CONSTRAINED MULTI-GROUP PROJECT ALLOCATION USING MAHALANOBIS DISTANCE

Optimal allocation is one of the most active research areas in operation research using binary integer variables. The allocation of multi constrained projects among several options available along a given planning horizon is an especially significant problem in the general area of item classification. The main goal of this dissertation is to develop an analytical approach for selecting projects that would be most attractive from an economic point of view to be developed or allocated among several options, such as in-house engineers and private contractors (in transportation projects). A relevant limiting resource in addition to the availability of funds is the in-house manpower availability. In this thesis, the concept of Mahalanobis distance (MD) will be used as the classification criterion. This is a generalization of the Euclidean distance that takes into account the correlation of the characteristics defining the scope of a project. The desirability of a given project to be allocated to an option is defined in terms of its MD to that particular option. Ideally, each project should be allocated to its closest option. This, however, may not be possible because of the available levels of each relevant resource. The allocation process is formulated mathematically using two Binary Integer Programming (BIP) models. The first formulation maximizes the dollar value of benefits derived by the traveling public from those projects being implemented subject to a budget, total sum of MD, and in-house manpower constraints. The second formulation minimizes the total sum of MD subject to a budget and the in-house manpower constraints. The proposed solution methodology for the BIP models is based on the branchand- bound method. In particular, one of the contributions of this dissertation is the development of a strategy for branching variables and node selection that is consistent with allocation priorities based on MD to improve the branch-and-bound performance level as well as handle a large scale application. The suggested allocation process includes: (a) multiple allocation groups; (b) multiple constraints; (c) different BIP models. Numerical experiments with different projects and options are considered to illustrate the application of the proposed approach

Correction: Wang et al. An Optimization on the Neuronal Networks Based on the ADEX Biological Model in Terms of LUT-State Behaviors: Digital Design and Realization on FPGA Platforms. <i>Biology</i> 2022, <i>11</i>, 1125

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An optimization on the neuronal networks based on the ADEX biological model in terms of LUT-state behaviors : digital design and realization on FPGA platforms

SIMPLE SUMMARY: The brain is an incredibly complex system possessing outstanding abilities to perform difficult tasks through a vast number of densely interconnected neurons. Aimed at discovering the underlying mechanisms of the brain, a number of spiking neural networks have been proposed to mimic biological neural dynamics. Subsequently, to perceive how the neural networks in the brain work, simulation and hardware realization of large-scale systems, similar to the brain, is an essential requirement. Behavior of a single neuron can be described by the mathematical equations in different levels of computing and biological accuracy. In this approach, a new modified ADEX model is presented based on sampling frequency by the nonlinear functions of the original model. This new model is capable for reproducing all aspects of the original model in low-error and high-degree of similarity conditions. Finally, the proposed model can be implemented on digital hardware platforms to have a real digital system. Digital results show the increase in system speed (frequency) and overall saving in hardware resources (compared by the original model and other similar works). This low-cost digital hardware is applied in large-scale neuronal networks. ABSTRACT: Design and implementation of biological neural networks is a vital research field in the neuromorphic engineering. This paper presents LUT-based modeling of the Adaptive Exponential integrate-and-fire (ADEX) model using Nyquist frequency method. In this approach, a continuous term is converted to a discrete term by sampling factor. This new modeling is called N-LUT-ADEX (Nyquist-Look Up Table-ADEX) and is based on accurate sampling of the original ADEX model. Since in this modeling, the high-accuracy matching is achieved, it can exactly reproduce the spiking patterns, which have the same behaviors of the original neuron model. To confirm the N-LUT-ADEX neuron, the proposed model is realized on Virtex-II Field-Programmable Gate Array (FPGA) board for validating the final hardware. Hardware implementation results show the high degree of similarity between the proposed and original models. Furthermore, low-cost and high-speed attributes of our proposed neuron model will be validated. Indeed, the proposed model is capable of reproducing the spiking patterns in terms of low overhead costs and higher frequencies in comparison with the original one. The properties of the proposed model cause can make it a suitable choice for neuromorphic network implementations with reduced-cost attributes