The floor Plan Optimization problem has two conflicting objectives: Area of the Laboratory (Maximizing function) and Cost of designing the workspace (Minimizing function). To solve this, we need to use a multi-objective decision-making method: Non-Dominated Sorting Genetic Algorithm.
Number of particles chosen = 10 Maximum Iterations = 30 The new Chemistry Workspace has 3 rooms - laboratory, equipment room, and sitting/meeting room.
According to the constraints given in the question, ● Laboratory: 10 <= x <= 15, 10 <= 25-y <= 18
● Sitting/Meeting room: length=25, 10 <= x <= 15
● Equipment Room: 10 <= 25-x <=15, 7 <= y <=15
Particles Size (10 x 8) - where 10 is the number of particles and 8 is the number of columns containing binary digits to represent 2 integer numbers from 0 to 15 for x & y. (Could have increased the number of binary digits to represent decimal numbers for x & y).
Methodology:
- Initialize all the 10 particles (x,y) in the ‘pop’ matrix.
- Decipher the integer values for x and y, then the functional values (area, cost), and put them in the matrix in columns 9, 10, 11, and 12 respectively.
- Determine their ranks using Non-Dominated Sorting and put it as column ‘13’.
- Sort the ‘pop’ matrix with respect to the 13th column containing the ranks.
- Now, we need to select 8 parents (Crossover Probability = 0.8) for the Crossover operation. Before that, we need to find whether we require to sort the particles within a rank.
- If yes, then, use the crowding distance method to sort the particles within a rank and put it in the main matrix.
- Select the top 8 particles randomly for crossover operation and generate 8 children.
- Determine the functional values for all these 8 children, assign all the 18 particles proper ranks, and sort the matrix with respect to these ranks.
- Now, select the top 10 particles after employing crowding distance to sort the particles within a rank.
- Repeat this process.
Video Link: https://youtu.be/VeRFErNBmdE
The video shared shows different Pareto Fronts or set of optimal solutions with increasing iterations in multi-objective optimization problems stands for a set of solutions that are non-dominated to each other but are superior to the rest of the solutions in the search space. In the end, we obtain a straight line that conveys the information of the sheer trade-off between the two objective functions.