We study a complex mixture with bidispersity in size and polydispersity in energy using computer simulation. The energy polydispersity between the bidisperse particles is introduced by considering random pair-wise interactions. Extensive molecular dynamics simulations are performed to compute potential energy and neighborhood identity ordering (NIO) parameter as a function of temperature for different size-ratios and concentrations of the two species by quenching it from a high-temperature fluid state to a solid state. Our findings demonstrate an enhancement of the neighborhood identity ordering on the addition of particles of different sizes, which also depends on particle concentration. Moreover, a comparatively higher increase in the NIO parameter is achieved by tuning the size-ratio of the particles. We also propose that the NIO parameter is a good marker to differentiate multicomponent systems (below the liquid to solid transition temperature) with different size-ratios and concentrations. © 2020 Informa UK Limited, trading as Taylor & Francis Group.