Tao Xu

Tao Xu, Jun He

Solving constrained optimization problems by multi-objective evolutionary algorithms has scored tremendous achievements in the last decade. Standard multi-objective schemes usually aim at minimizing the objective function and also the degree of constraint violation simultaneously. This paper proposes a new multi-objective method for solving constrained optimization problems. The new method keeps two standard objectives: the original objective function and the sum of degrees of constraint violation. But besides them, four more objectives are added. One is based on the feasible rule. The other three come from the penalty functions. This paper conducts an initial experimental study on thirteen benchmark functions. A simplified version of CMODE is applied to solving multi-objective optimization problems. Our initial experimental results confirm our expectation that adding more helper functions could be useful. The performance of SMODE with more helper functions (four or six) is better than that with only two helper functions.

Wenya Zhu, Xiankai Lu, Tao Xu et al.

Structure information is ubiquitous in natural scene images and it plays an important role in scene representation. In this paper, third order structure statistics (TOSS) and fourth order structure statistics (FOSS) are exploited to encode higher order structure information. Afterwards, based on the radial and normal slice of TOSS and FOSS, we propose the high order structure feature: third order structure feature (TOSF) and fourth order structure feature (FOSF). It is well known that scene images are well characterized by particular arrangements of their local structures, we divide the scene image into the non-overlapping sub-regions and compute the proposed higher order structural features among them. Then a scene classification is performed by using SVM classifier with these higher order structure features. The experimental results show that higher order structure statistics can deliver image structure information well and its spatial envelope has strong discriminative ability.