یک الگوریتم تکاملی چندهدفه برای بهبود مدلسازی هیبریدمحور شبکه‌های بیزین

Bayesian Networks are increasingly being used to model complex socio-economic systems by expert knowledge elicitation even when data is scarce or does not exist. In this paper, a Multi-Objective Evolutionary Algorithm (MOEA) is presented for assessing the parameters (input relevance/weights) of fuzzy dependence relationships in a Bayesian Network (BN). The MOEA was designed to include a hybrid model that combines Monte-Carlo simulation and fuzzy inference. The MOEA-based prototype assesses the input weights of fuzzy dependence relationships by learning from available output data. In socio-economic systems, the determination of how a specific input variable affects the expected results can be critical and it is still one of the most important challenges in Bayesian modeling. The MOEA was checked by estimating the migrant stock as a relevant variable in a BN model for forecasting remittances. For a specific year, results showed similar input weights than those given by economists but it is very computationally demanding. The proposed hybrid-approach is an efficient procedure to estimate output values in BN.

Remittances have been defined as “transfers made by migrants who are employed and have lived, at least one year, in other economies” [1]. In the case of developing countries, where the number of migrants by 2010 exceeds 171 million people (3% of the population), remittances have increased significantly over the past two decades, from US$60,000 MM in 1990 to US$325,000 MM in 2010 [2]. These financial flows amount to 2% of the GDP for developing countries and in some cases outnumber 25% of the GDP [3]. Remittance size, its counter-cyclical nature and their resilience have turned them into the second largest source of foreign currency for the developing world. Consequently, the sustainability debt of those countries is stronger, making their access to international capital markets also easier [3]. However, empirical studies have showed that remittances can also have negative effects on labor supply, inflation and real exchange rate, and mixed effects on the economic growth of the recipient economies [4]. In recipient economies, the estimation of the macroeconomic effects of remittances is critical. In this context, there have been some attempts to estimate remittance flows by using econometric techniques [5] and [6]. These studies highlighted that the lack of information and the poor quality of available data are the main obstacles for accurate forecasting. In addition, the economic literature about remittances reveals the complex nature of this phenomenon, in which a plethora of macroeconomic and microeconomic variables are involved [7]. On this basis, García-Alonso et al. [8] dealt with a remittance estimation problem by combining Bayesian Networks (BN), Monte Carlo simulation (MCS) and Fuzzy logic (FL). Expert-knowledge elicitation and learning from data can be used for stochastic assessment of BN. The former is a widely used alternative to develop BN when data is scarce or does not exist, but this process may be costly and time-consuming [9]. When data is available, several approaches can be used to develop BN, including structural equations [10] and learning algorithms [11]. Structural equations need prior expert knowledge to define the basic structure of the BN and then this method calculates the relevance of variables and their relationships according to a strong set of initial hypotheses [12]. Learning algorithms are devoted to discovering both the BN structure [13], [14] and [15] and its parameters [16], [17] and [18] from data. However, these algorithms can be very sensitive to the initial setting chosen by researchers and large amount of data are required [19]. In addition, given the complexity and stochastic nature of complex systems, algorithms have to operate in huge search spaces and they could be easily trapped into the numerous sub-optimal solutions [19]. To overcome some of these drawbacks, meta-heuristic approaches have been applied, such as evolutionary algorithms [20] and [21], evolutionary programming [22] and [23] and ant colony optimization [24] and [25]. Finally hybrid-approaches, combining expert knowledge and automated learning, have also being designed and developed to guide and speed up the process of learning efficient BN structures and parameters [26] and [27]. In this paper, the approach developed by [8] is enhanced by including a Multi-Objective Evolutionary Algorithm (MOEA). In [8], the relative importance (weight) of each input variable in its BN fuzzy dependence relationship (DR) is always defined by the experts as a random variable. The aim of this paper is to estimate these weights automatically when DR output values are known (secondary information). The determination of these weights can be seen as an Optimization Problem (OP), in which the combination of weights that optimizes a predefined fitness function could be found by using a bio-inspired searching procedure. Given an expert-based BN structure, including both probabilistic and fuzzy DR, the MOEA calculates input weights for the fuzzy ones knowing all or some output values. Thus, MOEA contributes to the evaluation of fuzzy DR and lets effective forecasting by learning the relative input relevance. Therefore, the hybrid-based approach offers a new strategy for stochastic evaluation of BN by combining the expert knowledge, Monte-Carlo simulation and Fuzzy inference with bio-inspired learning from data procedures. This paper is organized as follows. Section 2 briefly describes the hybrid-based approach for stochastic assessment of BN, focusing on the role of input variable weights in fuzzy DR. Section 3 explains the OP regarding to input weight determination and offers a detailed description of the MOEA. In Section 4, the complete hybrid-based approach is used to estimate the migrant stock, as a relevant variable in the remittances model, and empirical results from a real case are shown. Finally, Section 5 concludes and discusses the future work.

A hybrid-based approach is presented in this paper aiming to provide a new strategy for stochastic assessment of BN by combining expert knowledge and automated learning from available data, sometimes scarce. Given an expert-based structure of BN, the MCS was used to estimate the values of BN input variables throughout the time span. An inference engine was used to evaluate fuzzy DR and thus, expert knowledge is included into the simulation model making it possible to design all the rules needed and manage them in an automatic way. The MOEA aimed to reduce the number of parameters that expert must determine to design and evaluate these fuzzy rules. To do this, MOEA learns input weights (relevance) in the corresponding fuzzy DR from available output data. The proposed approach is successfully applied to estimate the stock of Ecuadorian migrants in Spain by 2000, as a relevant variable in the BN remittances model that estimate those financial flows from Spain to Ecuador [38]. In addition, the input weights calculated by MOEA exhibit the same order of relevance that is previously given by experts. Since the selection of input weights is critical in order to draw the characteristics of the complex system on, MOEA introduces a higher precision into the output assessment procedure and hence it will allow the model to fit real situations better. In addition, it is worth emphasizing the fact that the proposed approach can be applied not only to estimate remittance flows but also to any complex system under uncertainty, in which expert will be able to define a dependence relationship structure among domain variables and some guidelines about their behavior. Works are in progress to extend the MOEA procedure to calculate input weights throughout the time span. From a technical point of view, it can be easily managed by introducing new constraints into the fitness function. However, the challenging point is to determine how each input weight increases/decreases/keeps constant between periods throughout the time span. The input weights change over the time, but these changes are usually slight when socio-economic variables are involved, except in cases of revolutions, economic downturns, natural disasters, etc. Thus, the new constraints to be added and especially their corresponding parameters must be carefully chosen to capture the slight changes, but also the shocks on those variables.