Data-Driven Superstabilization of Linear Systems under Quantization

This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval ranges based on sensor quantization. Using an established characterization of input-logarithmically-quantized stabilization based on robustness to sector-bounded uncertainty, we formulate a nonconservative infinite-dimensional linear program that enforces superstabilization of all possible consistent systems under assumed priors. We solve this problem by posing a pair of exponentially-scaling linear programs, and demonstrate the success of our method on example quantized systems.Comment: 12 pages, 2 figures, 3 table

Systematic Literature Review Robust Graph Coloring on Electric Circuit Problems

Graph Coloring Problem (GCP) is the assignment of colors to certain elements in a graph based on certain constraints. GCP is used by assigning a color label to each node with neighboring nodes assigned a different color and the minimum number of colors used. Based on this, GCP can be drawn into an optimization problem that is to minimize the colors used. Optimization problems in graph coloring can occur due to uncertainty in the use of colors to be used, so it can be assumed that there is an uncertainty in the number of colored vertices. One of the mathematical optimization methods in the presence of uncertainty is Robust Optimization (RO). RO is a modeling methodology combined with computational tools to process optimization problems with uncertain data and only some data for which certainty is known. This paper will review research on Robust GCP with model validation to be applied to electrical circuit problems using a systematic review of the literature. A systematic literature review was carried out using the Preferred Reporting Items for Systematic reviews and Meta Analysis (PRISMA) method. The keywords used in this study were used to search for articles related to this research using a database. Based on the results of the search for articles obtained from PRISMA and Bibliometric R Software, it was found that there was a relationship between the keywords Robust Optimization and Graph Coloring, this means that at least there is at least one researcher who has studied the problem. However, the Electricity keyword has no relation to the other two keywords, so that a gap is obtained and it is possible if the research has not been studied and discussed by other researchers. Based on the results of this study, it is hoped that it can be used as a consideration and a better solution to solve optimization problems

A Systematic Review on Integer Multi-objective Adjustable Robust Counterpart Optimization Model Using Benders Decomposition

Multi-objective integer optimization model that contain uncertain parameter can be handled using the Adjustable Robust Counterpart (ARC) methodology with Polyhedral Uncertainty Set. The ARC method has two stages of completion, so completing the second stage can be assisted by the Benders Decomposition. This paper discusses the systematic review on this topic using the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA). PRISMA presents a database mining algorithm for previous articles and related topics sourced from Scopus, Science Direct, Dimensions, and Google Scholar. Four stages of the algorithm are used, namely Identification, Screening, Eligibility, and Included. In the Eligibility stage, 16 articles obtained and called Dataset 1, used for bibliometric mapping and evolutionary analysis. Moreover, in the Included stage, six final databases obtained and called Dataset 2, which was used to analyze research gaps and novelty. The analysis was carried out on two datasets, assisted by the output visualisation using RStudio software with the " bibliometrix" package, then we use the command 'biblioshiny()' to create a link to the “shiny web interface”. At the final stage of the article using six articles analysis, it is concluded that there is no research on the ARC multi-objective integer optimization model with Polyhedral Uncertainty Sets using the Benders Decomposition Method, which focuses on discussing the general model and its mathematical analysis. Moreover, this research topic is open and becomes the primary references for further research in connection

Adjustable Regret for Continuous Control of Conservatism and Competitive Ratio Analysis

A major issue of the increasingly popular robust optimization is the tendency to produce overly conservative solutions. This paper proposes a new parameterized robust criterion to offer smooth control of conservatism without tampering with the uncertainty set. Unlike many other intractable criteria, its tractability is attained for common types of linear problems by reformulating them into traditional linear robust optimization problems. Many properties of it are studied to help analyze multistage robust optimization problems for closed-form solutions and give rise to a new approach to competitive ratio analysis. Finally, the new criterion is applied to the well-studied robust one-way trading problem to demonstrate its potential. A closed-form solution is obtained, which not only facilitates a numerical study of its smooth control of conservatism, but leads to a much simpler competitive ratio analysis.Comment: 29 pages, 2 figure

A Machine Learning Approach to Two-Stage Adaptive Robust Optimization

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train a machine learning model that predicts high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. We also introduce an algorithm to reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy