Want to optimize Genetic algorithm ( GA ) goal with three different objectives of final response variables (Y1 maximize, Y2 minimized)

Introduction

Here polynomial regression equations Y1, Y2 and Y3 (Final response) depends upon different levels of X1, X2 and X3 (independent variables). While a, b, c.....p,q,r are some fixed numerical values.

Problem:

Y1 = aX1+bX2+cX3+dX1.X2+eX2.X3+fX3.X4;

Y2 = gX1+hX2+iX3+jX1.X2+kX2.X3+lX3.X4;

Y3 = mX1+nX2+oX3+pX1.X2+qX2.X3+rX3.X4;

Goal:

Furthermore, Y1 is desired performance hence its maximization would be preferred. While, Y3 is undesired performance so there minimum level will be more beneficial. And Y2 (another desired performance but not of much importance so even there moderate level may be ok.

My aim to find one or more possible solutions of X1, X2 and X3 which fulfill above-mentioned goal using genetic algorithm . Perhaps this come under multiobjective goal but I dont have any solution to put a syntax (code) with an aim of Y1, Y2 and Y3 as mentioned above.

Kindly assist me.

A video was posted by one of the user on youtube for similar issue but still its not a solution. click below to understand what my aim are.

<<Click here for Youtube video link for multiobjective optimization of goal by Genetic algorithm using Matlab >>

Below are the snapshot (image) of first page of a youtube showing multiobjective optimization goals (for quick understanding nature of problem)

Answer 1

[Greg Heath]

 Use the solutions for

   1. max(Y1)
   2. min(Y2)

to determine a and the starting point (X10,X20,X30) for

   3. max( Y1 - a*Y2 )

Hope this helps.

Thank you for formally accepting my answer

Greg