CA2 Evolutionary Computation

Posted 2023-04-24 yegwy88

CA2 Continuous Assignment - Evolutionary Computation 2022

1. Average and maximum path length of graphs.

(a) Calculate the average pathlength of the following graphs (with N vertices): line, ring, star, fully connected graph. Show all your reasoning. (You may restrict to odd or even N where convenient.) Marks: 2

(b) Identify which of these scale with N as O(1),O(N),O(N2). Use mathematical definition of the large O notation. Marks: 1

(c) State the diameter (maximal path length) of the above graphs (a hand-written sketch of a largest path is acceptable). Marks: 1

2. Use the adjacency matrix (or the link list) to represent graphs G with N nodes, and implement (and test, e.g. on examples from above) the following operations: Marks: 3

(a) Calculate the average path length =: f1(G)

(b) Calculate the diameter (maximal path length) =: f2(G) (c1) Calculate total number of links =: f3(G)

(c2) Check that G is connected

You may use libraries, but would need to demonstrate their correct working, e.g., on one connected and one not connected graph, for question (c2).

3. Network Mutation Operators. Implement the following operations: Marks: 3

(a) Add a link at a randomly chosen position (between two randomly chosen links). You will need to check the link was absent before, and eventually handle the case of a fully connected graph.

(b) Remove a randomly chosen link, provided that the graph stays connected.

(c) Random rewiring (a combination of above)

4. Evolutionary Algorithm:

(a) Implement an evolutionary agorithm that uses (with probabilities p1, p2, p3 = 1 ? p1 ?p2) the above mutation operators, using some fitness function(s) to be specified. Marks: 2

(b) Test the algorithm on maximizing f2(G) ? f1(G), i.e., finding a graph (of fixed size N) with largest difference between maximal and average path length. Choose a graph size 7 ≤ N ≤ 20 and display the graph (and f1, f2, f2 ? f1) for the three best graphs.

Marks: 2

(c) Comment on your results: were they as expected, and why? Marks: 1

5. From single to multiobjective optimization: Transportation networks. We assume dis- tances (travel times, costs) of each link to be equal and of value 1. Further, we assume revenue from tickets is independent of distance (or no revenue, if public transport is free). Further:

Assume transportation costs are per link, then the total cost is proportional to f1.

Assume network maintenance costs are proportional to the total number of links f3.

Assume complaint+refund cost sare proportional to the maximal path length f2.

(a) Use a linearly weighted fitness a1f1 + a2f2 + a3f3 =: fw and mimimize fw for three qualitatively different choices of the weights.

Display your results in a meaningful way and comment on your results. Marks: 3

(b) Implement a multiobjective evolutionary algorithm (of your choice), and aim at minimizing each of the three costs.

Display the 10 best solutions, projected on the (f1, f2), (f1, f3), (f2, f3) planes, and a table of their f1, f2, f3 values. Marks: 5

6. Challenge question (choose one of the following) Marks: 2

(a) The resulting networks may be unrealistic due to oversimplified assumptions. Try to define and optimize a modified fitness function and discuss your results.

(b) Calculate (and try to sketch / plot as a function of p) the expected values of f1, f2, f3, fw for a (N, p) random graph (you may use and properly cite results from the literature). Comment on the shape or fw(p) and what we learn from this about our problem.

Please submit on Canvas:

A self-contained report (pdf) with all results and comments / discussion (Note: you may prefer to include a scan of a handwritten solution of question 1).

A separage appendix file containing all of your code in a text file (txt, doc,, docx, or pdf).

A zip, tar or tgz or tar.gz file of your code (program text files preferred over notebook

files).

You may use matlab, java, c/c++, python or other common languages, but should include instructions to run the code or any other documention where appropriate. (In rare cases, you may be asked to demonstrate working of your code online.)

Overall 25 marks. - Late penalty: 5% per working day (for each of up to 5 working days).

 WX：codehelp

What is Evolutionary Rescue？

 

Basic concepts in evolutionary biology provide the framework for addressing this issue.One such concept is that of ‘evolutionary rescue’ (ER).

It describes the capacity of populations to survive rapid environmental change by evolving adaptations that allow survival in the new environment and restore positive population growth (Bell & Collins 2008; Gonzalez et al. 2013). If evolutionary rescue occurs, then the population dynamics are typically defined by a U-shaped curve, where a strong initial population decline is followed by an increase, as surviving (and adapted) individuals rapidly reproduce (Gomulkiewicz & Holt 1995; Bell & Gonzalez 2009; Martin et al. 2013).

The likelihood of ER depends on the effect size of the environmental stress and the rate at which environmental conditions deteriorate (Gonzalez et al. 2013). If an environmental change is sudden, then a large, rapid population decline is probable, increasing the chance of extinction. In this case, ER likely relies on existing genetic variation within the population or better adapted variants quickly entering the population through migration or mutation. In this scenario, it is argued that adaptation relies on a small number of mutations with large effects that fix rapidly (Bell 2013).

Conversely, if environmental change is more gradual, then adaptation may proceed by the slower fixation of many mutations of small effect as the population tracks the changing environmental conditions (Lynch & Lande 1993; Bell 2013). Gradual environmental degradation increases the likelihood of successful evolutionary rescue (Bell & Gonzalez 2011). Experimental studies have demonstrated that slower rates of environmental change can result in more adapted and thus more resilient, final populations or fewer extinctions (Huey et al. 1991; Perron et al. 2008; Collins & de Meaux 2009; Bell & Gonzalez 2011).

Rapidly deteriorating environments can limit both the availability of mutations due to reduced population size and can make some adapted genotypes evolutionarily inaccessible (Lindsey et al. 2013). Thus, the rate of environmental change affects both the likelihood of evolutionary rescue occurring, and the evolutionary trajectory and genetic architecture which results.

 

That text above was copied from the paper:

Killeen, J., Gougat-Barbera, C., Krenek, S., and Kaltz, O. (2017). Evolutionary rescue and local adaptation under different rates of temperature increase: a combined analysis of changes in phenotype expression and genotype frequency in Paramecium microcosms. Mol Ecol 26, 1734–1746.

 

Evolutionary rescue (ER) occurs when populations, which have declined due to rapid environmental change, recover through genetic adaptation. The success of this process and the evolutionary trajectory of the population strongly depend on the rate of environmental change. Here we investigated how different rates of temperature increase (from 23 to 32 °C) affect population persistence and evolutionary change in experimental microcosms of the protozoan Paramecium caudatum. Consistent with theory on ER, we found that those populations experiencing the slowest rate of temperature increase were the least likely to become extinct and tended to be the best adapted to the new temperature environment. All high-temperature populations were more tolerant to severe heat stress (35, 37 °C), indicating a common mechanism of heat protection. High-temperature populations also had superior growth rates at optimum temperatures, leading to the absence of a pattern of local adaptation to control (23 °C) and high-temperature (32 °C) environments. However, high-temperature populations had reduced growth at low temperatures (5–9 °C), causing a shift in the temperature niche. In part, the observed evolutionary change can be explained by selection from standing variation. Using mitochondrial markers, we found complete divergence between control and high-temperature populations in the frequencies of six initial founder genotypes. Our results confirm basic predictions of ER and illustrate how adaptation to an extreme local environment can produce positive as well as negative correlated responses to selection over the entire range of the ecological niche.