Background I am investigating, numerically, the problem of a chess team attempting to maximise its probability of winning a team match . Each of our N players independently chooses one of two strategies , or theoretically a convex combination of the two, before a move is made. The strategies available for each player depend on his or her expected score against their individual opponent. The convex feasible region is a zonotope, a vector sum of line segments. The objective function is to maximise the probability of an event, “winning” , obtained as the sum of terms from a finite probability generating function involving N variables and terms of degree at most N.
N even is of most interest. N=2 is solvable analytically. For N =4 , a nightmare scenario does occur , namely of 16 extreme points half are local maxima and half are local minima. For N=4, the vertices then naturally form a bipartite graph of valency 4 with 8 local maxima and 8 local minima. Ideally I would like to solve problems numerically up to N=16, when I hope Normality will kick in.
One genetic algorithm performs well compared with for example Nelder –Mead or Simulated Annealing for N=4.
Question Are there any books or journal articles which consider performance of non-linear constrained optimisation algorithms over zonotopes?