In this paper, a modified differential evolution algorithm, which is based on abstract convex lower approximation, is proposed for multimodal optimization. First, the original bound constrained optimization problem is converted to an increasing convex along rays (ICAR) function over a unit simplex by using the projection transformation method. Second, based on abstract convex theory, the study builds a lower approximation to original optimization problem by using a finite subset of biased sampling points comes from the population replacement scheme in the basic DE algorithm. Some properties of underestimation model are analyzed theoretically, and an N-ary tree data structure have also been designed and implemented to solve them. Furthermore, considering the difference between the original and its underestimated function values, the paper proposes a niche identify indicator based on biased DE sampling procedure, and also design a regional phylogenetic tree replacement strategy to enhance the exploitation capacity in niche. Experimental results confirm that the proposed algorithm can distinguish between the different attraction basins, and safeguard the consequently discovered solutions effectively. For the given benchmark problems, the proposed algorithm can find all the global optimal solutions and some good local minimum solutions.