Upper-level Variables Research Articles

A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem

We examine bilevel mixed-integer programs whose constraints and objective functions depend on both upper- and lower-level variables. The class of problems we consider allows for nonlinear terms to appear in both the constraints and the objective functions, requires all upper-level variables to be integer, and allows a subset of the lower-level variables to be integer. This class of bilevel problems is difficult to solve because the upper-level feasible region is defined in part by optimality conditions governing the lower-level variables, which are difficult to characterize because of the nonconvexity of the follower problem. We propose an exact finite algorithm for these problems based on an optimal-value-function reformulation. We demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior. Computational experiments demonstrate that our approach outperforms a state-of-the-art algorithm for solving bilevel mixed-integer linear programs.

Effect of Regional Characteristics on Injury Severity in Local Bus Crashes

As the importance of public transportation increases, the management of bus-involved crashes has become a crucial issue for traffic safety. However, there are relatively few studies on crash severity for buses in South Korea. This study investigated factors that influence the severity of injuries that occur in local bus crashes. The study used commercial vehicle crash data from a 5-year period from 2010 through 2014 in South Korea. To determine unobserved regional effects on crash severity, a hierarchical ordered model was applied to the analysis. Individual crash characteristics were set to lower-level variables, and regional characteristics were adopted as upper-level variables. At the lower level, the factors affecting severity of injuries included vehicle speed, vehicle age, road alignment, surface status, road class, and traffic light installation, as found in previous studies. At the upper level, the factors included pavement, emergent medical environment, traffic rate of compliance, and ratio of elderly in the community. There was a 5.1% unobserved variation between regions from the intraclass correlation analysis. The validity of a hierarchical model for local bus crashes was verified by applying the model to other long-distance buses, and it appeared there were no regional effects. This study found a regional effect for local bus crash severity, and thus this factor is important when developing prevention plans to reduce local bus crashes. These results contribute to the study of traffic safety.

Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping

Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level problem. Such a requirement makes the optimization problem difficult to solve, and has kept the researchers busy towards devising methodologies, which can efficiently handle the problem. Despite the efforts, there hardly exists any effective methodology, which is capable of handling a complex bilevel problem. In this paper, we introduce bilevel evolutionary algorithm based on quadratic approximations (BLEAQ) of optimal lower level variables with respect to the upper level variables. The approach is capable of handling bilevel problems with different kinds of complexities in relatively smaller number of function evaluations. Ideas from classical optimization have been hybridized with evolutionary methods to generate an efficient optimization algorithm for a wide class of bilevel problems. The performance of the algorithm has been evaluated on two sets of test problems. The first set is a recently proposed SMD test set, which contains problems with controllable complexities, and the second set contains standard test problems collected from the literature. The proposed method has been compared against three benchmarks, and the performance gain is observed to be significant. The codes related to the paper may be accessed from the website http://bilevel.org.

一类区间系数非线性优化问题的遗传算法

本文针对一类带区间系数的非线性优化问题，提出了一种基于均匀搜索的遗传算法。首先，将原问题分解为两个确定的双层规划问题；其次，对两个双层问题的上层变量进行编码，通过求解相应的双层规划获得对个体的评估；最后，为避免近亲繁殖产生相似后代，采用相对距离控制杂交运算；并且引进摆动式正交杂交算子产生后代个体，使后代尽可能均匀产生。数据仿真结果表明，该算法是可行有效的。 For a class of nonlinear programming problems with interval coefficients, a genetic algorithm based on a uniformly searching scheme is proposed in this paper. Firstly, the original problem is transformed into two exact bilevel programs. Secondly, the upper level variables are encoded as individuals, and these individuals are evaluated by solving the bilevel programs. Finally, in order to avoid producing similar offspring by inbreeding, a relative distance is adopted to provide a threshold value for crossover. Also, an orthogonal crossover operator with point oscillating is provided to generate offspring as uniformly as possible. The experimental data indicate that this algorithm is feasible and effective.

Anemia among indigenous women in Brazil: findings from the First National Survey of Indigenous People's Health and Nutrition.

