Abstract. We use the Local Optima Network model to study the structure of symmetric TSP fitness landscapes. The ‘big-valley’ hypothesis holds that for TSP and other combinatorial problems, local optima are not randomly distributed, instead they tend to be clustered around the global optimum. However, a recent study has observed that, for solutions close in evaluation to the global optimum, this...

We show a pointwise estimate for the Fourier transform involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the...

We prove that for a class of Zd shifts of finite type, d > 1, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

The basic idea of local search is to find a good local optima quickly enough to approximate the global optima. This idea is somewhat like hill climbing. Starting from an arbitrary point, we try to go down or climb up a little step and compare the objective value at the new point to that at the old point. We then choose the step that increase the objective value. In this manner, we finally reach...

This paper looks at proofs concerning Gray codes and the locality of local search; it is shown that in some cases such proofs can be generalized to Binary and real valued encodings, while in other cases such proofs do not hold for Binary encodings. The paper also looks at a modified form of Quad Search that is proven to converge in under 2L evaluations to a global optimum on unimodal 1-D biject...

The Variable Neighborhood Tabu Search consists of a constructive phase and a series of local searches that use tabu tools. When the local search stops at a nontabu local minimum, a shake procedure starts a new local search. The local searches and the shake procedure are based on a series of standard moves. The local search consists of applying the best possible move until no such move exists. T...

For the p-median problem we study complexity of finding a local minimum in the worst and the average cases. We introduce several neighborhoods and show that the corresponding local search problems are PLS-complete. In the average case we note that standard local descent algorithm is polynomial. A relationship between local optima and 0–1 local saddle points is presented.

Using a finite-difference time-domain method, it has been shown that focal spots generated when tightly focusing linearly polarized Gaussian beam by Fresnel zone plate (FZP) and with an embedded optical vortex spiral (SZP) have different patterns of the intensity energy flux. The most significant differences are observed value topological charge (TC) is equal to three. flux annular distribution...

In this report, we examine the potential use of Guided Local Search (GLS) for function optimization. In order to apply GLS, the function to be minimized is augmented with a set of penalty terms that enable local search to escape from local minima. The function F6 is used to demonstrate the proposed technique.

Analog Gradient Search This analog phase demodulation hill-climbing technique works for clean, quasi-Gaussian couplings already near optimal alignment. However it will lock-in on local maxima and “flat spots” which occur in multimode couplings, with imperfect devices, or far from optimum alignment. Nevertheless, instrumentation based on this principle was popular, though bulky and providing too...