List of Figures

Figure 1.1 Decision space of a constrained two-dimensional optimization problem. Figure 1.2 Schematic of global and local optimums in a one-dimensional maximizing optimization problem. Figure 1.3 Different types of decision spaces: (a) maximization problem with single-modal surface and one global optimum; (b) maximization problem with multimodal surface that has one global optimum. Figure 1.4 Demonstration of near optima in a one-dimensional maximizing optimization problem. Figure 1.5 Compound gear train made of four gears. Figure 1.6 Schematic of a two-bar truss. Figure 1.7 Schematic of a hydropower dam. Figure 2.1 Sampling grid on a two-dimensional decision space. Figure 2.2 General schematic of a simple algorithm; K denotes the counter of iterations. Figure 2.3 Diagram depicting the relation between a simulation model and an optimization algorithm. Figure 2.4 The main components of the optimization by meta-heuristic and evolutionary algorithms. Figure 2.5 Different solutions in a two-dimensional decision space. Figure 2.6 Selection probability of a set of solutions 1-10 of a hypothetical maximization problem. Figure 2.7 The flowchart of the general algorithm. Figure 2.8 Convergence history of an optimization algorithm toward the best solution in a minimization problem. Figure 2.9 Convergence of an optimization algorithm in which the best solution is not always transferred to the next iteration during the search in a minimization problem. Figure 2.10 Convergence of different runs of an optimization algorithm toward near-optimal solutions of a minimization problem. Figure 2.11 Convergence of different runs of an optimization algorithm in a minimization problem. Figure 3.1 The flowchart of the PS. Figure 3.2 Meshes generated by the GPS and MADS methods in a two-dimensional decision space. Figure 4.1 The flowchart of the GA. Figure 4.2 Demonstration of a roulette wheel. F?=?Fitness function value; P?=?probability of selecting a solution. Figure 4.3 Ranking chromosomes (or solutions) according to the fitness function (F) in a maximizing problem. Figure 4.4 The process of constituting a new generation from the previous generation. Figure 4.5 Different approaches of crossover: (a) one-point crossover, (b) two-point crossover, and (c) uniform crossover. Figure 4.6 An example of the mutation operator.62Figure 5.1The flowchart of the SA. Figure 6.1 The flowchart of the TS. Figure 6.2 The decision space of a two-dimensional optimization problem. Figure 6.3 Illustration of steps based on recency-based memory in a two-dimensional decision space. Figure 7.1 A double-bridge experiment with pathways of unequal length. Figure 7.2 The flowchart of the ACO. Figure 7.3 Representation of a solution in the ACO; there are M such solutions. Figure 8.1 The flowchart of the PSO. Figure 8.2 Concepts of the best individual position in a two-dimensional maximization problem. Figure 8.3 Concept of the global best position in a maximization problem. Figure 9.1 The flowchart of the DE. Figure 10.1 The flowchart of the HS. Figure 10.2 Generating a new solution based on memory strategy. Figure 11.1 The flowchart of the SFLA. Figure 11.2 Sorting frogs according to the fitness function F(X) in a maximizing problem. Figure 11.3 Assigning frogs to different memeplexes; Z?=?number of memeplexes and Y?=?number of frogs assigned to each memeplex. Figure 11.4 The representation of a memeplex and a submemeplex within the entire population. Figure 12.1 The flowchart of the HBMO algorithm. Figure 12.2 Determining the queen and trial solutions according to the fitness function F(X). Figure 12.3 Different crossover approaches: (a) one-point crossover, (b) two-point crossover, and (c) uniform crossover. Figure 12.4 Performance of mutation operator. Figure 13.1 The flowchart of the IWO. Figure 13.2 Number of seeds for each weed with respect to the fitness value. Figure 14.1 The flowchart of the CFO. Figure 14.2 Distribution of initial probes in the CFO algorithm. Figure 15.1 Species immigration and emigration pattern in a habitat. Figure 15.2 The flowchart of the BBO. Figure 15.3 Comparison of two solutions for one problem. Figure 15.4 Ranking habitats (solutions) according to their fitness values in a minimization problem. Figure 16.1 The flowchart of the FA. Figure 17.1 Gravity force between different particles; Force1 is the resultant force on Mass1. Figure 17.2 The flowchart of the GSA. Figure 18.1 The flowchart of the BA. Figure 19.1 The flowchart of the PPA. Figure 20.1 The flowchart of the WCA for a minimization problem. Figure 20.2 Classification of raindrops and relations between the sea, rivers, and streams according to their fitness values (F(X)) for a minimization problem where M?=?10 and R?=?3. Figure 20.3 Schematic of stream flowing toward a river at distance d: X: existing stream; X´: new stream. Figure 21.1 The flowchart of the SOS. Figure 22.1 The flowchart of the CEA. Figure 22.2 Illustration of a roulette wheel. Figure 22.3 Types of one-point cut crossover in the CEA: (a) Type 1 (new solution (1)) and type 2 (new solution (2)), (b) Type 3 (new solution (1)) and type 4 (new solution (2)), (c) Type 5 (new solution (1)) and type 6 (new solution (2)), (d) Type 7 (new solution (1)) and type 8 (new solution (2)), and (e) Type 9 (new solution (1)) and type 10 (new solution (2)). Figure 22.4 Types of two-point cut crossover in the CEA: (a) Type 11 (new solution (1)) and type 12 (new solution (2)), (b) Type 13 (new solution (1)) and type 14 (new solution (2)), (c) Type 15 (new solution (1)) and type 16 (new solution (2)), (d) Type 17 (new solution (1)) and type 18 (new solution (2)), and (e) Type 19 (new solution (1)) and type 20 (new solution (2)). Figure 22.5 Types of...