Related papers: When Gravity Fails: Local Search Topology
We study local search algorithms to solve instances of the random $k$-satisfiabi lity problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that…
This paper investigates what properties a neighbourhood requires to support beneficial local search. We show that neighbourhood locality, and a reduction in cost probability towards the optimum, support a proof that search among neighbours…
Metaheuristics are known to be strong in solving large-scale instances of computationally hard problems. However, their efficiency still needs exploration in the context of instance structure, scale and numerical properties for many of…
Local search is a successful approach for solving combinatorial optimization and constraint satisfaction problems. With the progressing move toward multi and many-core systems, GPUs and the quest for Exascale systems, parallelism has become…
The pancake puzzle is a classic optimization problem that has become a standard benchmark for heuristic search algorithms. In this paper, we provide full proofs regarding the local search topology of the gap heuristic for the pancake…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
We continue the study of Genetic Algorithms (GA) on combinatorial optimization problems where the candidate solutions need to satisfy a balancedness constraint. It has been observed that the reduction of the search space size granted by…
In this paper, we present our heuristic solutions to the problems of finding the maximum and minimum area polygons with a given set of vertices. Our solutions are based mostly on two simple algorithmic paradigms: greedy method and local…
One important feature of complex systems are problem domains that have many local minima and substructure. Biological systems manage these local minima by switching between different subsystems depending on their environmental or…
The unrestricted block relocation problem is an important optimization problem encountered at terminals, where containers are stored in stacks. It consists in determining the minimum number of container moves so as to empty the considered…
Among sub-optimal MAPF solvers, rule-based algorithms are particularly appealing since they are complete. Even in crowded scenarios, they allow finding a feasible solution that brings each agent to its target, preventing deadlock…
Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
In parameter determination for the heteroskedastic probit model, both in simulated data and in actual data, we observe a failure of traditional local search methods to converge consistently to a single parameter vector, in contrast to the…
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…
We consider the problem of finding a local minimum of a binary quadratic function, and show by an elementary construction that every descending local search algorithm takes exponential time in the worst case.
In recent years, combining neural networks with local search heuristics has become popular in the field of combinatorial optimization. Despite its considerable computational demands, this approach has exhibited promising outcomes with…
Run time analysis of evolutionary algorithms recently makes significant progress in linking algorithm performance to algorithm parameters. However, settings that study the impact of problem parameters are rare. The recently proposed W-model…