Strategic districting for the mitigation of educational segregation : a pilot model for school district optimization in Helsinki

Helsingin kaupunkirakenne on eriytynyt viimeisten vuosikymmenien aikana merkittävästi sosiaalisilla mittareilla tarkasteltuna. Kehitys on heijastunut kouluihin oppilaspohjien ja oppimistuloksien erojen kasvuna, minkä lisäksi Helsingissä on löydetty viitteitä myös itsenäisistä kouluvaikutuksista. Koulujen eriytymiskehityksen pelätään mainevaikutuksen kautta kiihdyttävän alueellista segregaatiota ja siten oppilaspohjien eriytymistä entisestään. Oppilaspohjien eroihin on kuitenkin mahdollista vaikuttaa määrittämällä oppilasalueet uudelleen tavalla, joka minimoi oppilasalueiden välisiä sosiaalisia eroja mahdollisimman tehokkaasti. Tätä varten tarvitaan uudenlaisia, koneoppimiseen perustuvia optimointityökaluja. Tämän opinnäytetyön päätavoitteena on tutkia mahdollisuutta optimoida Helsingin oppilasalueita väestöpohjiltaan sisäisesti heterogeenisemmiksi ja keskenään homogeenisemmiksi. Tavoitetta varten olen kehittänyt työssäni automatisoidun optimointimallin, joka minimoi sosiaalisten muuttujien varianssia oppilasalueiden välillä oppilasalueiden muotoa varioimalla. Mallin pilottisovelluksessa optimoin Helsingin oppilaaksiottoalueita tasaisemmiksi käyttäen optimoitavana muuttujana vieraskielisen väestön osuutta. Olemassa olevaa kouluverkostoa eli koulujen sijaintia, oppilasalueiden maantieteellistä yhtenäisyyttä, enimmäisoppilasmääriä koulukohtaisella marginaalilla sekä koulukohtaista koulumatkan enimmäispituutta on käytetty mallissa alueiden muodostamista rajoittavina tekijöinä. Tutkimukseni keskeinen löydös on, että oppilasaluerajoja siirtelemällä oppilasalueiden sosiaalisen pohjan eroihin voidaan vaikuttaa Helsingissä merkittävästi. Malli vaatii kuitenkin vielä perusteellista jatkokehittämistä soveltuakseen aluejakojen käytännön suunnitteluun, ja tässä vaiheessa sen merkittävimmät kehityskohteet liittyvät optimoitujen alueiden muotoon, mallin laskennalliseen vaativuuteen ja koulumatkojen turvallisuutta mittaavan optimointiparametrin puuttumiseen.The social urban structure of Helsinki has experienced a significant rise in spatial differences during the last two decades. This development has reflected on schools as rising differences between schools’ student compositions and learning outcomes. Additionally, signs of independent school effects have been observed in several studies. The differentiation of student compositions is feared to exacerbate residential segregation and differentiate schools’ operating environments further. It is possible, however, to intervene this development by drawing the school attendance districts such that the social differences between schools’ student compositions are effectively minimized. For this purpose, new machine learning based optimization tools are needed. The main objective of this master’s thesis study is to examine the possibility to optimize Helsinki’s school districts toward more internally heterogeneous and externally homogeneous social compositions. For this purpose, I have developed an optimization model that minimizes the variance of social variables between school districts by iteratively redrawing the districts’ borders. In a pilot application of the model I optimize the school districts of Helsinki by using the share of population with immigrant background as the optimization variable, while existing school infrastructure (the school locations and student capacities), spatial contiguity of the districts, and school-specific maximum travel distances are used as constraints restricting the shapes that the districts can take. The core finding of this study is that in Helsinki, the social compositions of school districts can be significantly evened out by redrawing the school district borders. However, for the model to be suitable for district planning in practice it needs further development. At this stage, the main limitations of the model are related to the shapes of the optimized districts, the model’s time complexity and the lack of a constraint or optimization parameter that accounts for the safety of children’s school trips