BackgroundAnemia is recognized as a major public health problem that disproportionately affects vulnerable populations. Indigenous women of reproductive age in Brazil are thought to be at high risk, but lack of nationwide data limits knowledge about the burden of disease and its main determinants. This study aimed to assess the prevalence of anemia and associated factors in this population using data from The First National Survey of Indigenous People’s Health and Nutrition in Brazil.MethodsData were collected from Indigenous women between 15 and 49 years old based on a nationwide sample of villages. The outcomes of interest were hemoglobin levels (g/dL) and anemia (< 12 g/dL for nonpregnant and < 11 g/dL for pregnant women). Multilevel models were used to explore associations with contextual (village) and individual (household/woman) level variables.ResultsBased on data for 6692 Indigenous women, the nationwide mean hemoglobin level was 12.39 g/dL (95 % CI: 12.29–12.50). Anemia prevalence was high (33.0 %; 95 % CI: 30.40–35.61 %) and showed pronounced regional disparities. No village-level characteristics were associated with anemia or hemoglobin levels in the multilevel model. Even after controlling for upper level variables, socioeconomic status, parity, body mass index, and having been treated for malaria were associated with anemia and hemoglobin levels.ConclusionThe prevalence of anemia in Brazilian Indigenous women was 12 % greater than the national estimates for women of reproductive age. Anemia prevalence and mean hemoglobin levels among Indigenous women appear to be partly explained by some previously recognized risk factors, such as socioeconomic status, body mass index, and malaria; however, part of the variability in these outcomes remains unexplained. Knowledge of health status and its potential determinants is essential to guide public policies aimed at controlling anemia burden in Indigenous communities.

Decomposition of the problem of approximating the Edgeworth–Pareto hull

For nonlinear block separable multicriteria optimization (MCO) problems, a decomposition method is proposed that simplifies the approximation of the Edgeworth–Pareto hull (EPH), i.e., the maximum (by inclusion) set having the same Pareto frontier as the set of feasible criteria vectors in the MCO problem. A two-level system is considered that consists of an upper coordinating level and lower-level subsystems interacting via the upper level. It is assumed that the criteria are related to the upper-level variables. According to the method, preliminarily constructed approximations to block EPHs are used to obtain an EPH approximation for the whole MCO problem. As an example, the EPH for an MCO problem arising in estimating the potential possibilities of water resource management for a cascade of reservoirs is constructed.

Atmospheric transport simulations in support of the Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE)

Abstract. This paper describes the atmospheric modeling that underlies the Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE) science analysis, including its meteorological and atmospheric transport components (polar variant of the Weather Research and Forecasting (WRF) and Stochastic Time Inverted Lagrangian Transport (STILT) models), and provides WRF validation for May–October 2012 and March–November 2013 – the first 2 years of the aircraft field campaign. A triply nested computational domain for WRF was chosen so that the innermost domain with 3.3 km grid spacing encompasses the entire mainland of Alaska and enables the substantial orography of the state to be represented by the underlying high-resolution topographic input field. Summary statistics of the WRF model performance on the 3.3 km grid indicate good overall agreement with quality-controlled surface and radiosonde observations. Two-meter temperatures are generally too cold by approximately 1.4 K in 2012 and 1.1 K in 2013, while 2 m dewpoint temperatures are too low (dry) by 0.2 K in 2012 and too high (moist) by 0.6 K in 2013. Wind speeds are biased too low by 0.2 m s−1 in 2012 and 0.3 m s−1 in 2013. Model representation of upper level variables is very good. These measures are comparable to model performance metrics of similar model configurations found in the literature. The high quality of these fine-resolution WRF meteorological fields inspires confidence in their use to drive STILT for the purpose of computing surface influences ("footprints") at commensurably increased resolution. Indeed, footprints generated on a 0.1° grid show increased spatial detail compared with those on the more common 0.5° grid, better allowing for convolution with flux models for carbon dioxide and methane across the heterogeneous Alaskan landscape. Ozone deposition rates computed using STILT footprints indicate good agreement with observations and exhibit realistic seasonal variability, further indicating that WRF-STILT footprints are of high quality and will support accurate estimates of CO2 and CH4 surface–atmosphere fluxes using CARVE observations.

Estimation of distribution algorithm for a class of nonlinear bilevel programming problems

In this paper, a novel evolutionary algorithm called estimation of distribution algorithm (EDA) is proposed for solving a special class of nonlinear bilevel programming problems (BLPPs) in which the lower level problem is a convex programming problem for each given upper level decision. This special type of BLPP is transformed into a equivalent single-level constrained optimization problem using the Karush-Kuhn-er conditions of the lower level problem. Then, we propose an EDA based on the statistical information of the superior candidate solutions to solve the transformed problem. We stress that the new population of individuals is sampled from the probabilistic distribution of those superior solutions. Thus, one of the main advantages of EDA over most other meta-heuristics is its ability to adapt the operators to the structure of the problem, although adaptation in EDA is usually limited by the initial choice of the probabilistic model. In addition, two specific rules are established in the initialization procedure to make use of the hierarchical structure of BLPPs and to handle the constraints. Moreover, without requiring the differentiability of the objective function, or the convexity of the search space of the equivalent problem, the proposed algorithm can address nonlinear BLPPs with non-differentiable or non-convex upper level objective function and upper level constraint functions. Finally, the proposed algorithm has been applied to 16 benchmark problem; in five of these problems, all of the upper level variables and lower level variables are 10-dimensional. The numerical results compared with those of other methods reveal the feasibility and effectiveness of the proposed algorithm.

