Integers, random number generators

A second facility that is sometimes useful is the random number generator function. There are several possible distributions, but the most usual is the normal distribution. It is necessary to specify a mean and standard deviation. If one wants to be able to return to the distribution later, also specify a seed, which must be an integer number. Figure A. 15 illustrates the generation of 10 random numbers coming from a distribution of mean 0 and standard deviation 2.5 placed in cells A1 -A10 (note that the standard deviation is of the parent population and will not be exactly the same for a sample). This facility is very helpful in simulations and can be employed to study die effect of noise on a dataset. 

The command to activate the random number generator is RND (Expr%). The generator will generate an integer from 1 to Expr. For example,... 

The random selection in step (iii) is carried out by generating uniform random numbers U e [0, 1], For example, the index of a random particle selected from a set of N particles will be n = intup(//N) where intuP() rounds the argument up to the nearest integer. Note that for constant-density, statistically stationary flow, the effective flow rates will be constant. In this case, steps (i) and (ii) must be completed only once, and the MC simulation is advanced in time by repeating step (iii) and intra-cell processes. For variable-density flow, the mean density field ((p)) must be estimated from the notional particles and passed back to the FV code. In the FV code, the non-uniform density field is held constant when solving for the mean velocity field.15... 

The two-stage mixed-integer stochastic program with recourse that includes a total number of200 scenarios for each random parameter is considered in this section. All random parameters were assumed to follow a normal distribution and the scenarios for all random parameters were generated simultaneously. Therefore, the recourse variables account for the deviation from a given scenario as opposed to the deviation from a particular random number realization. 

Figure 8-5 Generating 10 random numbers from 1 to 1000 by use of a spreadsheet. The random number function in Excel [=RAND ) ] generates random numbers between 0 and 1. The multiplier shown in the documentation ensures that the numbers generated in column B will be between 1 and 1000. To obtain integer numbers, we use the Format/Cells. .. command on the menu bar, choose Number and then 0 decimal places. So that the numbers do not change with every recalculation, the random numbers in column B are copied and then pasted as values into column C using the Edit/Paste Special.

Step 1 Generate a random integer a> within a range of [1, /] (where / is the length of the chromosome) to determine the number of exchanges. 

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