Using Differential Evolution for the Graph Coloring

Differential evolution was developed for reliable and versatile function optimization. It has also become interesting for other domains because of its ease to use. In this paper, we posed the question of whether differential evolution can also be used by solving of the combinatorial optimization problems, and in particular, for the graph coloring problem. Therefore, a hybrid self-adaptive differential evolution algorithm for graph coloring was proposed that is comparable with the best heuristics for graph coloring today, i.e. Tabucol of Hertz and de Werra and the hybrid evolutionary algorithm of Galinier and Hao. We have focused on the graph 3-coloring. Therefore, the evolutionary algorithm with method SAW of Eiben et al., which achieved excellent results for this kind of graphs, was also incorporated into this study. The extensive experiments show that the differential evolution could become a competitive tool for the solving of graph coloring problem in the future

Paired Comparisons-based Interactive Differential Evolution

We propose Interactive Differential Evolution (IDE) based on paired comparisons for reducing user fatigue and evaluate its convergence speed in comparison with Interactive Genetic Algorithms (IGA) and tournament IGA. User interface and convergence performance are two big keys for reducing Interactive Evolutionary Computation (IEC) user fatigue. Unlike IGA and conventional IDE, users of the proposed IDE and tournament IGA do not need to compare whole individuals each other but compare pairs of individuals, which largely decreases user fatigue. In this paper, we design a pseudo-IEC user and evaluate another factor, IEC convergence performance, using IEC simulators and show that our proposed IDE converges significantly faster than IGA and tournament IGA, i.e. our proposed one is superior to others from both user interface and convergence performance points of view

Nonuniform Dichotomy Spectrum and Normal Forms for Nonautonomous Differential Systems

The aim of this paper is to study the normal forms of nonautonomous differential systems. For doing so, we first investigate the nonuniform dichotomy spectrum of the linear evolution operators that admit a nonuniform exponential dichotomy, where the linear evolution operators are defined by nonautonomous differential equations $\dot x=A(t)x$ in $\R^n$. Using the nonuniform dichotomy spectrum we obtain the normal forms of the nonautonomous linear differential equations. Finally we establish the finite jet normal forms of the nonlinear differential systems $\dot x=A(t)x+f(t,x)$ in $\R^n$, which is based on the nonuniform dichotomy spectrum and the normal forms of the nonautonomous linear systems.Comment: 28 page

Two-Stage Eagle Strategy with Differential Evolution

Efficiency of an optimization process is largely determined by the search algorithm and its fundamental characteristics. In a given optimization, a single type of algorithm is used in most applications. In this paper, we will investigate the Eagle Strategy recently developed for global optimization, which uses a two-stage strategy by combing two different algorithms to improve the overall search efficiency. We will discuss this strategy with differential evolution and then evaluate their performance by solving real-world optimization problems such as pressure vessel and speed reducer design. Results suggest that we can reduce the computing effort by a factor of up to 10 in many applications