Manta Ray Foraging Optimization (MRFO) Algorithm Step-by-Step Explanatio...

Manta Ray Foraging Optimization (MRFO)

Manta ray foraging optimization (MRFO) is a new optimization approach for global optimization problems. The Manta ray optimization algorithm is developed by Zhao et al. (2020). Manta ray optimization algorithm is a bio-inspired optimization technique. Manta ray optimization algorithm is inspired by foraging strategies of manta rays. Manta ray optimization algorithm is used to solve optimization problems.

Manta Ray basic structure

Manta Ray foraging is often found in groups. Three main manta Rays Foraging Strategies: 

1. Chain Foraging
2. Cyclone Foraging
3. Somersault Foraging

Chain Foraging: More than 50 Manta Rays line up. One behind another. (the line is formed by Manta Rays). Manta Rays observe plankton’s position and swim towards it. Manta Rays form a foraging chain by line-up from head to tail. Assumed that BEST Solution is plankton with high concentration manta rays want to approach. In every generation, all individuals will update their position w.r.t. Solution in front of it and Best Solution Found. Mathematical Model for Manta Ray Chain foraging behavior:

Cyclone foraging: When plankton concentration is very high, Manta Rays gather together like a cyclone structure for foraging.  Manta rays form a long foraging chain and swim toward the target by spiral. Mathematical Model for Manta Ray Cyclone foraging behavior:

Somersault foraging: [Goal = Optimize Food Intake ]

When Manta-Ray finds out the food source they circle around the target (plankton). This strategy is random and contains cyclical movements. Each Individual swims to the new position. [position update is done around the best solution found]. Mathematical Model for Manta Ray CSomersault foraging behavior:

Manta Rays Optimization Algorithm Steps

Initialization Phase. Initialize the population size (N); Maximum Number of Iterations (MaxT); 2. Compute the fitness values for each search agent. 3. Find out current best solution in the population. 4. Check the stopping criteria (CurrentIteration ≤ MaximumIteration). 5. For i = 1: Population_Size if (rand < 0.5) { Perform Cyclone Foraging. } Else{ Chain Foraging } 6. Compute Fitness Values for each individual. 7. Select Current Best. 8. Perform Somersault foraging. 9. Compute the fitness values for each individual. 10. Select the Best Solution among all. End For 11. Return Best Solution.

Manta Ray Foraging Optimization (MRFO) Algorithm Example

Step 01: Initialize Population Size

Suppose, Population Size = 4;

Lower Bound = -10;

Upper Bound = 10;

Maximum Iteration = 4;

Suppose Initial Population

 1.1

 2

 0.9

 3

Step 02: Compute Fitness Value for each using fitness function.

Fitness Values

1.21

4

0.81

9

Step 03: Obtain Best Solution

Best solution = Minimum Fitness Value in the current population

Best Solution = 0.81

Step 04: Check Stopping Criteria

While (Current < Maximum Iteration)

 1 < 4   ((True) move to next step ) 

If stopping criteria is then stop and return the best cost.

Step 05: Update Position for each individual.

For i = 1 to PopulationSize

For i = 1:4

If (rand < 0.5) 

THEN Cyclone Foraging

Else

Chain Foraging

End if

Step 06: Compute Fitnee Value for Each individual and Select Best Individual.

Step 07: Perform Somersault Foraging. 

Step 08: Compute Fitness Value for Each.

End For

End While

Step 09: Return Best Solution Found.