Probabilistic Analysis of Edge Elimination for Euclidean TSP

One way to speed up the calculation of optimal TSP tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so several edge elimination approaches have been proposed in the past. In this work we investigate two of them in the scenario where the input consists of $n$ independently distributed random points in the 2-dimensional unit square with bounded density function from above and below by arbitrary positive constants. We show that after the edge elimination procedure of Hougardy and Schroeder the expected number of remaining edges is $\Theta(n)$, while after that the the non-recursive part of Jonker and Volgenant the expected number of remaining edges is $\Theta(n^2)$

Parameterized Complexity Analysis of Randomized Search Heuristics

This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running time of algorithms solving combinatorial problems in finer detail than traditional approaches from classical complexity theory. We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a graph, finding a maximum leaf spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of Evolutionary Computation: Recent Developments in Discrete Optimization", edited by Benjamin Doerr and Frank Neumann, published by Springe

Gamesourcing: Perspectives and Implementations

This chapter discusses game-based methods of problem solution and data processing, analysis, and information mining. Attention is mainly focused on swarm algorithm and principles used in the task of complex problem solving using computer games. We intensively discuss the interdisciplinary intersection between swarm systems dynamics and computer science, including a variety of data sources and examples. Possibilities of the new approach based on swarm algorithm used in a game or using principles of swarm algorithms to solve the problem are demonstrated here. More precisely, this chapter discusses modern methods of calculation and crowd use, so-called gamesourcing, i.e., game-driven crowdsourcing, from various points of view such as history, motivation, or paradigm and presents several examples of contemporary projects of this kind. Ideas, results, and methodologies reported and mentioned here are based on our previous results and experiments that are fully reported here for detailed study in the case of reader’s interest. Therefore, this chapter is an overview survey of our research

Are visual cortex maps optimized for coverage?

The elegant regularity of maps of variables such as ocular dominance, orientation, and spatial frequency in primary visual cortex has prompted many people to suggest that their structure could be explained by an optimization principle. Up to now, the standard way to test this hypothesis has been to generate artificial maps by optimizing a hypothesized objective function and then to compare these artificial maps with real maps using a variety of quantitative criteria. If the artificial maps are similar to the real maps, this provides some evidence that the real cortex may be optimizing a similar function to the one hypothesized. Recently, a more direct method has been proposed for testing whether real maps represent local optima of an objective function (Swindale, Shoham, Grinvald, Bonhoeffer, & Hilbener, 2000). In this approach, the value of the hypothesized function is calculated for a real map, and then the real map is perturbed in certain ways and the function recalculated. If each of these perturbations leads to a worsening of the function, it is tempting to conclude that the real map is quite likely to represent a local optimum of that function. In this article, we argue that such perturbation results provide only weak evidence in favor of the optimization hypothesis

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

Survey of Robot 3D Path Planning Algorithms

Robot 3D (three-dimension) path planning targets for finding an optimal and collision-free path in a 3D workspace while taking into account kinematic constraints (including geometric, physical, and temporal constraints). The purpose of path planning, unlike motion planning which must be taken into consideration of dynamics, is to find a kinematically optimal path with the least time as well as model the environment completely. We discuss the fundamentals of these most successful robot 3D path planning algorithms which have been developed in recent years and concentrate on universally applicable algorithms which can be implemented in aerial robots, ground robots, and underwater robots. This paper classifies all the methods into five categories based on their exploring mechanisms and proposes a category, called multifusion based algorithms. For all these algorithms, they are analyzed from a time efficiency and implementable area perspective. Furthermore a comprehensive applicable analysis for each kind of method is presented after considering their merits and weaknesses