Bikeshare systems have attracted increased research interest ranging from bikeshare planning analyses to operational improvement studies (e.g., rebalancing, or station optimization). However, the interaction between bikeshare station spatial distribution and actual bikeshare activities when addressing equity issues has not been thoroughly considered. Moreover, there is a paucity of research helping governments develop incentive programs for equitable bikeshare services. To fill this research gap, we develop a model to estimate the potential demand (i.e., bikeshare trip production and attraction) and its distribution, and evaluate performance over a set of objectives (e.g., maximization of annual revenue, accessibility improvements) to find the most equitable distribution of stations. We build a genetic algorithm to solve this multi-objective optimization. The study uses the Divvy bikeshare system in Chicago as a case study, and compares the solutions of the model with the system's expansion (new stations added) in 2016, which targeted disadvantaged areas. When selecting accessibility as the main objective, the results indicate the need to provide more stations in disadvantaged areas and those results overlap with the system's expansion in 2016. On the contrary, the goal of revenue maximization results in a smaller network of stations and fewer accessibility improvements, especially in disadvantaged communities. A sensitivity analysis uncovers the greatest obstacle (i.e., station cost) to adding more stations in disadvantaged areas. More importantly, a Pareto frontier of this multi-objective optimization supports several policy suggestions for incentivizing private bikeshare companies to target more disadvantaged populations. Our results show the importance of considering accessibility and other equity constraints in developing a more inclusive, equitable and sustainable transportation system, and we provide several planning suggestions.