A multi-start global minimization algorithm with dynamic search trajectories

The role of statistics in operations research: Some personal reflections

“…A feature of the particular algorithm in question (Snyman and Fatti [26]) was that the region of attraction of the global minimum (the region of starting points that would lead to this point) could be assumed to be larger than that of any other local minimum (however many local minima there may be). After n iterations of the algorithm, the current best point will have been reached by r ≥ 1 of them, and if r is large enough, then it is likely that this point is the global minimum, in view of the fact that it has the largest region of attraction.…”

Evolutionary Operators in Global Optimization with Dynamic Search Trajectories

“…A proper termination condition is to stop the trajectory once it reaches a point with function value close to F (x 0 ), while at the same time the relation ∇F Tẋ > 0 is satisfied, i.e. the movement is uphill [13]. Auxiliary trajectories are then generated to better utilize the knowledge of x m and its associated quantities.…”

“…A typical choice for α is α = 0.95 [13]. For each starting point, the minimization procedure is provisionally ended if, for some x k , the inequality ∇F (x k ) < ε holds for some prescribed small positive number ε > 0.…”

“…An analytic description of all the aforementioned concepts, as well as the pseudocode of the SF algorithm can be found in [13]. In the next section, the DE algorithm is briefly described.…”

“…This method has been widely discussed [1,16], especially with respect to its regions of attraction. The algorithm considered in this study is the Multi-start Global Minimization Algorithm with Dynamic Search Trajectories, developed by Snyman and Fatti [13] (henceforth denoted as SF). The SF algorithm probes the search space using trajectories that are generated by integrating the differential equationẍ…”