General Problem Formulation Research Articles

Slab assignment to non-identical reheat furnaces running in parallel mode

This article analyses a slab assignment problem for non-identical reheat furnaces in the steelmaking industry. We tackle the problem of assigning slabs to different types of reheat furnaces, a walking beam and a pusher type furnace. Furthermore, we need to determine the feed-in as well as the residence time for each slab. The aim is to (i) reduce the energy consumption, (ii) increase the production rate and (iii) the heating quality of the slabs which depends on the assigned furnace and to what extent the slabs are overheated. Moreover, the subsequent production stage (Hot Rolling Mill), needs to be synchronized with the furnaces which is essential for a smooth production. We specify the problem as a mixed integer optimization formulation that is solved with iterative parameter adjustment. Rapid convergence leads to a novel two-phase solution method that yields furnace schedules that are optimal for the adjusted parameter values in reasonable time. The results show that our proposed method performs better than an industry benchmark by increasing the production rate and increasing the reheating quality. Furthermore, the new generic problem formulation allows using standard software and can be applied to identical or non-identical furnaces highlighting its broad applicability across steel-making companies.

Deep reinforcement learning as multiobjective optimization benchmarks: Problem formulation and performance assessment

The successful deployment of Deep learning in several challenging tasks has been translated into complex control problems from different domains through Deep Reinforcement Learning (DRL). Although DRL has been extensively formulated and solved as single-objective problems, nearly all real-world RL problems often feature two or more conflicting objectives, where the goal is to obtain a high-quality and diverse set of optimal policies for different objective preferences. Consequently, the development of Multi-Objective Deep Reinforcement Learning (MODRL) algorithms has gained a lot of traction in the literature. Generally, Evolutionary Algorithms (EAs) have been demonstrated to be scalable alternatives to the classical DRL paradigms when formulated as an optimization problem. Hence it is reasonable to employ Multi-objective Evolutionary Algorithms (MOEAs) to handle MODRL tasks. However, there are several factors constraining the progress of research along this line: first, there is a lack of a general problem formulation of MODRL tasks from an optimization perspective; second, there exist several challenges in performing benchmark assessments of MOEAs for MODRL problems. To overcome these limitations: (i) we present a formulation of MODRL tasks as general multi-objective optimization problems and analyze their complex characteristics from an optimization perspective; (ii) we present an end-to-end framework, termed DRLXBench, to generate MODRL benchmark test problems for seamless running of MOEAs (iii) we propose a test suite comprising of 12 MODRL problems with different characteristics such as many-objectives, degenerated Pareto fronts, concave and convex optimization problems, etc. (iv) Finally, we present and discuss baseline results on the proposed test problems using seven representative MOEAs.

DAMPAK PKG TERHADAP KINERJA GURU DALAM KEGIATAN BELAJAR MENGAJAR MAN 1 PAMEKASAN

This research aims to find out the impact of teacher performance appraisal on teaching and learning activities at MAN 1 PAMEKASAN as well as the general problem formulation, namely the impact of teacher performance appraisal on teaching and learning activities at MAN 1 PAMEKASAN using qualitative descriptive research methods using interactive analysis mode. This research presents results based on observation guides and interviews which show the success of teachers in carrying out teaching and learning activities using appropriate methods and being able to guide students towards the school's vision and mission that has been created. Apart from that, this research also proves that teacher performance assessment can have a positive impact. significant impact on student learning outcomes because teachers will receive evaluation and motivation to develop effective learning methods in the classroom

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed EvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently -without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of EvoXBench is available at https://github.com/EMI-Group/EvoXBench.

Optimal supervisory control of discrete event systems for cyclic tasks

In this paper, we investigate the problem of optimal supervisory control for cyclic tasks in the context of discrete-event systems (DES). We consider the completion of each single task as the visit of a marked state, and overall control objective is to complete tasks cyclically in the sense that marked states are visited infinitely often. Following the standard optimal supervisory control framework, two types of costs, disable cost and occurrence cost, are considered. However, instead of considering the standard accumulated total cost or the average cost per event, we consider the measure for the control performance using the average cost per task. We show that such an optimality measure is more suitable for tasks that need to be completed cyclically. Our goal is to design a live and non-blocking supervisor such that the average cost per task in the worst-case is minimized. To solve the problem, we propose a game-theoretical approach by converting the optimal control problem as a two-player graph game. Structural properties of the converted game are discussed. In particular, we show that this game can be solved by a set of mean payoff decision problems, for which effective algorithms exist. Our problem can be considered as a special instance of the general ratio-game in the literature. However, by exploring new structural property for this problem, we achieve superior computational efficiency when compared to the conventional solution designed for more general problem formulations. Illustrative examples are provided to demonstrate the proposed algorithm.

