IB Case Study 2022 Genetic Algorithms/Traveling Salesman Problem

Cycle Crossover (CX)

-Allows for two parents chromosomes/cities to be combined/preserved -And not be duplicated during crossover -Ensures diversity of chromosomes/cities from parents -Accelerates the search process in genetic algorithms

Population size

-It is difficult to decide upon a population size -Too large a population will increase the likehood of a near-optimal solutions but will increase the length of time to run through a generation -A large enough population may have enough diversity to arrive at a near-optimal solution without any mutation -Too small a population may meen that you may never arrive at a near-optimal solutions; -Because there is not enough variation in the parents -This may require you to increase the mutation rate, which willa dd greater variation -But may also not arrive at a near-optimal solution

Hill Climbing

A heuristic, problem-solving strategy in which the current solution is compared to each of its "neighbours" and will move to a neighbour if it has a higher fitness. It suffers from the problem of getting stuck in local optima positions.

Simulated Annealing

A probabilistic technique used to find the global optimum of a function, where 'temperature', the explorative value of a search algorithm, gradually decreases to allow for more exploitation, the evaluation of surround values.

Heuristic

A problem solving approach to find a satisfactory solution when finding the perfect solution is computationally intractable.

Ranking

A process where each variable is compared/placed in order based on their fitness level from highest to lowest. (instead of variables/ they would be answers for the Travelling Sales problem)

tour

A trip or journey in which one usually returns to the starting point.

novelty search

A way of rewarding solutions that are "new" compared to existing solutions by calculating a novelty factor and adding this to the fitness function to "reward" novel solutions with a higher chance of selection. It can be used as a strategy to try to avoid premature convergence.

Brute force approach

An approach to problem solving in which every possible solution is calculated and the best is selected. For many problems this is impossible in reasonable time.

Elitism

Copying the best solutions present in a current generation straight into the next generation.

Selection strategy

Different selection processes (e.g. Tournament selection) are used to select possible solutions and advance them to the mating pool

Exploration vs. Exploitation

In evolutionary algorithms two main abilities maintained which are Exploration and Exploitation.In Exploration the algorithm searching for new solutions in new regions, while Exploitation means using already exist solutions and make refinement to it so it's fitness will improve.

Offspring

Is a term used in genetic algorithms to illustrate a child created after two parents under go any type of crossover (Partially mapped crossover PMX, Order crossover OX, Cycle crossover CX), they carry on features from their parent class.

Termination condition

It is a condition where the genetic algorithm will end and no further execute. It could be fitness level (remember for travelling sales problem the fitness level is measured by 1/d as the shorter the distance the higher the fitness), a certain amount of time, or certain number of iterations, or a certain number of iterations after which the best solution found does not change in fitness value.

Edge Recombination Crossover (ERX)

It is a crossover operator that observes the edges of solutions. It compares the neighboring solutions and makes its basis for the creation of a new child solution off of this.

Roulette wheel selection

It is a genetic operator used in genetic algorithms for selecting potentially useful solutions for recombination, giving a higher chance to the solutions with higher fitness to be chosen but allowing any other solution to be chosen.

Computational intractability

Problems for which there exist no efficient algorithms to solve them. For example, if we wanted to find the exact optimal solution for the TSP with current technology, it would take more than a year to achieve it.

local extrema

The local maximum and minimum values of a function.

Truncation Selection

The selection of the fittest, top portion of the population to be used in the mating pool. The mating pool then changes some values in cross-over methods.

Initialization parameters

They are variables that affect the genetic algorithms performance from the start of the process. It can be initialized by humans simply drawing lines between the cities in the way that they think the distance is the least.

Roulette Wheel Selection Advantages

This genetic operator is very effective with large sized problems as it is quite exploitative. It also allows even for low fitness solutions to be chosen, avoiding premature convergence and introduces some novelty search (increasing exploration).

Roulette Wheel Selection Disadvantages

This genetic operator though can be quite slow and may be less suitable for smaller search spaces. Before its execution, the population must be sorted on every cycle, this is for it to operate properly.

problem space

This is a way of visuallising the set of all possible solutions as being mapped onto 2D or 3D space. We can then imagine/describe different methods of "exploring" the space.

Optimisation

This is necessary to allow software to run as efficiently as possible.

Premature convergence

When a population converges too early so that their fitness level is suboptimal; the parents of the new generation cannot reliably generate an offspring that outperforms them through mutation, cross-over, or selection.

Convergence

When the fitness of the members of a population tend towards the same value, thereby indicating that an extrema, an optimal solution which could be local or global, is being reached or at least neared.

fitness landscape

a mapping of the fitness of all possible solutions onto an imaginary 2D or 3D space. It is used to help us think about, discuss and visualize methods of searching for solutions

Combinatorial optimization

a topic that consists of finding an optimal object form a finite series of objects

Mutation Rate

a value that controls the likelihood that any given solution will be altered by mutation. Typical rate is about 1% and it helps to escape local minima.

fitness function

a way of calculating the success of each solution. It is often mathematical and can be used to constrain the fitness within appropriate limits e.g. from 0 to 1 In the TSM it could simply be 1/total_distance

Mutation

a way of increasing randomness or exploration by altering a selected solution in a small and random way

crossover operator

controls the method by which selected solutions are recombined into child solutions

Stochastic universal sampling

generating a random position in a roulette wheel and adding an evenly spaced interval to get the next solutions

Fitness

is a measure of how successful each solution is for solving the current problem

crossover

mechanism by which the order of the cities of a child is created from a combination of its parents' solutions

Population

the total current solutions to the problem

Tournament selection

where chromosomes of possible solutions are compared to one another and whichever chromosome has a better fitness value than the other continues to the mating pool.

Mating pool

where possible solutions are put through crossover methods to explore more possible solutions to the problem