I am trying to optimize the design of some object with minimizing the operation energy and discomfort hours as objective function. But the used software only solve one-objective problem, so I have to use a global objective function with weight factors.
f(x)= A(OE) + B(PPD)
where OE is the operation energy, PPD is discomfort index, A and B are the weight factor, respectively (A+B=1)
You are perhaps lucky that there are only two objectives! :-)
If I were you I would discretize the interval [0,1] in as many points that you can handle, and then provide these as weights to the first objective the parameter value p, for the first objective, and 1-p for the other. Solve the one-objective problem for each of the weights, and then plot them in 2D. Check how the two objectives behave within this interval, and pick one that looks reasonable. What reasonable means is not an exact science, but you probably want one where the two objectives do not lie near an area with large fluctuations. Good luck!
In such cases, I set the weights based on the relative importance and criticality of the achievement of each objective. The objective of a higher relative importance is given a higher weight and vice-versa, such that the sum of all the weights should be one.
I have spent rather a lot talking with scientists about bi-objective or multi-objective problems and methods, and it's clear that there are plenty of mistakes that one can make. It's not enough to provide a lot of Pareto-optimal points; you must also allow the decision-maker to arrive at one of the Pareto points that are the most natural for her, and that may need to take time - hence do not rush through the procedure. Looking not only at the Pareto frontier, you may want to provide additional quantitative measures based on the utilization of resources as well, and you can do that by adding resource utilization as an extra objective, or just look at the resource utilization "on the side" - like an extra constraint. Because this is partly a subjective business, you need to allow the process to be slow, and to allow the decision-maker to back off and start over - as there is a lot of information to process - and to repeatedly look at all resources, profit, capacity, or whatever it is that are of interest. It's to some degree an exact science, but we all know that we are *not* always objective as we handle new information.
Hi brother
you can use excel solver to optimize any complex or simple problem as your function, please see the next examples;
https://www.youtube.com/watch?v=K4QkLA3sT1o
https://www.youtube.com/watch?v=wpbDB5JNy50
https://www.youtube.com/watch?v=6xa1x_Iqjzg
The objective function to be optimized contains many terms. Each term is multiplied by a weighting factor between (0 and 1). Based on the importance of each term the weighting factor is defined.
for example if j=w1*f1+w2*f2
the objective function j contains two terms f1 and f2,
based on the importance of the two terms w1 and w2 are assumed
If f1 and f2 are with the same importance so w1=w2=0.5
If f1 is more important w1=0.7 to 0.9 and w2 0.3 to 0.1 as an example
Assigning weights is one of obvious approaches, but I have a doubt here:
f(x)= A(OE) + B(PPD)
where OE is the operation energy, PPD is discomfort index,
What about units? Energy is measured in joules (or something like this), I guess and discomfort index is probably unitless. Does adding a value in joules to a no-unit value make sense? Shouldn't both OE and PPD be normalized to unitless [0,1] interval/range?
Assign weights based on the relative importance. try several weights and plot pareto.
You can use some multi-attribute decision-making techniques such as AHP, Best and Worst Method or you can use some simple but effective weight assigning methods like Rank Order Centroid Method, Ratio Method, Rank Sum Method, and so on to accomplish your task.
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