Maximization of nonsubmodular functions under multiple constraints with applications

We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the problem with provable approximation guarantees. The first algorithm exploits the structure of a special class of the general problem instance to obtain a better time complexity. The second algorithm is suitable for the general problem. We characterize the approximation guarantees of the two algorithms, leveraging the notions of submodularity ratio and curvature introduced for set functions. We then discuss particular applications of the general problem formulation to problems that have been considered in the literature. We validate our theoretical results using numerical examples.

On the utility of production scheduling formulations including record keeping variables

In this work we propose several reformulations of a general discrete-time mixed-integer formulation for production scheduling problems. Each reformulation involves the addition of new integer variables that we refer to as record keeping variables. Computational results show that the required CPU time is greatly reduced when record keeping variables are present in the optimization model. Additionally, we assess which of the individual aspects of traditional branch-and-bound solution procedures benefit from the inclusion of record keeping variables.

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. On shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

Two-dimensional models for waterflooding induced hydraulic fracture accounting for the poroelastic effects on a reservoir scale

This work focuses on the developing of a computationally efficient numerical model for a waterflooding induced planar hydraulic fracture in a poroelastic medium. In particular, under certain assumptions it is possible to decouple the fully coupled model into poroelastic reservoir and purely elastic fracture subproblems. Further, the general 3D problem formulation for a planar fracture is reduced to two dimensions for early time plane strain fracture and late time constant height fracture. Noticeably, the division of the problem into two subproblems allows us to use the displacement discontinuity approach for the fracture related part, and finite element method for the reservoir related part. The latter is especially important for the constant height fracture, which cannot be modeled using exclusively the finite element approach in two dimensions. The algorithm is benchmarked against the available analytical solutions, as well as compared to other numerical codes. The developed numerical method is used to study the influence of the heterogeneous pore pressure and the corresponding stress for different waterflooding fracturing situations. We consider the cases with both injection and production wells operating nearby. With the presence of such wells, the fracture growth becomes asymmetrical and both the well type and location are important. The qualitatively different fracture behavior is observed for various cases. Other numerical examples include the simulation of a step-rate test as well as investigation of the possibility of fracture control by altering the injection rate.

On Design and Implementation of Reinforcement Learning Based Cognitive Routing for Autonomous Networks

Cognitive routing is expected to be a key technology to realize intellectualized operation and administration for autonomous networks. Meanwhile, reinforcement learning (RL) excels especially in decision-making tasks by learning from trial and error, which is promising for solving various cognitive routing problems. Nevertheless, the research of RL-based cognitive routing has been severely constrained by a lack of general problem formulation and feasible network simulation frameworks. In this letter, we propose the first general problem formulation of RL-based cognitive routing. In addition, based on OpenAI Gym and ns-3, we implement the first packet-level network simulation framework, the RL4Net, that facilitates the rapid prototyping of RL-based cognitive routing algorithms. Finally, we conduct extensive experiments with the RL4Net to evaluate the effectiveness of RL-based cognitive routing. Numerical results demonstrate that our proposed RL-based cognitive routing effectively outperforms RL-based non-cognitive routing and the OSPF in terms of minimizing average end-to-end network delay.

Optimization-based modelling and game-theoretic framework for techno-economic analysis of demand-side flexibility: A real case study

This paper proposes a two-step framework for techno-economic analysis of a demand-side flexibility service in distribution networks. Step one applies optimization-based modelling to propose a generic problem formulation which determines the offer curve, in terms of available flexible capacity and its marginal cost, for flexible distribution-connected assets. These offer curves form an input to the second step, which uses a multi-agent iterative game framework to determine the benefits of demand-side flexibility for the Distribution System Operator (DSO) and the service providers. The combined two-step framework simultaneously accounts for the objectives of each flexibility provider, technical constraints of flexible assets, customer preferences, market clearing mechanisms, and strategic bidding by service providers, omission of any of which can lead to erroneous results. The proposed two-step framework has been applied to a real case study in the North East of England to examine four market mechanisms and three bidding strategies. The results showed that among all considered market mechanisms, flexibility markets that operate under discriminatory pricing, such as pay-as-bid and Dutch reverse auctions, are prone to manipulations, especially in the lack of competition. In contrast, uniform pricing pay-as-cleared auction provides limited opportunities for manipulation even when competition is low.

