Migrant Resettlement by Evolutionary Multi-objective Optimization

TL;DR

A new framework called migrant resettlement by evolutionary multiobjective optimization (MR-EMO), which reformulates migrant resettlement as a biobjective optimization problem that maximizes the expected number of employed migrants and minimizes the number of dispatched migrants simultaneously, and employs a multiobjective evolutionary algorithm (MOEA) to solve the biobjective problem.

Abstract

Migration has been a universal phenomenon, which brings opportunities as well as challenges for global development. As the number of migrants (e.g., refugees) increases rapidly in recent years, a key challenge faced by each country is the problem of migrant resettlement. This problem has attracted scientific research attention, from the perspective of maximizing the employment rate. Previous works mainly formulated migrant resettlement as an approximately submodular optimization problem subject to multiple matroid constraints and employed the greedy algorithm, whose performance, however, may be limited due to its greedy nature. In this paper, we propose a new framework MR-EMO based on Evolutionary Multi-objective Optimization, which reformulates Migrant Resettlement as a bi-objective optimization problem that maximizes the expected number of employed migrants and minimizes the number of dispatched migrants simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve the bi-objective problem. We implement MR-EMO using three MOEAs, the popular NSGA-II, MOEA/D as well as the theoretically grounded GSEMO. To further improve the performance of MR-EMO, we propose a specific MOEA, called GSEMO-SR, using matrix-swap mutation and repair mechanism, which has a better ability to search for feasible solutions. We prove that MR-EMO using either GSEMO or GSEMO-SR can achieve better theoretical guarantees than the previous greedy algorithm. Experimental results under the interview and coordination migration models clearly show the superiority of MR-EMO (with either NSGA-II, MOEA/D, GSEMO or GSEMO-SR) over previous algorithms, and that using GSEMO-SR leads to the best performance of MR-EMO.

Figures (5)

• Figure 1: (a) An illustration of a migrant resettlement problem instance, where each edge (migrant-locality pair) denotes that the migrant is assigned to the locality. (b) The heat map of a migrant resettlement problem instance (where six migrants go to two localities to find jobs under the interview migration model) in the solution space. The color of a point corresponds to the objective function value, i.e., the expected number of migrants who find employment, of a solution; a point with the darkest color (i.e., the value $-1$) implies an infeasible solution.
• Figure 2: A feasible solution (Boolean vector representation and matrix representation) of a migrant resettlement problem instance with six migrants and three localities, where each locality can accommodate at most two migrants.
• Figure 3: Examples illustration of (a) one-point crossover and (b) bit-wise mutation.
• Figure 4: Example illustration of (a) matrix-swap mutation by rows and (b) matrix-swap mutation by columns, and (c) repairing an infeasible solution.
• Figure 5: One each migration model, the objective value vs. runtime (i.e., number of objective evaluations) with $|V|=120$, $|L|=16$, $|J|=80$ and $|\Pi|=20$, respectively.

Theorems & Definitions (13)

• Definition 1: Migrant Resettlement
• Definition 2: $\epsilon$-Approximate Submodularity horel2016maximizationqian2019maximizing
• Definition 3: Domination
• Definition 4: Matrix-swap mutation
• Definition 5: Repair mechanism
• Theorem 1
• Definition 6: $(1+\delta)$-approximate $p$-local optimum
• Lemma 1
• Lemma 2: Lemma 1.1 in jonlee10
• Lemma 3: Lemma 1.2 in jonlee10