Genetic Process Miner

This is an algorithm from the family of Genetic Algorithms for mining business processes

  • it's much more resilient to noise
  • allows for incremental improvement
  • can be combined with other approaches


Overview

gm-overview.png

  • first we create the initial population
  • at each step we compute fitness for all the instances of a population
  • elitism - process of keeping the best ones
  • then all "survived" instances are considered as "parents"
    • cross-over - process of combining different petri nets (these petri-nets are already good solutions)
    • mutation adding some random changes for diversifying


Cross-Over

Cross-over

  • a process of producing a "child" by two parental instances
  • selecting parents
    • completely at random
    • using fitness to quicker converge to optima
    • note that we should not always select only "the best" - we need diversity


How to create a petri net from two other petri nets?

  • suppose we have two parental petri nets:
  • gm-crossover-p.png
  • we may find some minimal cut, cut the parents and make children from then
    • minimal cut is the minimal number of transitions to remove s.t. the net becomes completely disconnected
    • the same as in the Graph Theory: Minimal Cut
  • in this example:
    • can cut in $(e, f)$ because in both cases
    • from $e$ it goes to $g,h$ and on the left you have $a,b,c,d$
    • so it's ideal
  • we take $(e, f)$ out and get two disconnected components
    • combine left and right parts of the petri nets to form children
  • gm-crossover-c.png


Mutation

Examples of mutations:

  • remove or add a place
  • add an arc


Parameters

So there are quite a few parameters that we have to provide:

  • objective function we want to optimize (below)
  • the way we do the cross-over
  • how do you select parents?
  • the way we do the mutations
  • elitism - top 10%, certain threshold, etc
  • how large the population should be
  • how many generations you'll run before termination
  • when we kill some instances?


Change one parameter

  • $\Rightarrow$ different solution in the end

Also

  • a lot of randomness is involved
  • it may be computationally expensive


Cost Function: Fitness

Trace Level Fitness

Define trace-level fitness as:

  • $\text{fitness}(\sigma, N) = \cfrac{1}{2} \left( 1 - \cfrac{m}{c} \right) + \cfrac{1}{2} \left( 1 - \cfrac{r}{p} \right)$
  • $m$ - # of missing tokens
  • $c$ - # of consumed tokens
  • $r$ - # of tokens left over when something reaches the output place
  • $p$ - # of produced tokens


Example 1

Consider this example:

  • gm-fit-ex1.png
  • logtrace: $\sigma_1 = \langle abeg \rangle$
  • $m = 0, c = 0, r = 0, p = 1$
    • $p = 1$ because there's a token in the input place
  • $a$ fires - it generates 2 tokens
    • $p \leftarrow p + 2 = 3$
    • $c \leftarrow c + 1 = 1$
  • $b$ fires, produces one token, consumes one token
    • $p \leftarrow p + 1 = 4$
    • $c \leftarrow c + 1 = 2$
  • $e$ needs to fire
    • but it cannot: one token is missing, so we add it and fire $e$
    • $p \leftarrow p + 1 = 5$
    • $c \leftarrow c + 2 = 4$
    • $m \leftarrow m + 1 = 1$
  • $g$ fires and we're done
    • $p \leftarrow p + 1 = 6$
    • $c \leftarrow c + 1 = 5$
  • but there's one remaining token that was left over after firing $a$
    • $r \leftarrow r + 1 = 1$
  • and finally we remove one token from the output place
    • $c \leftarrow c + 1 = 6$
  • $\text{fitness}(\sigma_1, N_1) = \cfrac{1}{2} \left( 1 - \cfrac{1}{6} \right) + \cfrac{1}{2} \left( 1 - \cfrac{1}{6} \right) = \cfrac{5}{6}$


Example 2

gm-fit-ex2.png

  • logtrace: $\sigma_2 = \langle adceh \rangle$
  • $p = 1, c = 0, m = 0, r = 0$
  • $a$ fires, produces 1, consumes 1
    • $p \leftarrow 2, c \leftarrow 1$
  • $d$ needs to fire
    • but there's no token in the place before $d$, so we need to put it there
    • $m \leftarrow 1$
    • $d$ fires: $p \leftarrow 3, c \leftarrow 2$
  • $c$ fires
    • $p \leftarrow 4, c \leftarrow 3$
    • note that $c$ and $d$ were executed in order different from the order that the model can produce
  • $e$ fires
    • $p \leftarrow 5, c \leftarrow 4$
  • $h$ fires
    • $p \leftarrow 6, c \leftarrow 5$
  • we're done
    • one token is left: $r \leftarrow 1$
    • taking the last token from $c$: $c \leftarrow 6$
  • $\text{fitness}(\sigma_2, N_2) = \cfrac{1}{2} \left( 1 - \cfrac{1}{6} \right) + \cfrac{1}{2} \left( 1 - \cfrac{1}{6} \right) = \cfrac{5}{6}$


Log Level Fitness

Log-level fitness is

  • fitness, calculated for each trace and aggregated
  • [math]\text{fitness}(L, N) = \cfrac{1}{2} \left( 1 - \cfrac{\sum_{\sigma \in L} L(\sigma) \times m_{N, \sigma}}{\sum_{\sigma \in L} L(\sigma) \times c_{N, \sigma} } \right) + \cfrac{1}{2} \left( 1 - \cfrac{\sum_{\sigma \in L} L(\sigma) \times r_{N, \sigma}}{\sum_{\sigma \in L} L(\sigma) \times p_{N, \sigma} } \right)[/math]
  • $L(\sigma)$ how many times the trace $\sigma$ occurred in log $L$


Links

Sources

Share your opinion