A mathematical model and application on the prevention of gerrymandering

The significance of the political districting also known as redistricting has been recognized by several countries across the world since electoral district boundaries can be manipulated for a political gain. This manipulation practice is known as gerrymandering and has serious influences on the results of an election. In this thesis, we tried to show how easy policymakers can misuse the redistricting practice to gain a political advantage such as increasing the number of their representatives in the parliament. Two different mathematical models have been developed for different types of election systems. Single-member district electoral system in which the only representative can be elected from each electoral district is one of them. Every county in ˙Istanbul has been tried to be divided into their single-member districts considering the total number of representatives of the county. In addition to the first model, another formulation has been developed to also cover the multi-member district systems. The main drawback of the mathematical models is that they are only working on the small cases in terms of the total number of political units. Tabu search algorithm has been developed to answer the cases that cannot be classified as small. The required algorithm steps such as initialization, neighborhood change structure etc. are explained in detail. The results of the mathematical models and the algorithm have been achieved and visualized aesthetically

A benchmark test problem toolkit for multi-objective path optimization

Due to the complexity of multi-objective optimization problems (MOOPs) in general, it is crucial to test MOOP methods on some benchmark test problems. Many benchmark test problem toolkits have been developed for continuous parameter/numerical optimization, but fewer toolkits reported for discrete combinational optimization. This paper reports a benchmark test problem toolkit especially for multi-objective path optimization problem (MOPOP), which is a typical category of discrete combinational optimization. With the reported toolkit, the complete Pareto front of a generated test problem of MOPOP can be deduced and found out manually, and the problem scale and complexity are controllable and adjustable. Many methods for discrete combinational MOOPs often only output a partial or approximated Pareto front. With the reported benchmark test problem toolkit for MOPOP, we can now precisely tell how many true Pareto points are missed by a partial Pareto front, or how large the gap is between an approximated Pareto front and the complete one

Districting Problems - New Geometrically Motivated Approaches

This thesis focuses on districting problems were the basic areas are represented by points or lines. In the context of points, it presents approaches that utilize the problem\u27s underlying geometrical information. For lines it introduces an algorithm combining features of geometric approaches, tabu search, and adaptive randomized neighborhood search that includes the routing distances explicitly. Moreover, this thesis summarizes, compares and enhances existing compactness measures

An ontology of ethnicity based upon personal names: with implications for neighbourhood profiling

Understanding of the nature and detailed composition of ethnic groups remains key to a vast swathe of social science and human natural science. Yet ethnic origin is not easy to define, much less measure, and ascribing ethnic origins is one of the most contested and unstable research concepts of the last decade - not only in the social sciences, but also in human biology and medicine. As a result, much research remains hamstrung by the quality and availability of ethnicity classifications, constraining the meaningful subdivision of populations. This PhD thesis develops an alternative ontology of ethnicity, using personal names to ascribe population ethnicity, at very fine geographical levels, and using a very detailed typology of ethnic groups optimised for the UK population. The outcome is an improved methodology for classifying population registers, as well as small areas, into cultural, ethnic and linguistic groups (CEL). This in turn makes possible the creation of much more detailed, frequently updatable representations of the ethnic kaleidoscope of UK cities, and can be further applied to other countries. The thesis includes a review of the literature on ethnicity measurement and name analysis, and their applications in ethnic inequalities and geographical research. It presents the development of the new name to ethnicity classification methodology using both a heuristic and an automated and integrated approach. It is based on the UK Electoral Register as well as several health registers in London. Furthermore, a validation of the proposed name-based classification using different datasets is offered, as well as examples of applications in profiling neighbourhoods by ethnicity, in particular the measurement of residential segregation in London. The main study area is London, UK

