I am using a stochastic optimization algorithm to find the optimal size of hybrid renewable energy system based on Total Net Present Cost of the system. Details of Optimization Problem are as follows:

Objective Function: TNPC[$]: f(Number of components)=f(N_pv N_bat N_inv)

Lower Bound: [1 1 1] Upper Bound: [700 200 2]

Constraints:

1. System size is within allowed min. and max. system size.

2. Battery SOC remains within allowed limit

3. Renewable Energy Fraction greater than set limit.

4. System reliability Constraint 1

5. System reliability Constraint 2

Due to stochastic nature, the optimization algorithms tend to vary the results with different runs. So, I am running the Algorithm for about 30 runs under exactly same conditions and out of those 30 times only for 1-5 runs the algorithm provides the expected results. For the remaining runs, it end up with lower limit as optimal value (which in reality does not even satisfy all the constraints) and the optimal objective function value it comes up with is including the penalty value(that is associated with constraint violation). Now, I want to ask:

• Why that might be happening?
• What to do to mitigate it?
• Is it acceptable behavior?

What I have tried and found:

• Varying the number of iterations or Search Agents seems to have increased the number of runs for which the algorithm end up with lower bound values as optimal values or distinctly different values as optimal.
• I tested different Algorithms, same happens with everyone of them.

I am attaching an image showcasing the results for one such Algorithm. Also, I know for a fact there exists a system combination which is low cost and satisfy all the constraints. Another question, not directly related to the first question is:

• How should I decide the upper bounds of the decision variables in this case of energy system sizing? Should it be based on Load or on Area or constraints in problem or something else?

Thank You