Effect of GA Parameters on Convergence

Dear MATLAB Community,

I am working on a genetic algorithm (GA)–based optimization problem and would appreciate your insights.

In my model, the GA optimizes the x and y coordinates of a set of knots. These knots are then connected using NURBS to compute cross-sectional information. The number of decision variables is therefore 2N, where N is the number of knots.

The key GA parameters in my study are:

• Number of knots (N)
• Population size, defined as PopulationSize = PopulationMultiplier×N
• EliteCount
• CrossoverFraction

For example, when N=10 and the population multiplier is 200, the population size is 2000, which I believe is reasonable for a 20-variable problem.

My main objective is to understand how to select appropriate values for EliteCount, PopulationSize, and CrossoverFraction as the number of knots changes. However, when I analyze and plot the results, I do not observe a clear trend.

Intuitively, I expect that increasing the population size should allow the GA to better explore the search space and approach the global optimum more reliably. However, in some cases, increasing the population size results in very irregular or “weird” shapes in the optimized geometry.

I tested the following combinations:

%%% OPTIMIZATION DESIGN SPACE
NumberOfKnotsArray =[6 8 10]; 
%%% GA PARAMETERS
PopMultipArray = [200 400 800];
EliteCountArray = [0 5 10];
CrossoverFractionArray = [0 0.4 0.8];

As an example, one configuration is:

• N=6
• PopulationMultiplier = 200
• EliteCount = 0
• CrossoverFraction = 0

Based on my observations so far:

• For small numbers of knots (e.g., N=4,5,6), changing GA parameters does not significantly affect the results; the algorithm seems robust enough in this regime.
• As N increases, the behavior becomes less predictable, and no clear trend emerges with respect to GA parameter changes.

In my plots, the pink region represents the design space. The first and last knots are allowed to lie outside this space.

I would appreciate feedback on the following questions:

1. Why might increasing the population size lead to unexpected or irregular solutions?
2. Is it possible to identify a reasonably “global” GA parameter combination that works well across a wide range of knot numbers (at least up to some limit)?
3. Is the assumption that a higher population size generally leads to better convergence to the global optimum or more reproducible results incorrect?
4. Are there other important effects or interactions among these parameters that I should be considering?

Any comments, suggestions, or references would be greatly appreciated.

Thank you for your time and help.

Here is the expected result

Here are the GA results for different parameter combinations:

Answer 1

[Matt J]

You need to look at the final fval achieved as a function of N. If the irregular solutions have a lower fval than the regular solutions, it will support your intuition tha larger N gives better minimization performance. It would then suggest that ga is doing its job properly, but that there is a problem with your fitness function.