Lucas Martínez-Bernabeu

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.

A Parallel evolutionary algorithm for the hub location problem with fully interconnected backbone and access networks

This paper proposes a parallel evolutionary algorithm to tackle the Fully Interconnected Network Design Problem (FINDP), a specific application of hub location to network design. The FINDP has been recently proposed as an NP-hard combinatorial optimization problem formed by two smaller sub-problems: first, given the nodes which form the network, classify them as belonging to the backbone network or not. The second sub-problem consists of assigning the access network to a hub (node of the backbone network). In this paper we propose a parallel evolutionary algorithm to tackle the FINDP. We describe the architecture and how to structure the algorithm to solve the problem. Experimental tests have been carried out in several synthetic instances, and a comparison with existing approaches have shown the good performance of our algorithm.

Specific crossover and mutation operators for a grouping problem based on interaction data in a regional science context

This paper proposes a set of specific crossover and mutation operators for the delineation of functional regions through evolutionary computation. We consider a problem of dividing a given territory into local labor market areas based on spatial interaction data. Such areas are defined so that a high degree of inter-regional separation and intra-regional integration - in both cases in terms of commuting flows - exist. A genetic algorithm has been designed based on the maximization of a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Additional requirements, typical of any functional regionalization, include the absence of overlapping between delineated regions and an exhaustive coverage of the whole territory (so all basic spatial units must be allocated to one and only one-region). The complex set of restrictions results in conventional operators often generating invalid solutions, impeding or delaying the evolutionary process. This is the reason why an extensive set of operators has been designed that incorporates knowledge about the problem, allowing the evolution of the set of solutions towards the final result.

An evolutionary approach to the delimitation of labour market areas: an empirical application for Chile

ABSTRACT An evolutionary approach to the delimitation of labour market areas: an empirical application for Chile. Spatial Economic Analysis. Labour market areas (LMAs) are argued to represent a more appropriate policy framework than administrative units for the analysis of spatial labour market activity. This article develops LMAs for Chile by applying an evolutionary computation approach. This innovative approach defines LMAs through an optimization process by maximization of internal cohesion, subject to restrictions of minimum levels of self-containment and population. To evaluate the appropriateness of the LMAs, comparative analyses are performed between alternative delimitations based on different parameter configurations of the proposed method versus administrative boundaries and the most widely used method for official LMA delimitation, the travel-to-work areas method.

Inside the metropolis: the articulation of Spanish metropolitan areas into local labor markets

In this article, we delimit local labor markets (LLMs) in order to analyze the internal structure and organization of Spanish metropolitan areas. LLMs are defined as self-contained and cohesive areas in terms of commuting flows. Unlike the conventional approach to polycentrism based on the analysis of commuting flows that begins with the identification of subcenters, our analytical strategy does assume any a priori structure and is compatible with the relationship between places of work and residence having other locational and spatial organization patterns. The analysis is performed at three different scales of detail linked to three self-containment levels for the LLMs delimited and three population groups (total, males, and females). The results show that metropolitan areas are complex, fuzzy, multidimensional spaces, where the conditions of spatial organization are manifested in different ways depending on the parameters and variables used.

Adaptive evolutionary algorithms 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. The experimentation process showed that the rate of success of each operator in generating good individuals is different and evolves with time. We therefore propose different adaptive alternatives that modify the probabilities of application of each operator throughout the evolutionary process, and compare the results of such adaptive approaches with previous results and a greedy method.

An evolutive approach for the delineation of local labour markets

This paper presents a new approach to the delineation of local labour markets based on evolutionary computation. The main objective is the regionalisation of a given territory into functional regions based on commuting flows. According to the relevant literature, such regions are defined so that (a) their boundaries are rarely crossed in daily journeys to work, and (b) a high degree of intra-area movement exists. This proposal merges municipalities into functional regions by maximizing a fitness function that measures aggregate intra-region interaction under constraints of inter-region separation and minimum size. Real results are presented based on the latest database from the Census of Population in the Region of Valencia. Comparison between the results obtained through the official method which currently is most widely used (that of British Travel-to-Work Areas) and those from our approach is also presented, showing important improvements in terms of both the number of different market areas identified that meet the statistical criteria and the degree of aggregate intra-market interaction.