Fig. 1

Illustration of the ADSB algorithm. A Consider a current set V\(^{(t)}\) composed of \(k = 7\) points. At each step, v\(_{c}\) and two other points (v\(_{1}\),v\(_{2}\)) are randomly drawn from V\(^{(t)}\) and used to construct the direction of movement u\(^*\). A uniform random step \(\lambda ^*\) is taken along a cord passing through v\(_{c}\) and parallel to u\(^{*}\). A new point v\(^{*} =\) v\(_{c} + \lambda ^*\) u\(^{*}\) is proposed. If v\(^{*} \notin \varvec{\Omega }_{\text{loopless}}\), then v\(^*\) is rejected and the initial cord is shrunk. B The length of the initial cord is shrunk and a new step is taken. This time the new point v\(^*\) lands on a feasible region and it is therefore accepted. C Once a feasible point is found, v\(^{*}\) is swapped for v\(_{c}\) in the current set V\(^{(t+1)}\) and the algorithm is repeated