Matlab Linear programming; how to minmize maximum of decision variable?

I am trying to minimize and objective function. It is a multiobjective function using weighted sum option. One of the objectives is to minimize the maximum of the decision variable. However, the maximum of decision variable is not know prior and i cannot use the 'max(decisionvariable)' command in optimization tool box. I am using Problem-Based Optimization tool box, so is there a way to replace the xommand to find maximum of decision variable? Problem Description: I have energy consumption data for 24 hours. I want to reduce the peak of the load after shifting the load to different times. Its also known as peak to average ration minimization. I need to minimize the peak of load after shifting bu i cannot include 'max' or 'mean' in the objective function. My variables are load values 'L' 1*48 matrix (half hourly energy records), Price 'P' again 48 values. I want to minimize the cost of energy consumed during 24 hours which is cost=L*P and i want to achieve this with minimum peak value of the L.

[Matt J]

We need to see a full mathematical description of the problem in equation form. It's not even clear how this is a linear program if you are seeking a min-max objective.

[zafar khan]

I have energy consumption data for 24 hours. I want to reduce the peak of the load after shifting the load to different times. Its also known as peak to average ration minimization. I need to minimize the peak of load after shifting bu i cannot include 'max' or 'mean' in the objective function.

[Matt J]

Again, we need to see a description in equation form.... What are the decision variables? How does peak load depend on them? What are the constraints?

[Torsten]

You might be able to replace the maximum of n variables x1,x2,...,xn by a new variable "M" which is linked to x1,x2,...,xn by the constraints

x1 <= M
x2 <= M
...
xn <= M

Best wishes

Torsten.

[zafar khan]

My variables are load values 'L' 1*48 matrix (half hourly energy records), Price 'P' again 48 values. I want to minimize the cost of energy consumed during 24 hours which is cost=L*P and i want to achieve this with minimum peak value of the L.

Answer 1

[Steven Lord]

Consider the fminimax function in Optimization Toolbox.

[zafar khan]

I am using problem-based optimization and am unable to find a way to implement this fminmax in that.

[Matt J]

Problem-based optimization is not appropriate for your situation. It is for single-objective linear programming only. You appear to have two objectives ( namely you are minimizing both P*L and max(L) ), one of which is non-linear.

Answer 2

[Matt J]

You might wish to look at Performing a Multiobjective Optimization Using the Genetic Algorithm