Multi-period sales districting problem

In the sales districting problem, we are given a set of customers and a set of salesmen in some area. The salesmen have to provide services at the customers' locations to satisfy their requirements. The task is to allocate each customer to one salesman, which partitions the set of customers into subsets, called districts. Each district is expected to have approximately equal workload and travel time for each salesman to promote fairness among them. Also, the districts should be geographically compact since they are more likely to reduce unnecessary travel time, which is desirable for economic reasons. Moreover, each customer can require recurring services with different visiting frequencies such as every week or two weeks during a planning horizon. This problem is called the `Multi-Period Sales Districting Problem (MPSDP)' and can be found typically in regular engineering maintenance and sales promotion. In addition to determining the sales districts, we also want to get valid weekly visiting schedules for the salesmen corresponding to the customers' visiting requirements. The schedules should result in weekly districts with the following desirable characteristics: each weekly district should be balanced in weekly workload and geographically compact. The compactness in the schedules provides benefits when a salesman has to deal with short-term requests from customers or change a visiting plan during the week. Namely, the salesman can postpone a visit to another day if necessary, without increasing the travel time too much compared to the original schedule. This is beneficial when the salesman has to deal with unexpected situations, for example, road maintenance, traffic jams, or short notice of time windows from customers. Although the problem is very practical, it has been studied only recently. Since most of the previous literature on general scheduling problems did not consider compactness, a few recent studies have begun to focus on solving the scheduling part of the problem. The purpose of this research is to develop a more sophisticated exact solution approach as well as an efficient high-quality heuristic to solve the scheduling part. Eventually, with an effective elaborate method to solve the scheduling part, we aim for a robust algorithm to solve the districting and scheduling part of the problem simultaneously. This thesis contains three main parts. The first part introduces the problem and provides a mixed-integer linear programming formulation for only the scheduling part and formulation for the whole problem. The second part presents solution approaches, including an exact method and a heuristic, for only the scheduling part. The last part is dedicated to further development of a successful approach from the second part to solve the districting and scheduling part of the problem simultaneously. For solving the scheduling part, Benders' decomposition is developed as a new exact solution method. The linear relaxation of the problem is strengthened by adding several Benders' cuts derived from fractional solutions at the beginning of the algorithm. Moreover, a good-quality integer solution derived from a location-allocation heuristic is used to generate cuts beforehand, which significantly improves the upper bound of the objective function value. Nondominated optimality cuts are implemented to guarantee the strongest Benders' cuts in each iteration. Also, instead of generating a Benders' cut per iteration, we exploit the decomposable structure of the problem formulation to generate multiple cuts per iteration, resulting in a noticeable improvement in the lower bound of the objective function value. In the classical Benders' decomposition, one of the main factors that slow down the algorithm is that one has to solve the integer programmes from scratch in each iteration. To alleviate this problem, a modern implementation creates only one branch-and-bound tree and adds Benders' cuts derived from a solution in each node in a solution cut pool. This method is called branch-and-Benders' cut. To assess the suitability of the algorithm, we compare its performance on small data instances that contain 30$-$50 customers to the Benders' algorithm in CPLEX and show that our algorithm is highly competitive. Since an exact solution method usually struggles to solve realistic large data instances, a meta-heuristic called tabu search is proposed. A high-quality initial solution to start the algorithm is derived from the location-allocation heuristic. Three different neighbourhoods based on information about week centres or customers' week patterns are created within which we search for the best solution. An infeasible solution is allowed in the search to expand the search space. During the search, the size of a whole neighbourhood can be excessively large, so we limit the search to promising areas of the solution space to save computational time. Also, a surrogate objective value is used to save on computational time in cases when computing the real objective value is too time-consuming. Although the tabu search defines a list of forbidden moves to avoid the cycle of solutions, the algorithm can still struggle to avoid being trapped around a local optimum. Therefore, a diversification scheme is proposed for such cases. The algorithm is also accelerated by combining all neighbourhoods and selecting the appropriate neighbourhood for each iteration by a roulette wheel selection. It shows impressive results in small data instances that contain 30$-$50 customers. The comparison with built-in heuristics in CPLEX confirms the robustness of the tabu search algorithm. Finally, we combine the tabu search algorithm with our developed Benders' decomposition. Numerical results show that the tabu search method improves the upper bound of the Benders' decomposition algorithm. However, the overall performance is not satisfying so the combination of these two techniques still requires more proper development. As the tabu search algorithm performs well on the scheduling part, it is extended to solve the whole problem, i.e., the districting and scheduling part at the same time. Computational results on large data instances, which contain between 100 and 300 customers, demonstrate its capacity to derive a high-quality solution within a reasonable amount of time, i.e., less than 17 minutes. At the same time, the Benders' decomposition algorithm in CPLEX, which is a benchmark in this case, and the built-in heuristics in CPLEX cannot even find any feasible integer solution for most of the instances within an hour. Importantly, there is a conflict between the districting part and the scheduling part so we recommend solving both parts simultaneously for tackling the MPSDP. The multi-period sales districting problem is highly practical and challenging to solve. To the best of our knowledge, we are the first to propose a single integrated solution approach to solve the whole problem. Further studies including adding more realistic planning requirements into consideration and effective solution approaches to solve the problem are still required