An efficient evolutionary algorithm for the ring star problem

This paper addresses the ring star problem (RSP). The goal is to locate a cycle through a subset of nodes of a network aiming to minimize the sum of the cost of installing facilities on the nodes on the cycle, the cost of connecting them and the cost of assigning the nodes not on the cycle to their closest node on the cycle. A fast and efficient evolutionary algorithm is developed which is based on a new formulation of the RSP as a bilevel programming problem with one leader and two independent followers. The leader decides which nodes to include in the ring, one follower decides about the connections of the cycle and the other follower decides about the assignment of the nodes not on the cycle. The bilevel approach leads to a new form of chromosome encoding in which genes are associated to values of the upper level variables. The quality of each chromosome is evaluated by its fitness, by means of the objective function of the RSP. Hence, in order to compute the value of the lower level variables, two optimization problems are solved for each chromosome. The computational results show the efficiency of the algorithm in terms of the quality of the solutions yielded and the computing time. A study to select the best configuration of the algorithm is presented. The algorithm is tested on a set of benchmark problems providing very accurate solutions within short computing times. Moreover, for one of the problems a new best solution is found.

Solving dual problems using a coevolutionary optimization algorithm

In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which suggests that under certain conditions the optimal dual function value is smaller than or equal to the optimal primal objective value. The dual problem is a special case of a bilevel programming problem involving Lagrange multipliers as upper-level variables and decision variables as lower-level variables. Another interesting aspect of dual problems is that both lower and upper-level optimization problems involve only box constraints and no other equality of inequality constraints. In this paper, we propose a coevolutionary dual optimization (CEDO) algorithm for co-evolving two populations—one involving Lagrange multipliers and other involving decision variables—to find the dual solution. On 11 test problems taken from the optimization literature, we demonstrate the efficacy of CEDO algorithm by comparing it with a couple of nested smooth and nonsmooth algorithms and a couple of previously suggested coevolutionary algorithms. The performance of CEDO algorithm is also compared with two classical methods involving nonsmooth (bundle) optimization methods. As a by-product, we analyze the test problems to find their associated duality gap and classify them into three categories having zero, finite or infinite duality gaps. The development of a coevolutionary approach, revealing the presence or absence of duality gap in a number of commonly-used test problems, and efficacy of the proposed coevolutionary algorithm compared to usual nested smooth and nonsmooth algorithms and other existing coevolutionary approaches remain as the hallmark of the current study.

Determinants of leptospirosis in Sri Lanka: Study Protocol

BackgroundLeptospirosis is becoming a major public health threat in Sri Lanka as well as in other countries. We designed a case control study to determine the factors associated with local transmission of leptospirosis in Sri Lanka, in order to identify major modifiable determinants of leptospirosis. The purpose of this paper is to describe the study protocol in detail prior to the publishing of the study results, so that the readership will be able to understand and interpret the study results effectively.MethodsA hospital based partially matched case control design is proposed. The study will be conducted in three selected leptospirosis endemic districts in central Sri Lanka. Case selection will include screening all acute fever patients admitted to selected wards to select probable cases of leptospirosis and case confirmation using an array of standard laboratory criteria. Age and sex matched group of acute fever patients with other confirmed diagnosis will be used as controls. Case to control ratio will be 1:2. A minimum sample of 144 cases is required to detect 20% exposure with 95% two sided confidence level and 80% power. A pre tested interviewer administered structured questionnaire will be used to collect data from participants. Variables included in the proposed study will be evaluated using conceptual hierarch of variables in three levels; Exposure variables as proximal; reservoir and environmental variables as intermediate; socio-demographic variables as distal. This conceptual hierarch hypothesised that the distal and intermediate variables are mediated through the proximal variables but not directly. A logistic regression model will be used to analyse the probable determinants of leptospirosis. This model will evaluate the effect of same level and upper level variables on the outcome leptospirosis, using three blocks.DiscussionThe present national control programme of leptospirosis is hampered by lack of baseline data on leptospirosis disease transmission. The present study will be able to provide these essential information for formulation of better control strategies.