2individuals surviving from the previous generation Basic ConceptsSimulated Annealing Tabu SearchversusGenetic Algorithmsa single solution is carried over from one iteration to the nextpopulation based methodIndividuals (or members of population or chromosomes)individuals surviving from the previous generation+childrengeneration
3Fitness of an individual (a schedule) is measured by the value of the associated objective function RepresentationExample from scheduling problems:the order of jobs to be processed can be represented as a permutation: [1, 2, ... ,n]InitialisationHow to choose initial individuals?High-quality solutions obtained from another heuristic technique can help a genetic algorithm to find better solutions more quickly than it can from a random start.
4ReproductionCrossover: combine the sequence of operations on one machine in one parent schedule with a sequence of operations on another machine in another parent.Example 1. Ordinary crossover operator is not useful!Cut PointP1 = [ ]P2 = [ ]O1 = [ ]O2 = [ ]Example 2. Partially Mapped CrossoverCut Point 1Cut Point 2314255P1 = [ ]P2 = [ ]O1 = [ ]O2 = [ ]
5Example 3. Preserves the absolute positions of the jobs taken from P1 and the relative positions of those from P2Cut Point 1P1 = [ ]P2 = [ ]O1 = [ ]O2 = [ ]Example 4. Similar to Example 3 but with 2 crossover points.Cut Point 1Cut Point 2P1 = [ ]P2 = [ ]O1 = [ ]
6Mutation enables genetic algorithm to explore the search space Mutation enables genetic algorithm to explore the search space not reachable by the crossover operator.Adjacent pairwise interchange in the sequence[1,2, ... ,n][2,1, ... ,n]Exchange mutation: the interchange of two randomly chosen elements of the permutationShift mutation: the movement of a randomly chosen element a random number of places to the left or rightScramble sublist mutation: choose two points on the string in random and randomly permuting the elements between these two positions.
7SelectionRoulette wheel: the size of each slice corresponds to the fitness of the appropriate individual.slice for the 1st individualslice for the 2nd individualselected individual.Steps for the roulette wheel1. Sum the fitnesses of all the population members, TF2. Generate a random number m, between 0 and TF3. Return the first population member whose fitness added to the preceding population members is greater than or equal to m
8Tournament selection1. Randomly choose a group of T individuals from the population.2. Select the best one.How to guarantee that the best member of a population will survive?Elitist model: the best member of the current population is set to be a member of the next.
9AlgorithmStep 1.k=1Select N initial schedules S1,1 ,... , S1,N using some heuristicEvaluate each individual of the populationStep 2.Create new individuals by mating individuals in the current population using crossover and mutationDelete members of the existing population to make place for the new membersEvaluate the new members and insert them into the populationSk+1,1 ,... , Sk+1,NStep 3.k = k+1If stopping condition = true then return the best individual as the solution and STOPelse go to Step 2
10ExampleMetric: minimize total tardiness (tardiness of a job is the amount bywhich it exceeds its deadline)Population size: 3Selection: in each generation the single most fit individual reproduces using adjacent pairwise interchange chosen at random there are 4 possible children, each is chosen with probability 1/4 Duplication of children is permitted. Children can duplicate other members of the population.Initial population: random permutation sequences
11Generation 1IndividualCostSelected individual: with offspring 13245, cost 20Generation 2IndividualCostAverage fitness is improved, diversity is preservedSelected individual: with offspring 12354, cost 17Generation 3IndividualCostSelected individual: with offspring 12435, cost 11
12Generation 4IndividualCostSelected individual: 12435This is an optimal solution.Disadvantages of this algorithm:Since only the most fit member is allowed to reproduce (or be mutated) the same member will continue to reproduce unless replaced by a superior child.
13Practical considerations Population size: small population run the risk of seriously under-covering the solution space, while large populations will require computational resources. Empirical results suggest that population sizes around 30 are adequate in many cases, but are more common.Mutation is usually employed with a very low probability.