This　paper　discusses　energy-efficient　synchronization　in　multilayer　networks　under　fixed-time　(FT)　and　preassigned-time　(PT)　switching　control　frameworks.　First,　the　energy　consumption　(EC)　upper　bound　is　obtained　through　two　FT/PT　switching　control　schemes.　Subsequently,　a　quantitative　benchmark　of　energy-efficient　synchronization　in　multilayer　architectures　is　established　by　parametric　optimization　of　the　upper　bound　of　EC.　Fundamental　relationships　between　topological　networks　configurations,　control　parameters　and　EC　metrics　are　revealed,　enabling　the　development　of　a　framework　that　integrates　networks　architecture　optimization　with　controller　parameter　selection.　Finally,　theoretical　methods　are　validated　through　two　numerical　simulations,　with　results　confirming　both　the　precision　of　deriv5ed　EC　bounds　and　the　operational　effectiveness　of　the　proposed　strategy.　©　2025　Elsevier　B.V.