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1 Diversity-Based Adaptive Evolutionary Algorithms

In evolutionary algorithms (EAs), preserving the diversity of the population, or minimizing its loss, may benefit the evolutionary process in several ways, such as, by preventing premature convergence, by allocating the population in distinct Pareto optimal solutions in a multi objective problem, and by permitting fast adaptation in dynamic problems. Premature convergence may lead the EA to a non-optimal result, that is, converging to a local optimum. In static problems, standard EAs work well. However, many real world problems are dynamic or other uncertainties have to be taken into account, such as noise and fitness approximation. In dynamic problems, the preservation of diversity is a crucial issue because EAs need to explore the largest number of regions possible. Standard genetic algorithms (SGA) are not suitable for solving dynamic problems because their population quickly converges to a specific region of the solution space. The loss of diversity is caused by selection pressure and genetic drift, two factors inherent in EAs. The loss of diversity may lead the EA to a non-optimal result, despite the fact that after a period of time, EA tends to find the global optimum. In static problems, loss of diversity might not be a very critical problem. However in dynamic environments lack of diversity may degrade EA performance. Especially in dynamic problems, the preservation of diversity is a crucial issue because an EA needs to explore the search space aggressively. One option for reacting to a change of the environment is to consider each change as the arrival of a new optimization problem to be solved. This is a viable alternative if there is time available to solve the problem. However, the time available for finding the new optimum may be short and also sometimes the algorithm cannot identify the environmental change. When the new optimum is close to the old one, the search can be restricted to the neighborhood of the previous optimum. Thus, some knowledge about the previous search space can be used. However, reusing information from the past may not be promising depending on the nature of the change. If the change is large or unpredictable, restarting the search may be the only viable option. The approaches that handle dynamic environments, addressing the issue of convergence, can be divided into the following categories (Jin & Branke, 2005): (i) generating diversity after a change, (ii) preserving diversity throughout the run, (iii) memory-based approaches, and (iv) multi-population approaches. The first two approaches cover the diversity problem.