In this study, a novel chessboard model with stream splits is proposed for mass exchange network synthesis (MENS) to achieve the minimum total annual cost (TAC). The proposed chessboard model presents a streamlined and concise representation of mass exchange networks (MENs), enabling adaptable configurations of streams. This model exhibits structural diversity and reduces the computational complexity of the MEN calculation. An improved stochastic algorithm called the random walk algorithm with compulsive evolution (RWCE) is applied to solve MENs represented by the chessboard model. The simultaneous method is employed to address three instances of singlecomponent MEN examples and a multicomponent MEN case study. The obtained optimal solutions outperformed the solutions previously reported in the literature. These findings demonstrate the viability and usefulness of the chessboard model with stream splits and the modified RWCE algorithm for addressing MENS.