+ front: the file contains class Metric for evaluating all posible solution (population of obtained fronts).
+ pfront (Pareto front): the file contains class Metric for evaluating the obtained front from each test case.
+ tpfront: (True pareto front): the file contains class Metric for evaluating the obtained front and True pareto front
 (Reference front). Means, you need to pass the Reference front in this class.

+ True pareto front (Reference front) can be obtained by:
    1) You provide it (If you know the True Pareto front for your problem)
    2) Calculate from all possible fronts obtained from all test case.
        + Assumption you have N1 algorithms to test. 
        + Each algorithm give you a Obtained front. 
        + Each algorithm you run N2 independent trials --> Number of all possible fronts: N1 * N2 
        + Pass all N1*N2 front in our function to calculate the Non-donminated Solutions (Reference front
 - Approximate Pareto front - True Pareto front)


import pfevaluator

## Some avaiable performance metrics for evaluate each type of Pareto front.
pfront_metrics = ["UD", "NDC"]
tpfront_metrics = ["ER", "ONVG", "MS", "GD", "IDG", "MPFE", "S", "STE"]
volume_metrics = ["HV", "HAR"]

pm = pfevaluator.metric_pfront(obtained_front, pfront_metrics)              # Evaluate for each algorithm in each trial
tm = pfevaluator.metric_tpfront(obtained_front, reference_front, tpfront_metrics)        # Same above
vm = pfevaluator.metric_volume(obtained_front, reference_front, volume_metrics, None, all_fronts=matrix_fitness)

## obtained_front: is your front you found in each test case (each trial of each algorithm)
## reference_front (True Pareto front): is your True Pareto front of your problem.
##      If you don't know your True Pareto front, do the above step to get it from population of obtained fronts.
##      Using this function: reference_front = pfevaluator.find_reference_front(matrix_fitness)
##          matrix_fitness is all of your fronts in all test cases.

## The results is dict such as:     pm = { "UD": 0.2, "NDC": 0.1 } 

@article{nguyen2019efficient,
  title={Efficient Time-Series Forecasting Using Neural Network and Opposition-Based Coral Reefs Optimization},
  author={Nguyen, Thieu and Nguyen, Tu and Nguyen, Binh Minh and Nguyen, Giang},
  journal={International Journal of Computational Intelligence Systems},
  volume={12},
  number={2},
  pages={1144--1161},
  year={2019},
  publisher={Atlantis Press}
}