The first part ofthis paperpresents a modified algorithm to improve the element exchange method(EEM)for topologyoptimization. First, it uses a bilinear function to determine the number of exchanged elements. Second, the concept of "influence zone" is proposed to weightthe strain energy of elements in a circularzone,which surrounds the elements with higher strain energy such as boundary, loaded, or supportelements. Third, ituses a volume-changeable function to modify the number of exchanged elements in case the initial volume of solid elements isnot the same as its objective volume. Based on the numerical results, the proposed IEEM is able to find almostinitial-topology-independence results.The second part presents applications of the elementexchange method (EEM) in three-dimensional structural topology optimization, andalso extends the EEM to deal with multi-material structural topologyoptimization