores returned by the "gamultiobj" function are values of the fitness functions evaluated at each member of the population. If you have 'n' members in your population and 'nf' fitness functions, you’ll get an 'n-by-nf' array of scores. Each row represents a member of the population, and each column represents a fitness function. If there are nonlinear constraints, and a member of the population does not satisfy these constraints, then the scores for that member are set to 'Inf', indicating that it is infeasible.
Rank is a measure of performance based on Pareto dominance, where individuals are sorted into ranks based on whether they are dominated by other individuals in the population. Rank 1 individuals are not dominated by any others, and higher ranks are assigned to individuals that are dominated by those with lower ranks. Lower ranks are preferable as they indicate a better position with respect to the Pareto front.
You can refer to this link to understand the algorithm used:
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