Genetic Algorithms

 

 

 

 

1) Let us assume that we have a problem we want to solve in which we encode chromosomes with sequences of 8 binary bits. The fitness function values are calculated as the number of zeros (‘0’) in each chromosome. The current population consists of the following chromosomes 11001101, 11100110, 10101100, 00110111, 10100100, 10001101. The roulette wheel selection method is used. Construct this roulette (probabilities of selection for each individual).

 

2) Let us assume that we want to develop a genetic algorithm which solves the following problem:

Find 4 numbers between 0 and 255 whose binary representation includes an equal number of zeros and ones.

i) How you would encode the chromosomes and what fitness function would you define for this problem?

ii) Describe the selection, crossover and mutation steps involved in the first iteration of the algorithm using an initial population of 4 chromosomes.

 

3) Describe a problem from your work environment or your everyday environment, which you think that could be solved efficiently using genetic algorithms(max 2 paragraphs).

 

Sample Solution

 

to resist being ‘bought-off’ by a dictator. Emerging middle classes therefore diminish the extent to which non-democratic leaders can bribe their winning coalition with private goods, as the prospect of doing so becomes increasingly expensive as the size and wealth of the middle classes grow as a result of development, while the loyalty norm weakens too.
We may also see a rise in post-materialist values as the population becomes wealthier, since “after a period of sharply rising economic and physical security, one would expect to find substantial differences [in] value priorities, […] for example, post-materialists […] are markedly more tolerant of homosexuality”[6]. This could erode the extent to which the population would be morally willing to accept such bribes, regardless of magnitude. Subsequently, economic development might lead to the demise of such a regime.
An additional economic explanation could be the ‘resource curse’, which suggests that countries “with abundant reserves of non-renewable mineral resources, such as Nigerian oil [and] DRC gold […] produce less diversified and less competitive economies, more income inequality [and] heightened danger of state capture and rent-seeking by ruling elites”[25]. This is because the revenue streams in these countries are so concentrated to the elites and ruling classes, providing only menial low-paid labour to politically-insignificant lower classes. Moreover, since they are primary-product-export dependent, manufacturing industries develop overseas where economies of scales are subsequently built; diminishing the ability of local entrepreneurs to set up competing businesses and increase their wealth. The likelihood of a democratic transition is therefore low, since “democracy is expected to increase redistribution and reduce inequality”[26]; something which is not in the interest of the elite ruling classes.
Moreover, economic crises can have a large role to play in mobilising a population against the elites and causing the fall of a non-democratic government. Although the elites do have “the monopoly over large scale violence, […] states in crisis can […] slide […] into even more instability”[7], particularly if a popular revolution is supported by a large proportion of the population, or, as in the case of Syria, the “improving […] economic conditions of the large Syrian refugee communities in neighbouring countries [provide] economic alternatives to joining armed groups”[8]; decreasing the state’s military stronghold over its population.
It is certain, however, that the likelihood of the collapse of a non-democratic regime as a result of an economic shock depends on its depth and severity, and the degree to which there is the resulting loss in welfare incentivising the population to mobilise. Furthermore, if the state is able to reallocate resources effectively des

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