Optimisation modelling tools and solving techniques for integrated precinct-scale energy–water system planning

This invited review paper presents state-of-the-art applications to energy–water system optimisation with multiple technologies, implying possible (non)monetary benefits/impacts for facility custodians in urban precincts. To solve outstanding problems, optimisation modelling frameworks were examined in the quest for undertaking an integrated precinct-scale energy–water system planning. Underlying optimisation methods were identified for addressing nested long/short-term capital/managerial decisions that ensure cost-effectiveness and system reliability, especially selecting diversified investment portfolios to allocate controllable assets across energy and water resources. Despite the ongoing energy–water nexus investigations, the integrated energy–water system planning seems to lack a general optimisation problem formulation that reveal synergies between energy and water. Considering the dynamic and nonlinear nature of energy–water interactions, mathematical properties must be carefully treated for tackling complex integrated energy–water system planning optimisation problems. To optimise integrated precinct-scale energy–water system plans, classical and heuristic techniques can be jointly implemented for solving (re)formulated problems with hard constraints and desirable cost/resource-saving objectives. Critical energy–water system sizing/scheduling tasks were discussed while covering deterministic and probabilistic procedures to support decision-making under uncertainty. Although different combined stochastic programs have been proposed incorporating actual outcomes and empirical measurements as well as prior information and expert knowledge, inherent energy–water demand/supply uncertainties should be realistically characterised by parameterising representable random perturbation sets. To find robust optimal feasible solutions to sensitive parameters during extreme load/cost volatility situations, historical energy–water usage data can be randomly perturbed for uncertainty realisation in prospective scenarios, capturing spatiotemporal correlations that avoid overconservative worst-case expected values. From the scientific paradigm of physics-informed data-driven optimisation modelling, robust approaches can be adopted for severe societal/natural events to advance state-of-the-art applications in integrated precinct-scale energy–water system planning and engineering design.

Optimal Sensor Placement for Source Localization: A Unified ADMM Approach

Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), and Received Signal Strength (RSS) based. Since the Cram\'{e}r-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA and RSS based localization scenarios. We first unify the three localization models by a generalized problem formulation based on the CRLB-related metric. Then a unified optimization framework for optimal sensor placement (UTMOST) is developed through the combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM) techniques. Unlike the majority of the state-of-the-art works, the proposed UTMOST neither approximates the design criterion nor considers only uncorrelated noise in the measurements. It can readily adapt to to different design criteria (i.e. A, D and E-optimality) with slight modifications within the framework and yield the optimal sensor placements correspondingly. Extensive numerical experiments are performed to exhibit the efficacy and flexibility of the proposed framework.

A General Non-Fourier Stefan Problem Formulation that Accounts for Memory Effects

A General Non-Fourier Stefan Problem Formulation that Accounts for Memory Effects

WaterSafe: A Water Network Benchmark for Fault Diagnosis Research

Currently, in the water distribution systems literature, fault detection methods are typically evaluated on benchmark water networks that do not include real-time experimental data, or on private commercial datasets, which prohibit the reproducibility of the results. Moreover, realistic modeling of faults on hydraulic system components, sensors and actuators is often unavailable. In this work, we provide a framework for the application of fault-diagnosis methodologies on WaterSafe, a water network benchmark for fault diagnosis. The WaterSafe benchmark is a small scale replica of a water transport network constructed using industrial components and devices, while the communications are implemented in a way that resemble a water utility's Supervisory Control and Data Acquisition system. A general problem formulation for fault-diagnosis on water systems is provided, in accordance to the mathematical model of the benchmark. Moreover, we provide a calibrated simulation model including system, sensor and actuator faults, based on observations from the real system. Finally, we provide open access to the datasets generated from the experiments containing the aforementioned faults.

GGLasso - a Python package for General Graphical Lasso computation

We introduce GGLasso, a Python package for solving General Graphical Lasso problems. The Graphical Lasso scheme, introduced by (Friedman 2007) (see also (Yuan 2007; Banerjee 2008)), estimates a sparse inverse covariance matrix $\Theta$ from multivariate Gaussian data $\mathcal{X} \sim \mathcal{N}(\mu, \Sigma) \in \mathbb{R}^p$. Originally proposed by (Dempster 1972) under the name Covariance Selection, this estimation framework has been extended to include latent variables in (Chandrasekaran 2012). Recent extensions also include the joint estimation of multiple inverse covariance matrices, see, e.g., in (Danaher 2013; Tomasi 2018). The GGLasso package contains methods for solving a general problem formulation, including important special cases, such as, the single (latent variable) Graphical Lasso, the Group, and the Fused Graphical Lasso.

