Fuzzy Linear Programming in DSS for Energy System Planning

Energy system planning requires the use of planning tools. The mathematical models of real-world energy systems are usually multiperiod linear optimization programs. In these models, the objective function describes the total discounted costs of covering the demand for final energy or energy services. The demand for various forms of energy or energy services is the driving force of the models. By using such linear programming (LP) formulations, decision makers can elaborate suitable strategies for solving their planning problems, such as the development of emission reduction strategies. Uncertainties that affect the process of energy system planning can be divided into parameter and decision uncertainties. Data or parameter uncertainties can be addressed either by stochastic optimization or by the methodology of fuzzy linear programming (FLP). In addition, FLP allows explicit incorporation of decision uncertainties into a mathematical model. This paper therefore aims at evaluating the methodology of FLP with respect to the support that it offers the decision-making process in energy system planning under uncertainty. Employing the parallels between multi-objective linear programming (MOLP) and FLP, problems of FLP in decision support system applications are pointed out and solutions are offered. The proposed modifications are based on the methodology of aspiration-reservation based decision support and still enable modeling of uncertainties in a fuzzy sense. A case study is documented to show the application of the modified FLP approach

Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.Multi-criteria decision aiding; Multi-attribute utility theory; Choquet integral; Free software

Decomposition approaches to integration without a measure

Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of decompositions: sub-decomposition based integrals (in economics linked with optimization problems to maximize the possible profit) and super-decomposition based integrals (linked with costs minimization). We provide several examples (both theoretical and realistic) to stress that our approach generalizes that of Even and Lehrer [3] and also covers problems of linear programming and combinatorial optimization. Finally, we introduce some new types of integrals related to optimization tasks.Comment: 15 page

Optimal Biocompatible Solvent Design by Mixed-integer Hybrid Differential Evolution

In this study, a flexible optimization approach is introduced to design an optimal biocompatible solvent for an extractive fermentation process with cell-recycling. The optimal process/solvent design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objectives and the constraints. A flexible or fuzzy optimization approach is applied to soften the rigid requirement for maximization of the production rate, extraction efficiency and to consider the solvent utilization rate as the softened inequality constraint to the process/solvent design problem. Such a trade-off problem is then converted to the goal attainment problem, which is described as the constrained mixed-integer nonlinear programming (MINLP) problem. Mixed-integer hybrid differential evolution with multiplier updating method is introduced to solve the constrained MINLP problem. The adaptive penalty updating scheme is more efficient to achieve a global design

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

Efficient Data Driven Multi Source Fusion

Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification