The component model for elementary landscapes and partial neighborhoods

Theoretical Computer Science, 545, (2014), pp. 59-75Local search algorithms exploit moves on an adjacency graph of the search space. An “elementary landscape” exists if the objective function f is an eigenfunction of the Laplacian of the graph induced by the neighborhood operator; this allows various statistics about the neighborhood to be computed in closed form. A new component based model makes it relatively simple to prove that certain types of landscapes are elementary. The traveling salesperson problem, weighted graph (vertex) coloring and the minimum graph bisection problem yield elementary landscapes under commonly used local search operators. The component model is then used to efficiently compute the mean objective function value over partial neighborhoods for these same problems. For a traveling salesperson problem over n cities, the 2-opt neighborhood can be decomposed into ⌊n/2−1⌋ partial neighborhoods. For graph coloring and the minimum graph bisection problem, partial neighborhoods can be used to focus search on those moves that are capable of producing a solution with a strictly improving objective function value.Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422

Elementary Landscape Decomposition of the Hamiltonian Path Optimization Problem

There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that dis- play this structure are called “Elementary Landscapes” and they have a number of special mathematical properties. The problems that are not elementary landscapes can be decomposed in a sum of elementary ones. This sum is called the elementary landscape decomposition of the problem. In this paper, we provide the elementary landscape decomposi- tion for the Hamiltonian Path Optimization Problem under two different neighborhoods.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Quasi-elementary Landscapes and Superpositions of Elementary Landscapes

Whitley, D., & Chicano F. (2012). Quasi-elementary Landscapes and Superpositions of Elementary Landscapes. (Hamadi, Y., & Schoenauer M., Ed.).Learning and Intelligent Optimization - 6th International Conference, LION 6, Paris, France, January 16-20, 2012, Revised Selected Papers. 277–291.There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called “Elementary Landscapes” and they have a number of special mathematical properties. The term “Quasi-elementary landscapes” is introduced to describe landscapes that are “almost” elementary; in quasi-elementary landscapes there exists some efficiently computed “correction” that captures those parts of the neighborhood structure that deviate from the normal structure found in elementary landscapes. The “shift” operator, as well as the “3-opt” operator for the Traveling Salesman Problem landscapes induce quasi-elementary landscapes. A local search neighborhood for the Maximal Clique problem is also quasi-elementary. Finally, we show that landscapes which are a superposition of elementary landscapes can be quasi-elementary in structure.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-11-1-0088. Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)

FUNCTIONAL BARRIERS IN IASI URBAN AREA

The forced industrialisation of cities resulted in the construction of giant sites in outlying areas. December 1989 triggered the decline of industrial activities, wich could not be sustained any longer. Gradually, industrial halls have been abandoned, turning into ghosts of past glory, „black spots” that visually pollute the city’s image. The article highlitghts the tendency of these abandoned spaces to become true functional barriers. Occupying large spaces, the former industrial units are a barrier to communication (moving obstacle) and for the development of certain areas. Perceveid as dangerous places, with a low security level, the problem of abandoned areas would be a subject for the terriorial marketing strategies. in this regard, putting into value the results of a field survey, the article studies the perception of the urban brownfields, applied for Ia?i as a case study.industrial zone, functional barrier, communication, perception, image.

Simon-Ando decomposability and fitness landscapes

In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems

Elementary landscape decomposition of the frequency assignment problem

Theoretical Computer Science 412(43),2011, pp.6002-6019The Frequency Assignment Problem (FAP) is an important problem that arises in the design of radio networks, when a channel has to be assigned to each transceiver of the network. This problem is a generalization of the graph coloring problem. In this paper we study a general version of the FAP that can include adjacent frequency constraints. Using concepts from landscapes’ theory, we prove that this general FAP can be expressed as a sum of two elementary landscapes. Further analysis also shows that some subclasses of the problem correspond to a single elementary landscape. This allows us to compute the kind of neighborhood information that is normally associated with elementary landscapes. We also provide a closed form formula for computing the autocorrelation coefficient for the general FAP, which can be useful as an a priori indicator of the performance of a local search method.This work has been partially funded by the Spanish Ministry of Science and Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project). Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422