1. Gerstner Lab, CTU Prague 1Motivation Typically,  an evolutionary optimisation framework considers the EA to be used to evolve a population of candidate solutions to the problem at hand  candidate solution encodes a complete solution (a complete set of problem control parameters, a complete schedule in JSP, a complete tour for TSP, etc. Here,  EA does not handle the solved problem as a whole  EA is employed within the iterative optimisation framework  its role is to evolve the best modification of the current solution prototype in each iteration

2. Gerstner Lab, CTU Prague 2 Outline of POEMS algorithm generate(Prototype); repeat BestSequence  EA(Prototype); if(apply_to(BestSequence, Prototype) is_better_than Prototype); then Prototype  apply_to(BestSequence, Prototype); until(POEMS termination condition); return Prototype;

3. Gerstner Lab, CTU Prague 3 Implementation Issues Action Sequence Representation  linear chromosomes of maximal length MaxGenes  gene = (action_type, parameters)  noop void action with no effect on the prototype, regardless of the values of its parameters one or more noop actions allowed in a chromosome variable effective length of chromosomes Genetic Operators  Tournament selection  Crossover – generalised uniform  Mutation – action_type or parameters changed (1 gene per sequence) Evolutionary Model  Generational / Steady-state

4. Gerstner Lab, CTU Prague 4 Simple Generational EA initialize(OldPop); BestSequence  best_of(OldPop); repeat NewPop  BestSequence; // elitism repeat Parents  select(OldPop); Children  cross_over(Parents); mutate(Children); evaluate(Children); NewPop  Children; until(NewPop is completed); BestSequence = best_of(NewPop); switch(OldPop, NewPop); until(EA termination condition); return BestSequence;

5. Gerstner Lab, CTU Prague 5 Steady-state EA initialize(Population); repeat Parents  select(Population); Children  cross_over(Parents); mutate(Children); evaluate(Children); Replacement = find replacement(Population); Population[Replacement]  Child1; Replacement = find replacement(Population); Population[Replacement]  Child2; until(EA termination condition); BestSequence  best of(Population); return BestSequence;

6. Gerstner Lab, CTU Prague 6 Elementary Functions Binary String Optimisation Problems  invert(gene) … inverts the specified gene of the prototype  linkage independent Travelling Salesman Problem  move(city1, city2) moves city1 right after city2 in the tour  invert(city1, city2) inverts a subtour between city1 and city2  swap(city1, city2) swaps city1 and city2 Job Shop Scheduling Problem  …

7. Gerstner Lab, CTU Prague 7 Example of POEMS execution: TSP Initial tour 965.134after iteration 1after iteration 2after iteration 3 Final tour 824.8

8. Gerstner Lab, CTU Prague 8 Example of Evolved Solutions Initial prototype of length 4403Initial prototype of length 3655

9. Gerstner Lab, CTU Prague 9 Comparison with other Approaches POEMSE-RSOM citiesmeanstdevbestmeanstdevbestmeanstdevbest 100818.614.5786.1935.127.1884.1830.413.0811.7 2001132.916.21098.11406.154.61289.11155.412.41124.7 5001746.313.51718.02753.366.42666.61776.014.01751.2 10002523.015.02491.63799.691.43679.82533.012.02508.4 20003692.220.43655.15983.595.15875.83725.314.93695.6