The present study develops a new mathematical approach to the pressure-mediated streaming potential flow of couple-stress Casson fluids with the influence of slip-dependent zeta potential between two parallel plates in a microchannel. The lateral electric and transverse magnetic fields are externally applied to control the fluid flow. A multi-objective optimization technique was implemented by utilizing the non-dominated sorting genetic algorithm (NSGA-II) by varying different constraints to maximize the electrokinetic energy conversion efficiency and minimize the irreversibility of the system. The present results show that the couple stress and Casson parameters influence the development of streaming potential, electrokinetic energy conversion (EKEC) efficiency, temperature, Nusselt number, and Bejan number for asymmetric velocity slip and temperature jump circumstances. The viscous dissipation, Joule heating, and thermal radiation parameters significantly affect the heat transfer. According to the present results, the EKEC efficiency increases with a slip-dependent zeta potential of couple stress Casson fluid, couple stress fluid, Casson fluid, and Newtonian fluid by 45.92 %, 47.10 %, 42.81 %, and 37.68 %, respectively, compared to that for the slip-independent zeta potential. At the centre of the microchannel for the jump boundary conditions, temperature increases by 2.95 % compared to no jump boundary conditions.