An evolutive algorithm for the delineation of local labour market areas
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An evolutive approach for the delineation of local An evolutive approach for the delineation of local labour markets labour markets Local Labour Market (LLM): Area where the majority of the interaction between workers seeking jobs and employeers recruiting labour occurs. LLMs are an alternative to the use of local and regional administrative areas based on geographical or historical reasons. Traditional methods Depart from the identification of the potential centres of the LLMs and proceed by merging iteratively residual geographical units to them. Coombes method or variants of it are employed in the UK, Italy, Spain, New Zealand, Australia,… Eurostat established a code of good practices when delineating LLMs, such as self-containment, contiguity, flexibility of the method,… Our proposal Maximization of market’s internal cohesion in terms of travel-to-work flows subject to constraints of: • self-containment: most of the LLM’s workers live in that market and most of the area’s employed residents should work locally, and • minimum size: minimal allowed population of a LLM Evolutive approach where specific operators have been designed. Given a set of areas (territory). The objective is to obtain the grouping of these areas into disjoint regions to maximize a fitness function. Fitness function is based on the interaction index f(·) between an area and the rest of the areas of the same region. Maximizing the division of the territory (getting more regions) is also well considered. Individual representation Each individual represents the aggregation of all the geographical basic areas composing the whole territory into no overlapping LLMs. Vector of n components, each of which correspond to an area, and takes the value of the region the area belongs to: Recombination operators Large number of constraints led to the design of specific operators which allow a more rapid evolution to acceptable solutions. Five operators were created. Offspring is created from the recombination of two parents choosing a crossover point or a crossover region identifier. Problems because same region could have different identifier for each parent. This fact is considered in the crossover operation. Mutation operators Extensive set (ten) of operators, some of them specifically designed for the delineation of LLMS, with the aim to accelerate the obtaining of valid individuals. For instance: • Changing the region an area belongs to. • Merging an area with its optimal region (the region with a higuer interaction index with it). • Merging two regions. • Splitting a region into two. • Reassigning the areas that belongs to a set of regions. Experimentation Delineation of local labour markets in the Region of Valencia, Spain, using the data about travel-to-work derived from the Spanish Census of Population (2001). Number of municipalities (areas): 541 Population size: 100 Offspring by crossover: 25 Offspring by mutation: 98 (division operators are over- considered) Generations without changes in the best individual: 1000 Parameters of self-containment β 1 : 0.7 β 2 : 0.75 Parameters of minimum size (population) β 3 : 20,000 β 4 : 3,500 Traditional method Our evolutive proposal (best run) Comparison ⇑ Number of LLMs (regions) (62 vs. 46, Δ35%) ⇑ fitness function (191.03 vs. 129.18, Δ48%) The number of non-contiguous regions is similar Similar improved results are obtained for other parameters of self-containment and minimum size Results analysis (100 runs) Almost all the areas are grouped into the same region for every run. Assignation to the same region Number of areas Histogram Evolution of the best individual In few generations, our proposal reach the number of markets and fitness function of the traditional method. 0 10 20 30 40 50 60 70 1 1001 2001 3001 4001 5001 generations #LLMs 0,00E+00 5,00E-03 1,00E-02 1,50E-02 2,00E-02 2,50E-02 Fitness function #LLMs our proposal #LLMs Traditional Fitness our proposal Fitness Traditional Work in progress Improving convergence time for big problems Reduce the uncertainty Application of parallel approaches, Grouping Genetic algorithms, multi-objective optimization,… F. Flórez-Revuelta 1 , J.M. Casado-Díaz 2 and L. Martínez-Bernabeu 1 , 1 Department of Computing Technology, 2 Institute of International Economics, University of Alicante, P.O. Box 99, E-03080, Alicante, Spain
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Poster presented at the 9th International Conference on Parallel Problem Solving from Nature (PPSN 2006): 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 in-teraction. Note: the title included the term evolutive instead of evolutionary. I suppose it was a misspeling in a late version.
