Continuity Constraint in a Optimization Problem

I'm working on an optimization algorithm and I should insert a continuity constraint on a variable x to be optimized. In other words, I have some appliances and I have to match active/off periods. This is my optimization variable :

x = optimvar('x',8,24,'Type','integer','LowerBound',0,'UpperBound',1);

I have to try to write a constraint to keep appliances running consecutively. How can I do?

[Matt J]

What does "consecutively" mean in relation to the 8x24 structure of x?

Answer 1

[Alberto Chavez]

Sometimes it is better to write the functions and contraints by hand using a small scale problem, and then try to write your code so that you have a clear idea of what you need to do. What I believe you are trying to do is a scheduling constraint, so that if one appliance stops running the next takes over, correct?

In that case, it's not only one constraint, but a set of constraints. If you have 2 appliances for example:

appliance 1 : x11, x12

appliance 2: x21, x22

Variables xij , index "i" represents the appliance name, index "j" represents the order in which it is used.

constraint set 1:

x11+x12+x21+x22 = 2 (this set permits only 2 elements in the schedule)

constraint set 2:

x11+x12 = 1

x21+x22 = 1 (this set permits only one order for each appliance)

constraint set 3:

x11+x21 = 1

x12+x22 = 1 (this set permits only one appliance for each order)

Results:

If x11=1, then x12=0, x22=1, x21=0

this means that appliance 1 runs first and then appliance 2.

If x11=0, then x12=1, x22=0, x21=1

this means that appliance 1 runs second and appliance 2 runs first.

Is that helpful?

Edit:

the 2 indexes in xij can be transformed into one:

instead of x11, x12, x21, x22, it would be x1, x2, x3, x4