An evolutionary approach to the delineation of functional areas based on travel-to-work flows

This paper presents a new approach to the delineation of local labor markets based on evolutionary computation. The aim of the exercise is the division of a given territory into functional regions based on travel-to-work flows. Such regions are defined so that a high degree of inter-regional separation and of intra-regional integration in both cases in terms of commuting flows is guaranteed. Additional requirements include the absence of overlap between delineated regions and the exhaustive coverage of the whole territory. The procedure is based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. In the experimentation stage, two variations of the fitness function are used, and the process is also applied as a final stage for the optimization of the results from one of the most successful existing methods, which are used by the British authorities for the delineation of travel-to-work areas (TTWAs). The empirical exercise is conducted using real data for a sufficiently large territory that is considered to be representative given the density and variety of travel-to-work patterns that it embraces. The paper includes the quantitative comparison with alternative traditional methods, the assessment of the performance of the set of operators which has been specifically designed to handle the regionalization problem and the evaluation of the convergence process. The robustness of the solutions, something crucial in a research and policy-making context, is also discussed in the paper.

Grouping genetic operators for the delineation of functional areas based on spatial interaction

The delineation of functional economic areas, or market areas, is a problem of high practical relevance, since the delineation of functional sets such as economic areas in the US, Travel-to-Work Areas in the United Kingdom, and their counterparts in other OECD countries are the basis of many statistical operations and policy making decisions at local level. This is a combinatorial optimisation problem defined as the partition of a given set of indivisible spatial units (covering a territory) into regions characterised by being (a) self-contained and (b) cohesive, in terms of spatial interaction data (flows, relationships). Usually, each region must reach a minimum size and self-containment level, and must be continuous. Although these optimisation problems have been typically solved through greedy methods, a recent strand of the literature in this field has been concerned with the use of evolutionary algorithms with ad hoc operators. Although these algorithms have proved to be successful in improving the results of some of the more widely applied official procedures, they are so time consuming that cannot be applied directly to solve real-world problems. In this paper we propose a new set of group-based mutation operators, featuring general operations over disjoint groups, tailored to ensure that all the constraints are respected during the operation to improve efficiency. A comparative analysis of our results with those from previous approaches shows that the proposed algorithm systematically improves them in terms of both quality and processing time, something of crucial relevance since it allows dealing with most large, real-world problems in reasonable time.

A memetic algorithm for the delineation of local labour markets

Given a territory composed of basic geographical units, the delineation of local labour market areas (LLMAs) can be seen as a problem in which those units are grouped subject to multiple constraints. In previous research, standard genetic algorithms were not able to find valid solutions, and a specific evolutionary algorithm was developed. The inclusion of multiple ad hoc operators allowed the algorithm to find better solutions than those of a widely-used greedy method. However, the percentage of invalid solutions was still very high. In this paper we improve that evolutionary algorithm through the inclusion of (i) a reparation process, that allows every invalid individual to fulfil the constraints and contribute to the evolution, and (ii) a hillclimbing optimisation procedure for each generated individual by means of an appropriate reassignment of some of its constituent units. We compare the results of both techniques against the previous results and a greedy method.

The circumstellar environment and evolutionary status of the supergiant B[e] star Wd1-9

Context. Historically, supergiant (sg)B[e] stars have been difficult to include in theoretical schemes for the evolution of massive OB stars. Aims. The location of Wd1-9 within the coeval starburst cluster Westerlund 1 means that it may be placed into a proper evolutionary context and we therefore aim to utilise a comprehensive multiwavelength dataset to determine its physical properties and consequently its relation to other sgB[e] stars and the global population of massive evolved stars within Wd1. Methods. Multi-epoch R- and I-band VLT/UVES and VLT/FORS2 spectra are used to constrain the properties of the circumstellar gas, while an ISO-SWS spectrum covering 2.45−45μm is used to investigate the distribution, geometry and composition of the dust via a semi-analytic irradiated disk model. Radio emission enables a long term mass-loss history to be determined, while X-ray observations reveal the physical nature of high energy processes within the system. Results. Wd1-9 exhibits the rich optical emission line spectrum that is characteristic of sgB[e] stars. Likewise its mid-IR spectrum resembles those of the LMC sgB[e] stars R66 and 126, revealing the presence of equatorially concentrated silicate dust, with a mass of ~10−4M⊙. Extreme historical and ongoing mass loss (≳ 10−4M⊙yr−1) is inferred from the radio observations. The X-ray properties of Wd1-9 imply the presence of high temperature plasma within the system and are directly comparable to a number of confirmed short-period colliding wind binaries within Wd1. Conclusions. The most complete explanation for the observational properties of Wd1-9 is that it is a massive interacting binary currently undergoing, or recently exited from, rapid Roche-lobe overflow, supporting the hypothesis that binarity mediates the formation of (a subset of) sgB[e] stars. The mass loss rate of Wd1-9 is consistent with such an assertion, while viable progenitor and descendent systems are present within Wd1 and comparable sgB[e] binaries have been identified in the Galaxy. Moreover, the rarity of sgB[e] stars - only two examples are identified from a census of ~ 68 young massive Galactic clusters and associations containing ~ 600 post-Main Sequence stars - is explicable given the rapidity (~ 104yr) expected for this phase of massive binary evolution.

Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Mathematical morphology has been an area of intensive research over the last few years. Although many remarkable advances have been achieved throughout these years, there is still a great interest in accelerating morphological operations in order for them to be implemented in real-time systems. In this work, we present a new model for computing mathematical morphology operations, the so-called morphological trajectory model (MTM), in which a morphological filter will be divided into a sequence of basic operations. Then, a trajectory-based morphological operation (such as dilation, and erosion) is defined as the set of points resulting from the ordered application of the instant basic operations. The MTM approach allows working with different structuring elements, such as disks, and from the experiments, it can be extracted that our method is independent of the structuring element size and can be easily applied to industrial systems and high-resolution images.

Multi-objective adaptive evolutionary strategy for tuning compilations

Tuning compilations is the process of adjusting the values of a compiler options to improve some features of the final application. In this paper, a strategy based on the use of a genetic algorithm and a multi-objective scheme is proposed to deal with this task. Unlike previous works, we try to take advantage of the knowledge of this domain to provide a problem-specific genetic operation that improves both the speed of convergence and the quality of the results. The evaluation of the strategy is carried out by means of a case of study aimed to improve the performance of the well-known web server Apache. Experimental results show that a 7.5% of overall improvement can be achieved. Furthermore, the adaptive approach has shown an ability to markedly speed-up the convergence of the original strategy.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).