Mop-up Evaluation might be applied at decided late endgame positions without any pawns, where one side has a winning advantage to checkmate and likely a rook or queen (or even two different colored bishops). The winning side wants to drive the losing king to the edges and corners, and has therefor a bonus for Center distance (Center Manhattan-distance) of the losing king, and a bonus for a minimum distance of both kings. In practice one often uses some term based on the (weighted) sum of the Chebyshev distance and the Manhattan distance, to have a higher bonus for the corners and straight rather than diagonal opposition.
For instance, Chess 4.x Mop-up evaluation was based on sum of absolute rank- and file-distances , something like this (ignoring knights, which were equally considered like the king) from the stronger side of view:
PosEval = 4.7 * CMD + 1.6 * (14 - MD)
CMD is the Center Manhattan distance of the losing king and MD the Manhattan distance between both kings. Of course part of such terms might be covered by piece-square tables of that very late game stage, and most of these positions are handled by interior node recognizer nowadays.
- Simple method for simple mates for programs without TBs by J. Wesley Cleveland, CCC, November 25, 2016 » Center Manhattan-Distance, KBNK Endgame