Engineering Optimization

35Analysis of Leapfrogging

35.1 Introduction

Leapfrogging is a relatively new procedure and can benefit from the depth of analysis that has been established for other optimizers. This chapter provides some analysis to reveal fundamentals about the technique and statements about critical aspects for an application user and reveals the analysis paths and opportunities for others to explore.

Leapfrogging (LF) is a multiplayer (multi‐particle) optimization algorithm. In it, trial solutions (players) are randomly initialized throughout feasible decision variable (DV) space, and the objective function (OF) value for each is determined. There is a player at the best position (the trial solution with the best OF value; the default here is a minimum) and a player with the worst position. The worst leaps over the best, like the children’s leapfrogging play, into a random spot in the reflected DV space, and the OF of the new trial solution (TS) is evaluated.

The basic algorithm determines the leaping player new position from this equation:

(35.1)

in which x represents a DV value, for dimension j, and r is a uniformly distributed random number. The subscript “best” represents the x‐position of the best player, the subscript “old” represents the leap‐from x‐position of the leaping player, and the subscript “new” represents the leap‐to x‐position of the leaping player. The subscript j indicates ...