An Evolutionary Frog Leaping Algorithm for Global Optimization Problems and Applications

Shuffled frog leaping algorithm, a novel heuristic method, is inspired by the foraging behavior of the frog population, which has been designed by the shuffled process and the PSO framework. To increase the convergence speed and effectiveness, the currently improved versions are focused on the local search ability in PSO framework, which limited the development of SFLA. Therefore, we first propose a new scheme based on evolutionary strategy, which is accomplished by quantum evolution and eigenvector evolution. In this scheme, the frog leaping rule based on quantum evolution is achieved by two potential wells with the historical information for the local search, and eigenvector evolution is achieved by the eigenvector evolutionary operator for the global search. To test the performance of the proposed approach, the basic benchmark suites, CEC2013 and CEC2014, and a parameter optimization problem of SVM are used to compare 15 well-known algorithms. Experimental results demonstrate that the performance of the proposed algorithm is better than that of the other heuristic algorithms.

Evolutionary Algorithm with a Configurable Search Mechanism

In this paper, we propose a new population-based evolutionary algorithm that automatically configures the used search mechanism during its operation, which consists in choosing for each individual of the population a single evolutionary operator from the pool. The pool of operators comes from various evolutionary algorithms. With this idea, a flexible balance between exploration and exploitation of the problem domain can be achieved. The approach proposed in this paper might offer an inspirational alternative in creating evolutionary algorithms and their modifications. Moreover, different strategies for mutating those parts of individuals that encode the used search operators are also taken into account. The effectiveness of the proposed algorithm has been tested using typical benchmarks used to test evolutionary algorithms.

On totally global solvability of controlled second kind operator equation

We consider the nonlinear evolutionary operator equation of the second kind as follows $\varphi=\mathcal{F}\bigl[f[u]\varphi\bigr]$, $\varphi\in W[0;T]\subset L_q\bigl([0;T];X\bigr)$, with Volterra type operators $\mathcal{F}\colon L_p\bigl([0;\tau];Y\bigr)\to W[0;T]$, $f[u]$: $W[0;T]\to L_p\bigl([0;T];Y\bigr)$ of the general form, a control $u\in\mathcal{D}$ and arbitrary Banach spaces $X$, $Y$. For this equation we prove theorems on solution uniqueness and sufficient conditions for totally (with respect to set $\mathcal{D}$) global solvability. Under natural hypotheses associated with pointwise in $t\in[0;T]$ estimates the conclusion on univalent totally global solvability is made provided global solvability for a comparison system which is some system of functional integral equations (it could be replaced by a system of equations of analogous type, and in some cases, of ordinary differential equations) with respect to unknown functions $[0;T]\to\mathbb{R}$. As an example we establish sufficient conditions of univalent totally global solvability for a controlled nonlinear nonstationary Navier-Stokes system.

Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

The graph coloring problem is an NP-hard combinatorial optimization problem and can be applied to various engineering applications. The chromatic number of a graph G is defined as the minimum number of colors required to color the vertex set V(G) so that no two adjacent vertices are of the same color, and different approximations and evolutionary methods can find it. The present paper focused on the asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number. The asymptotic analysis of different crossover and mutation operators helps in choosing the better evolutionary operator to minimize the problem search space and computational complexity. The choice of the right genetic operators facilitates an evolutionary algorithm to achieve faster convergence with lesser population size N through an adequate distribution of promising genes. The selection of an evolutionary operator plays an essential role in reducing the bounds for minimum color obtained so far for some of the benchmark graphs. This research also focuses on the necessary and sufficient conditions for the global convergence of evolutionary algorithms. The stochastic convergence of recent evolutionary operators for solving graph coloring is newly analyzed.