Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems

Swarm Intelligence: Theoretical Proof That Empirical Techniques are Optimal

“…Thus, an optimal function P (r) can be determined as the one for which the transition from the old probabilities (3) to the new probabilities (4), (6) can be described by the (fractionally linear) Bayes formula (8).…”

“…There are numerous effective global optimization techniques that reduce the general global optimization problems to convex ones; see, e.g., [17,38]. Empirically, among these techniques, the best are αBB method [4,5,17,27] and its modifications recently proposed in [6,7]. It turns out [18] that this empirical optimality can also be explained via shift-and scale-invariance.…”

New technique for solving univariate global optimization

“…Adjiman et al [5] presented the detailed implementation of the alpha BB approach and computational studies in process design problems such as heat exchanger networks, reactor-separator networks, and batch design under uncertainty. Akrotirianakis and Floudas [6] presented computational results of the new class of convex underestimators embedded in a branch-and-bound framework for box-constrained NLPs. They also proposed a hybrid global optimization method that includes the random-linkage stochastic approach with the aim of improving the computational performance.…”

Towards Optimal Techniques for Solving Global Optimization Problems: Symmetry-Based Approach

“…In other words, the optimal generalized αBB scheme is either the original αBB, or the scheme with exponential functions described in [3,4]. Thus, we have answers to both above questions:…”

“…In [3,4], several different non-linear functions have been tried, and it turned out that among the tested functions, the best results were achieved for the exponential functions g i (x i ) = exp(γ i · x i ) and h i (x i ) = − exp(−γ i · x i ). For these functions, the expression (2) can be somewhat simplified: indeed,…”