Hesitant adaptive search (HAS) extends the ideas of PAS by accommodating hesitation, or pausing, at objective function values for both continuous and discrete problems. At each iteration the HAS algorithm can either generate a point in the improving region with a certain “bettering” probability, or it “hesitates” and stays at the current point. PAS is a special case of HAS, occurring when the ... [Show full abstract] bettering probability is equal to one. The HAS algorithm goes a step further than PAS in modeling stochastic algorithms, because it allows hesitation at each iterate which may represent rejecting a sampled point. The bettering probability depends on the objective function value, so it can capture the realistic effect of it being harder to find an improving point as the objective function value gets smaller.