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PSO and ASO Variants/Hybrids/Example Applications & Results. Lecture 12 of Biologically Inspired Computing. Purpose: Not just to show variants/etc … for these specific algorithms, but to indicate these as examples of typical ways in which
Lecture 12 of Biologically Inspired Computing
Not just to show variants/etc … for these specific algorithms,
but to indicate these as examples of typical ways in which
these and similar methods (especially EAs) are engineered,
combined, etc … in attempt to get the best performance possible
on a given problem.
Too often stuck in suboptimal areas
Much too slow progress – high risk/low reward
In EAs, it may seem sensible for mutation strength to start low, say at mS and gradually increase linearly, say to mF. (e.g. perhaps 1/L and 5/L). Given a limit of 1,000 generations, say, the rate will increase by a simply pre-calculated amount per generation.
But this is not really adapting to the current situation in the search process. It may be fine for some problems, but on others the population may converge at 100 generations, or it may still be very diverse at 1,000 generations, or (of course), the rates themselves may be very unsuitable for the problem.
So it is common to use `truly’ adaptive techniques that react to the current state of the population. The mutation rate may be based directly on measures of diversity in the current population, measures of success in the last few mutation events, and so on.
Distance between two individuals:
Hamming distance: no. of genes that are different
Euclidean distance: only suitable for …. ?
Permutations 1. ABCDEF and 2. EDFABC
are how different?
Edge-sets: 1. AB, BC, CD, DE, EF, FA
2. AB, BC, CE, ED, DF, FA
There are various ways to base a distance metric on edge sets
Distance metric for grouping problems?
Mean values and variances for each gene.
Mean distance between pairs of individuals
Population diversity measures applied to set of ants’ solution
Diversity measures for the amount of pheromome per linkures
Mutation strength =
(where D varies from 0 (all the same) to 1 (maximally different)
Or: a form of genewise mutation:
Prob of mutating gene rises as the variance of that gene in the population falls.
Or: Run EA as normal, but:
pop diversity > Dthresh: only use crossover
pop diversity < Dthresh – only use mutation.
Or: Run PSO as normal, but:
pop diversity < Dthresh: do one iteration where the particle velocities are randomly chosen, then move on.
A number of vehicles are at the depot. Each customer has to be visited precisely once. Each vehicle needs a route that takes it from the depot and back to the depot. What is the least cost
Several vehicles normally needed, since (e.g. visiting 3 or 4 customers may take the whole day, but all customers need to be serviced today. Also, vehicles have capacity constraints.
Reconnect in a different way (there is only one valid new way)
2-opt turns out to be an excellent mutation operator for the TSP
and similar problems.
The “2-opt heuristic” is an algorithm based on it. There are variants,
But it comes down to Hillclimbing for n trials, until no further
improvement its possible, using 2-opt as the mutation operator.
The main difference
Standard transition rule
Extra pheromone is laid by
the ant with best tour
AS (ant) is pretty near state of the art, with good run times.