Optimisation Method Genetic Algorithm

Optimisation algorithms are executed iteratively to find optimal or satisfactory solutions [88]. They can be classified into two categories, i.e. deterministic algorithms and stochastic algorithms. Deterministic algorithms follow a rigorous procedure or specific rules so that the solution can gradually approach to a better solution. But despite

the optimisation process, the same output will be produced for a particular input. By contrast, stochastic algorithms always involve some degree of randomness so that its optimisation paths and values are not exactly repeatable.

Nowadays, two kinds of stochastic algorithms are popularly used in the practice of optimisation. They are heuristic and metaheuristic algorithms. Heuristics are a kind of greedy problem-dependent techniques. They can be adapted to different problems. It can help to find a reasonably good solution, but it is possible to be trapped in local optimums. As opposed to heuristics, metaheuristics are a sort of problem-independent techniques. Therefore, they can work like a black box. Since they allow to explore more in space, they can usually perform better in achieving the purpose of optimisation.

In this thesis, optimisation is conducted to find the optimal layouts, configurations, and maintenance strategies for the AGV systems. The purpose is to minimise the cost of production while maximising the production in a given time duration simultaneously. The obtained optimal solution will enable the AGV system to achieve the best performance in multiple aspects. Since deterministic algorithms are not good at dealing with discontinuity problems [88], it is not suitable to undertake the optimisation of the problems that involve many discrete variables, like the problems considered in this thesis. For this reason, only metaheuristic algorithms were considered when selecting an appropriate optimisation tool in this thesis.

So far, Genetic Algorithm (GA) has been widely regarded as a most mature metaheuristics for dealing with multi-objective optimisation problems attributed to its powerful capability of achieving universal optimisation regardless of initial conditions [89, 90]. Inspired by the biological evolution of living species, the GA was proposed first by John Holland in 1970s [91]. It has several outstanding advantages over other metaheuristics. For example, as compared to the simulated annealing algorithm that uses only one point moving in a search space to find better solution [92], the GA uses a population to explore the whole search space. Therefore, it is less likely to fall in local

optimums. Also, the GA is particularly good at dealing with discrete problems while other metaheuristics like particle swarm optimisation were designed mainly for solving continuity problems [88, 93]. In the area of AGVs, the GA has now been applied to solving various problems in AGV systems, such as the scheduling and dispatching problems considered in [94, 95, 96, 97].

To implement the GA, an initial population of individuals (also known as chromosomes consisting of genes) will be generated first, and the fitness of every chromosome in the population will be evaluated by using the predefined fitness functions, which is constructed based on the optimisation objectives. Then, any two individuals in the population will be randomly selected as parents for carrying out evolution by the approach of either crossover or mutation mechanism. The offspring chromosomes will be judged again by calculating their fitness values, and then based on which to select a new generation of parents for carrying out evolution again. The same evolution process will be iterated until the predefined number of iterations is reached or a satisfactory population is obtained, depending on the termination condition set in the GA algorithm. Herein, it is worth noting that at every time of evolution, the chromosomes with higher fitness values will always have more chance to be selected as parents so that their genes will have higher probability to be passed on. The crossover of the parents’ genes is conducted based on the principle of randomness. In the process, the mutation of an individual’s genes may happen also randomly, which will be beneficial to prevent early or premature convergence of the solution. The premature convergence of the solution may not only slow the iterations to reach a globally optimal solution, but could also lead to a local optimum [98]. Through repeating the evolution, the average fitness of the individuals in the population will be increased gradually and a saturated value will be finally obtained when the GA calculation is normally terminated. Then, the individual that has the largest fitness value will represent the optimal solution of the problem of interest.

which are randomly selected based on a predefined crossover rate. The genes from two ‘parent’ individuals are combined by using crossover mechanism to generate the genes of a new offspring. Today, a few notable crossover methods have been developed, such as single-point, multi-point, and uniform crossovers [99]. In a single-point crossover operation, a random crossover point can be selected at any point within the genes of the chromosomes. By combing two sets of genes from both parent chromosomes, an offspring chromosome can be produced. An example of the process of single-point crossover is illustrated in Figure 2.8.

Figure 2.8 One-point crossover operator

In the figure, assume the randomly selected crossover point is after the 4th _number.

Then the new offspring chromosome is produced by combining the first four numbers in the genes of the top parent chromosome and the bottom parent chromosome’s genes starting from the 5th number.

Multi-point crossover is a generalisation of the single-point crossover, wherein alternating segments are swapped between multiple crossover points to get new offspring chromosomes. In a uniform crossover, the parent chromosomes are independent with each other. Each number or bit of the offspring chromosome is chosen from the two parents according to a distribution. These crossover operators are generic

and their efficiency and effectiveness could vary for different problems.

An example of the operation of mutation is illustrated in Figure 2.9. As mentioned earlier, mutation is helpful to maintain the genetic diversity of the population and prevents the solutions trapping to the local best by restoring the lost genes during the evolution and finding more unexplored information beyond the given population. During a mutation operation, the value of each gene of a chromosome could be modified based on a given probability. It is worth noting that both the values of the crossover and mutation rates are usually found by experimental approaches.

Figure 2.9 Mutation operator