Stochastic engines or random number generators are commonly used to initialize metaheuristic approaches. This chapter discusses the incorporation of extreme value distributions into stochastic engines to improve the performance of optimization techniques when solving the complex four-objective GT-AC optimization problem.
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The differential evolution (DE) approach is employed to tackle this problem. Using two extreme value distributions, two DE variants are developed by modifying their stochastic engines: Pareto-DE and Extreme-DE. The algorithms are then applied to optimize a complex MO Gas Turbine – Absorption Chiller system.
As engineering systems become more complex, there is a growing need for advanced and innovative techniques for optimizing these systems. Metaheuristics have been widely used to tackle such engineering problems – especially in industries related to power generation (Marmolejo et al., 2017). MO settings are also becoming commonplace in engineering; where the engineer has to consider multiple target objectives when making critical decisions. MO optimization problems could be broadly divided into two classes. The first is bi-objective problems which have lower complexity as compared to its many-objective counterparts. These problems are endowed with only two objectives and there are well established methods for solving them: Non-Dominated Sorting Genetic Algorithm (NSGA-II) (Sadeghi et al., 2014) and Strength Pareto Evolutionary Algorithm (SPEA-2) (Maheta and Dabhi, 2014). As for problems with many objectives, scalarization approaches are among the most effective strategies. Examples of scalarization approaches are the weighted sum (Yang et al., 2013) and the Normal-Boundary Intersection (NBI) (Charwand et al., 2015; Brito et al., 2014) methods. Using scalarization approaches, the multiple objectives are aggregated and the problem is transformed to a single-objective problem. This reduction in complexity then makes the problem easier to solve.
In engineering and other real-world applications, the penalty factor approach is also employed for dealing with situations with multiple objectives. Similar to the weighted sum approach, this method involves the weighted aggregation of the objectives. The distinction with the weighted sum approach is that the penalty factor method converts all the objectives into financial terms forming a single cost function. For instance, in Sheng et al., (2013), an optimization of a distributed generation (DG) power system was carried out using evolutionary algorithms. The penalty factor method was used as a basis to solve the problem; where the DG utilization was maximized while minimizing the system’s losses and environmental pollution. Another application using this method could be seen in the works of Daryani and Zare, (2016). In that work, the authors used the Modified Group Search Algorithm (MGSA) in tandem with the penalty factor approach to solve a MO problem in power and emission dispatch.
The Pareto distribution is among the first non-Gaussian distributions encountered in statistics. In economics this distribution shows large amounts of wealth are owned by a smaller percentage of individuals in any society. The idea is often expressed as the 80-20 Rule; 20 percent of the population owns 80 percent of the wealth (Sanders, 1987). Ever since its appearance, the Pareto distribution has found diverse applications – stretching out to other applications besides economics. In quantum statistics, the variant of Pareto distributions has been employed to study particle distributions (Biró et al., 2015). These distributions have also seen application in stochastic physical processes; particularly in sub-recoil laser cooling (Bardou, 1995). It has also been used to design and assess software reliability models using failure data (Faqih, 2013; Karagrigoriou and Vonta, 2014). In Fernández et al., (2016), Pareto distributions were used to improve the signal quality of radar systems. In that work the Pareto distribution coupled with a neural network was employed to estimate and eliminate background echoes in radar signals known as ‘sea clutter’. Similarly in Lenz (2016), a variant of the Pareto distribution called the Generalized Pareto Distribution was employed in the field of microscopy. In that application, the distribution became critical for the construction of an efficient autofocus system.