Script to calculate best scavenging splits - TribalWars

matlab_tw_scavenging.m

% script to calculate best scavenging splits - TribalWars
% author: PhilipsNostrum (@guipenedo)

% calculate best split using fmincon for 1 spear, up to *upper* spears
upper=500;


% scavenge time (C is the loot capacity, for instance, 1 spear = 25 loot capacity)
% ((C*LF*10)^(2*DE)+DIS)*DF

global c_tot LF DE DIS DF
% these factors may be found on TW's source code (search for "ScavengeScreen")
LF = [0.1, 0.25, 0.5, 0.75]; % loot factor
DE = 0.45; % duration exponent
DIS = 1800; % duration initial seconds
DF = 0.6830201284; % duration factor

x0 = ones(4,1); % initial point: 1 (close to 0)
options = optimoptions('fmincon','Display','iter','Algorithm','sqp','MaxFunctionEvaluations',100000,'MaxIterations',2000);

res = zeros(4,upper);

for sp=1:upper
    c_tot = 25*sp;
    x = floor(fmincon(@f, x0, [], [], [], [], zeros(4,1), [], @g, options)/25);
    res(:,sp) = x;
end

function [cost] = f(c)
    global LF
    cost = 0;
    for i=1:4
        cost = cost + (c(i)*LF(i))/(t(c(i),LF(i)));
    end
    cost = 1/cost;
end

function [v] = t(ci,LFi)
    global DE DIS DF
    v = ((ci*ci*LFi*LFi*100).^DE+DIS)*DF;
end

function [c, ceq] = g(cs)
    global c_tot
    c = 0;
    ceq = -c_tot;
    for i=1:4
        ceq = ceq + cs(i);
    end
end

Could you explain the formula for time calculation of scavenging trips. I am trying to understand what are the variables involved.