Selection of variables for sensitivity analysis study

I have a meeting in about 2 hours with my adviser and intent to have all variables selected for my journal article.

Within GenOpt (http://gundog.lbl.gov/GO/) the algorithm being used for optimization is the Generalized Pattern Search Particle Swarm Optimization (GPSPSO) Algorithm. This algorithm has been selected for is ability to optimize both discrete and continuous variables.

The PSO algorithm contains several control variables that need to be set. Neighborhood topology describes the way that the particles are able to communicate with each other in regards to the social component to the particle position vector (described fully in my thesis). For this I use the VonNeumann topology as it has been found to be the best in previous research. What I intend to to is investigate the effects of the three control methods and level of control on the time and value of optimization.

The three control methods include:

1. Inertial weight (Eberhart and Shi) - Requires an initial inertial weight (w_0) and a final inertial weight (w_1). The suggested values from the GenOpt manual are w_0=1.2 and w_1=0 based on Parsopoulos and Vrahatis work.
2. Constriction Coefficient (Clerc and Kennedy) - Requires a velocity clamping (k) coefficient which is applied to both the social and cognitive terms of the PSO algorithm as well as cognitive (c_1) and social (c_2) acceleration coefficients. Based on the work of Carlisle and Dozier, they found that the best values for these variables were to have no velocity clamping (k=1) and to have c_1=2.8 and c_2=1.3.
3. The final method of control is through a mesh. For this control method, a mesh size divider and an initial mesh size exponent need to be specified. Wetter suggests that, "Good numerical results have been obtained by selecting s ∈ Rnc and r, s ∈ N such that about 50 to 100 mesh points are located along each coordinate direction." Not too sure what that means.

What I might suggest to Prof. Horton is that I select one of these control methods to investigate as the design space starts to become too large otherwise (possible combination of variables needs to stay small when the simulation takes two days each on a twelve core machine... The constriction coefficient method was used for my research as it is supposed to provide the best control for discrete variables which I am dealing with entirely in the optimization of homes.

If I am to do the constriction coefficient method only, I would leave k=1 as this term is multiplied by both the acceleration factors, so the variance in those two can be captured by changing them independently. To capture a broad design space with limited iterations I might do an doubling type method with the starting suggested acceleration factors. If I do this and go two below and above the suggested factors, that gives 5 cognitive and 5 social variables giving 25 possible combinations. Even with overlapping simulations, this is nearly a month of computation before I can start the second paper. This makes me think of two issues/assumptions that need to be addressed.

• First, the very nature of this is that there is randomization in the optimization . There is nothing to say that the best combination of acceleration factors one time won't be different the next time.
• I could simplify the building optimization, but this defeats the purpose of having developed a complex building LCCA optimization tool.

What am I trying to optimize in this case? I think the objective functions of my optimization are to note the number of iterations before finding an optimal value and the value of that optimum as compared to other data runs. What do I count as finding the optimal value? many times the optimization gets very close to finding an optimum and then searches around tat value for a long time. The graph tends to look like an inverse relationship curve in most cases. I could look at time to get within x% of the optimum value found or simply look at the optimum value found. I think the best bet might be to wait until I get the data and then go based off of that.

Another idea could be to do 3 social, 3 acceleration, and then 3 numbers of particles. which would be 27 combinations.

Stuff to think about I guess.