Transcript of An evolutive algorithm for the delineation of local labour market areas
An evolutive approach for the delineation of local An evolutive approach for the delineation of local labour marketslabour markets
Local Labour Market (LLM): Area where the majority ofthe interaction between workers seeking jobs andemployeers recruiting labour occurs.
LLMs are an alternative to the use of local and regional administrative areas based on geographical or historicalreasons.
Traditional methods
Depart from the identification of the potentialcentres of the LLMs and proceed by mergingiteratively residual geographical units to them.
Coombes method or variants of it are employed in the UK, Italy, Spain, New Zealand, Australia,…
Eurostat established a code of good practices when delineating LLMs, such as self-containment, contiguity, flexibility of the method,…
Our proposal
Maximization of market’s internal cohesion in terms of travel-to-work flows subject to constraints of:• self-containment: most of the LLM’s workers live in that market and most of the area’s employed residents
should work locally, and• minimum size: minimal allowed population of a LLM
Evolutive approach where specific operators have been designed.
Given a set of areas (territory). The objective is to obtain the grouping of these areas into disjoint regions to maximize a fitness function. Fitness function is based on the interaction index f(·) between an area and the rest of the areas of the same region. Maximizing the division of the territory (getting more regions) is also well considered.
Individual representation
Each individual represents the aggregation of all the geographical basic areas composing the whole territory into no overlapping LLMs.
Vector of n components, each of which correspond to an area, and takes the value of the region the area belongs to:
Recombination operators
Large number of constraints led to the design of specific operators which allow a more rapid evolution to acceptable solutions.
Five operators were created. Offspring is created from the recombination of two parents choosing a crossover point or a crossover region identifier.
Problems because same region could have different identifier for each parent. This fact is considered in the crossover operation.
Mutation operators
Extensive set (ten) of operators, some of them specifically designed for the delineation of LLMS, with the aim to accelerate the obtaining of valid individuals.
For instance:• Changing the region an area belongs to.• Merging an area with its optimal region (the
region with a higuer interaction index with it).• Merging two regions.• Splitting a region into two.• Reassigning the areas that belongs to a set of
regions.
Experimentation
Delineation of local labour markets in the Region of Valencia, Spain, using the data about travel-to-work derived from the Spanish Census of Population (2001).
Number of municipalities (areas): 541
Population size: 100
Offspring by crossover: 25Offspring by mutation: 98 (division operators are over-considered)
Generations without changes in the best individual: 1000
Parameters of self-containmentβ1: 0.7β2: 0.75
Parameters of minimum size (population)β3: 20,000β4: 3,500
Traditionalmethod
Our evolutiveproposal (best run)
Comparison
⇑ Number of LLMs (regions)(62 vs. 46, Δ35%)
⇑ fitness function(191.03 vs. 129.18, Δ48%)
The number of non-contiguous regions is similar
Similar improved results are obtained for other parameters of
self-containment and minimum size
Results analysis (100 runs)
Almost all the areas are grouped into the same region for every run.
Assignation to the same region
Num
ber o
f are
as
Histogram
Evolution of the best individual
In few generations, our proposal reach the number of markets and fitness function of the traditional method.
0
10
20
30
40
50
60
70
1 1001 2001 3001 4001 5001
generations
#LLM
s
0,00E+00
5,00E-03
1,00E-02
1,50E-02
2,00E-02
2,50E-02
Fitn
ess
func
tion
#LLMs our proposal #LLMs TraditionalFitness our proposal Fitness Traditional
Work in progress
Improving convergence time for big problems Reduce the uncertainty
Application of parallel approaches, Grouping Genetic algorithms, multi-objective optimization,…
F. Flórez-Revuelta1, J.M. Casado-Díaz2 and L. Martínez-Bernabeu1, 1Department of Computing Technology, 2Institute of International Economics, University of Alicante, P.O. Box 99, E-03080, Alicante, Spain
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