Exploration of the scalability of LocFaults approach for error localization with While-loops programs

A model checker can produce a trace of counterexample, for an erroneous program, which is often long and difficult to understand. In general, the part about the loops is the largest among the instructions in this trace. This makes the location of errors in loops critical, to analyze errors in the overall program. In this paper, we explore the scala-bility capabilities of LocFaults, our error localization approach exploiting paths of CFG(Control Flow Graph) from a counterexample to calculate the MCDs (Minimal Correction Deviations), and MCSs (Minimal Correction Subsets) from each found MCD. We present the times of our approach on programs with While-loops unfolded b times, and a number of deviated conditions ranging from 0 to n. Our preliminary results show that the times of our approach, constraint-based and flow-driven, are better compared to BugAssist which is based on SAT and transforms the entire program to a Boolean formula, and further the information provided by LocFaults is more expressive for the user

Robust Temporal Logic Model Predictive Control

Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints given as formulas of signal temporal logic (STL). We introduce a (conservative) computationally efficient framework to synthesize control strategies based on mixed integer programs. The designed controllers satisfy the temporal logic requirements, are robust to all possible realizations of the disturbances, and optimal with respect to a cost function. In case the temporal logic constraint is infeasible, the controller satisfies a relaxed, minimally violating constraint. An illustrative case study is included.Comment: This work has been accepted to appear in the proceedings of 53rd Annual Allerton Conference on Communication, Control and Computing, Urbana-Champaign, IL (2015

Diagnosing Infeasible Optimization Problems Using Large Language Models

Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering and manufacturing, transportation, and health care. Optimization models are mathematical abstractions of the problem of making the best decision while satisfying a set of requirements or constraints. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, also known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility

Analyzing Multi-Objective Linear and Mixed Integer Programs by Lagrange Multipliers

A new method for multi-objective optimization of linear and mixed programs based on Lagrange multiplier methods is developed. The method resembles, but is distinct from, objective function weighting and goal programming methods. A subgradient optimization algorithm for selecting the multipliers is presented and analyzed. The method is illustrated by its application to a model for determining the weekly re-distribution of railroad cars from excess supply areas to excess demand areas, and to a model for balancing cost minimization against order completion requirements for a dynamic lot size model

Wireless Backhaul Node Placement for Small Cell Networks

Small cells have been proposed as a vehicle for wireless networks to keep up with surging demand. Small cells come with a significant challenge of providing backhaul to transport data to(from) a gateway node in the core network. Fiber based backhaul offers the high rates needed to meet this requirement, but is costly and time-consuming to deploy, when not readily available. Wireless backhaul is an attractive option for small cells as it provides a less expensive and easy-to-deploy alternative to fiber. However, there are multitude of bands and features (e.g. LOS/NLOS, spatial multiplexing etc.) associated with wireless backhaul that need to be used intelligently for small cells. Candidate bands include: sub-6 GHz band that is useful in non-line-of-sight (NLOS) scenarios, microwave band (6-42 GHz) that is useful in point-to-point line-of-sight (LOS) scenarios, and millimeter wave bands (e.g. 60, 70 and 80 GHz) that are recently being commercially used in LOS scenarios. In many deployment topologies, it is advantageous to use aggregator nodes, located at the roof tops of tall buildings near small cells. These nodes can provide high data rate to multiple small cells in NLOS paths, sustain the same data rate to gateway nodes using LOS paths and take advantage of all available bands. This work performs the joint cost optimal aggregator node placement, power allocation, channel scheduling and routing to optimize the wireless backhaul network. We formulate mixed integer nonlinear programs (MINLP) to capture the different interference and multiplexing patterns at sub-6 GHz and microwave band. We solve the MINLP through linear relaxation and branch-and-bound algorithm and apply our algorithm in an example wireless backhaul network of downtown Manhattan.Comment: Invited paper at Conference on Information Science & Systems (CISS) 201

Empirical Bounds on Linear Regions of Deep Rectifier Networks

We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However, enumerating these regions is prohibitive and the known analytical bounds are identical for networks with same dimensions. In this work, we approximate the number of linear regions through empirical bounds based on features of the trained network and probabilistic inference. Our first contribution is a method to sample the activation patterns defined by ReLUs using universal hash functions. This method is based on a Mixed-Integer Linear Programming (MILP) formulation of the network and an algorithm for probabilistic lower bounds of MILP solution sets that we call MIPBound, which is considerably faster than exact counting and reaches values in similar orders of magnitude. Our second contribution is a tighter activation-based bound for the maximum number of linear regions, which is particularly stronger in networks with narrow layers. Combined, these bounds yield a fast proxy for the number of linear regions of a deep neural network.Comment: AAAI 202

Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art

PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations

In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond the traditional DC power flow by capturing reactive power, to convex relaxations, which provide solution quality and runtime performance guarantees. Unfortunately, the sophistication of these emerging methods often presents a significant barrier to evaluating them on a wide variety of power system optimization applications. To address this issue, this work proposes PowerModels, an open-source platform for comparing power flow formulations. From its inception, PowerModels was designed to streamline the process of evaluating different power flow formulations on shared optimization problem specifications. This work provides a brief introduction to the design of PowerModels, validates its implementation, and demonstrates its effectiveness with a proof-of-concept study analyzing five different formulations of the Optimal Power Flow problem