Towards an intelligent HVAC system automation using Reinforcement Learning

HVAC systems are among the biggest energy consumers in buildings and therefore in the focus of optimal control research. In practice, rule-based control and PID controllers are typically used and implemented at the beginning of the building operation. Since this approach neither guarantees optimal or even good control, optimal control algorithms (which can be predictive and adaptive) are in the focus of research. The problem with most of the approaches is that a model of the system is often needed which comes with high engineering efforts. Further, the required computing power can quickly exceed the capacities, even in modern buildings. Therefore, in this paper we investigate the application of a state-of-the-art Reinforcement Learning (RL) algorithm, as a self-calibrating valve controller for two water-air heat exchangers of a real-world air handling unit. We choose a generic problem formulation to pre-train the algorithm with a simulation of an admixing heater and use it to control an injection heater and a throttle cooler. Our results show that after only 70 hours, the control quality significantly increases. Therefore, it seems evident that with pre-trained RL algorithms, a self-improving HVAC automation can be realized with little hardware requirements and without extensive modelling of the system dynamics.

A General Purpose Variational Formulation for Boundary Value Problems of Orders Greater than Two

We develop a new general purpose variational formulation, particularly suitable for solving boundary value problems of orders greater than two. The functional related to this variational formulation requires only Η1 regularity in order to be well-defined. Using the finite element method based on this new formulation thus becomes simple even for domains in dimensions greater than one. We prove that a saddle-point solution to the new variational formulation is a weak solution to the associated boundary value problem. We also prove the convergence of the numerical methods used to find approximate solutions to the new formulation. We provide numerical tests to demonstrate the efficacy of this new paradigm.

Derivation of Heat Conductivity from Temperature and Heat Flux Measurements in Soil

The general inverse problem formulation for a heat conductance equation is adopted for the types of measurement routinely carried out in the soil active layer. The problem solution delivers a constant thermal diffusivity coefficient a0 (in general, different from true value a) and respective heat conductivity λ0 for the layer, located between two temperature sensors and equipped with a temperature or heat flux sensor in the middle. We estimated the error of solution corresponding to systematic shifts in sensor readings and mislocation of sensors in the soil column. This estimation was carried out by a series of numerical experiments using boundary conditions from observations on Mukhrino wetland (Western Siberia, Russia), performed in summer, 2019. Numerical results were corroborated by analytical estimates of inverse problem solution sensitivity derived from classical Fourier law. The main finding states that heat conductivity error due to systematic shifts in temperature measurements become negligible when using long temperature series, whereas the relative error of a is approximately twice the relative error of sensor depth. The error a0−a induced by heat flux plate displacement from expected depth is 3–5 times less than the same displacement of thermometers, which makes the requirements for heat flux installation less rigid. However, the relative errors of heat flux observation typical for modern sensors (±15%) cause the uncertainty of a above 15% in absolute value. Comparison of the inverse problem solution to a estimated from in situ moss sampling on Mukhrino wetland proves the feasibility of the method and corroborates the conclusions of the error sensitivity study.

Generating Artificial Outliers in the Absence of Genuine Ones — A Survey

By definition, outliers are rarely observed in reality, making them difficult to detect or analyze. Artificial outliers approximate such genuine outliers and can, for instance, help with the detection of genuine outliers or with benchmarking outlier-detection algorithms. The literature features different approaches to generate artificial outliers. However, systematic comparison of these approaches remains absent. This surveys and compares these approaches. We start by clarifying the terminology in the field, which varies from publication to publication, and we propose a general problem formulation. Our description of the connection of generating outliers to other research fields like experimental design or generative models frames the field of artificial outliers. Along with offering a concise description, we group the approaches by their general concepts and how they make use of genuine instances. An extensive experimental study reveals the differences between the generation approaches when ultimately being used for outlier detection. This survey shows that the existing approaches already cover a wide range of concepts underlying the generation, but also that the field still has potential for further development. Our experimental study does confirm the expectation that the quality of the generation approaches varies widely, for example, in terms of the dataset they are used on. Ultimately, to guide the choice of the generation approach in a specific context, we propose an appropriate general-decision process. In summary, this survey comprises, describes, and connects all relevant work regarding the generation of artificial outliers and may serve as a basis to guide further research in the field.