Reduction of passenger waiting time in a multiple elevator system is an important goal in the lift industry. Genetic algorithms (GAs) have been applied to the dispatching problem in vertical transportation. In this paper, we present an approach based on a GA with several relevant adjustments to adapt this type of algorithm to this problem. The algorithm serves calls currently registered in the system to create a dispatch plan, under the assumption that just one passenger has made each call (i.e. without passenger forecasting). We develop and investigate various versions of the GA incorporating one or more adjustments in this research area. The algorithms were implemented and evaluated using ELEVATE, for two different building configurations, in terms of incoming, outgoing and interfloor profiles. To compare results, one-factor analysis of variance tests were applied to passenger waiting times. The performance of the basic GA was significantly improved upon by making these adjustments. These adjustments turn out to be essential for a successful implementation of a GA in the dispatching problem.