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By adjusting the oxidation voltage, electrolyte, anodizing time and other parameters, TiO₂ nanotubes with high aspect ratio can be prepared by oxidation in organic system because anodic oxidation method has the advantage of simple preparation process, low material cost and controllable morphology. This review focusses on the influence of anodizing parameters on the morphology of TiO₂ nanotube arrays prepared by anodizing. In order to improve the photocatalytic activity of TiO₂ nanotubes under visible light and to prolong the life of photo-generated carriers, the research status of improving the photocatalytic activity of TiO₂ nanotubes in recent years is reviewed. This review focusses on the preparation and modification of TiO₂ nanotubes by anodic oxidation, which is helpful to understand the best structure of TiO₂ nanotubes and the appropriate modification methods, thus guiding the application of TiO₂ nanotubes in practical photocatalysis. Finally, the development of TiO₂ nanotubes is prospected.

This paper proposed a modified differential evolution algorithm (MCDE) to solve constraints optimization problems. The method used three simple selection criteria based on feasibility to guide the search in the feasible region. The proposed approach did not adopt the penalty function method, in contrast to the penalty function method, the constraint-handing technique of this paper is very simple, dose not require additional parameters. In addition, this paper incorporated the center point of the population into the DE algorithm, and modified the crossover factor of DE algorithm. Simulation and comparisons based on four testing functions and one engineering example demonstrate the effectiveness, efficiency and robustness of the proposed MCDE.