Quadratic unconstrained binary optimization for environmental control system equipment design and assessment

The aircraft environmental control system (ECS) is a critical aircraft system that provides the appropriate environmental conditions to ensure the safe transport of air passengers and equipment. The functionality and reliability of ECS have elicited an increasing amount of attention in recent years. The heat exchanger is a particularly significant component of ECS because its failure reduces the system’s efficiency and can lead to catastrophic consequences. Health assessment and fault diagnosis for the heat exchanger are necessary to perform maintenance and prevent risks in a timely manner. This paper presents fault-related parameter estimation methods based on strong tracking filter (STF) and logistic regression (LR) algorithm for heat exchanger health assessment and root cause classification, respectively. Heat exchanger fault simulation is conducted to generate performance degradation data, through which the proposed methods are validated. Results demonstrate that the proposed methods are capable of providing stable, effective, and accurate heat exchanger health assessment and root cause classification.

The aircraft Environmental Control System (ECS) enables the aircraft to maintain a comfortable and safe environment for its passengers throughout its operating envelope. The Pressurised Air Conditioner (PACK) is the heart of the ECS, and is composed of multiple sub-systems: heat exchangers, valves, compressor, turbine, and a water separator. The PACK’s principle function is to enable conditioning of the hot, high pressure bleed air from the engine or APU, for temperature, pressure and humidity against the cabin requirements. The operation of the PACK is governed by a control system which has the ability to mask degradation in its component during operation until severe degradation or failure results. The required maintenance is then both costly and disruptive. The PACK has been reported as major driver of unscheduled maintenance by the operators. The aviation industry is currently proactively exploring innovative health management solutions that aid the maintenance of aircraft key systems based on predictive based maintenance approaches using online condition monitoring techniques. This paper presents a comprehensive review of the simulation and diagnostic methodologies applicable to fault diagnostics of the ECS PACK. The existing literature suggests that model-based and data-driven methods are effective for conducting fault detection and isolation of the PACK system. The conceived findings indicate that the model-based diagnostic approach have been extensively employed to conduct PACK diagnostics at component level only. Their successful implementation requires robust experimental verification and validation against the actual data under healthy and faulty conditions. Although a substantial amount of work has been reported on developing first principles based simulation models and diagnostic strategies for the ECS, the acquired findings suggest that there is a compelling need for a verified and validated ECS simulation model to enable accurate PACK system-level diagnostics based on single and multiple component level degradation scenarios. It has also been identified that the existing literature lacks the evaluation of humidity regulation and the effect of the control system on the PACK performance characteristics. Finally, a taxonomy of diagnostic techniques and simulation models is compiled based on the available literature.

Quadratic unconstrained binary optimization (QUBO) has gained popularity over the past ten years both for the wide range of problems that can be expressed in this form and for its compatibility with many quantum computing architectures. More recently, quantum annealers have advanced to the point where the scaling of qubits makes real-world applications increasingly feasible; however, current architectures remain restricted to solving quadratic unconstrained binary optimization problems, which can represent at most two-body interactions. Here we systematically examine the shortcomings of the QUBO framework and modern quantum annealers through the lens of the high-dimensional, exponentially scaling problem of RNA structure prediction, and find results that are generalizable to QUBO formalisms writ large. We find that using the QUBO framework to predict RNA structures results in poor accuracy, which becomes worse as system size scales. We determine that the fundamental constraint of two-body interactions prevents emergent correlations in the system, which are crucial to accurate structure prediction. Furthermore, we highlight that explicit, higher-order, empirical terms that are needed to improve structure prediction are incompatible with a QUBO framework. Finally, we show that our energy landscape has many deep local minima, which lead to local minima trapping and prevent permutation invariance. The relevance of these findings to other applications of QUBO, and therefore to modern quantum annealers more broadly, are discussed, with our work providing the first explicit explanation of why these formalisms have failed and will continue to fail in high-dimensional systems with similar constraints.

Low-density parity-check (LDPC) codes have previously been considered as combinatorial optimization problems (COPs) in respect to its decoding. However, after defining it as such, none have gone so far as to convert the LDPC code into a quadratic unconstrained binary optimization (QUBO) problem. Thus, a new method is created: one that converts the LDPC code to a QUBO problem, inputs the QUBO problem into Ising machines (computers based on the Ising model that are designed to solve the QUBO problem), obtains the QUBO solution and converts it to a LDPC solution. By utilizing an actual Ising machine, LDPC solutions with code length of 256-bits have been obtained with an accuracy of 93.9% by average annealing time 214.0ms. The benefit of this newfound methodology goes beyond its theoretical imprint of obtaining LDPC solutions more accurately. It has only been a few years since the Ising machine has been developed. Therefore, in formulating this method, one expands the currently scope of studies involving Ising machines, helping current and future researchers unlock its full range of capabilities and possibilities.

Traffic congestion is one of the major issues in urban areas, particularly when traffic loads exceed the road’s capacity, resulting in higher petrol consumption and carbon emissions as well as delays and stress for road users. In Asia, the traffic situation can be further deteriorated by road sharing of scooters. How to control the traffic flow to mitigate the congestion has been one of the central issues in transportation research. In this study, we employ a quantum annealing approach to optimize the traffic signals control at a real-life intersection with mixed traffic flows of vehicles and scooters. Considering traffic flow is a continuous and emerging phenomenon, we used quadratic unconstrained binary optimization (QUBO) formalism for traffic optimization, which has a natural equivalence to the Ising model and can be solved efficiently on the quantum annealers, quantum computers or digital annealers. In this article, we first applied the QUBO traffic optimization to artificially generated traffic for a simple intersection, and then we used real-time traffic data to simulate a real "Dongda-Keyuan" intersection with dedicated cars and scooter lanes, as well as mixed scooter and car lanes. We introduced two types of traffic light control systems for traffic optimization: C-QUBO and QUBO. Our rigorous QUBO optimizations show that C-QUBO and QUBO outperform the commonly used fixed cycle method, with QUBO outperforming C-QUBO in some instances. It has been found that QUBO optimization significantly relieves traffic congestion for the unbalanced traffic volume. Furthermore, we found that dynamic changes in traffic light signal duration greatly reduce traffic congestion.

With the recent advancements in the field of combinatorial optimization, QUBO (quadratic unconstrained binary optimization) has become a topic of intense interest, as a problem format acceptable to several hardware heuristics such as quantum and digital annealers. Accordingly, transforming hard mathematical problems into QUBO problems is of particular importance. In this paper, we restate three problems in NP-complete and NP-hard classes as QUBO problems with proofs of equivalence. Our problems of interest are the numerical three-dimensional matching problem, the monochromatic triangle problem and the optimum facility location problem. Furthermore, we comment on the feasibility of these formulations on sophisticated QUBO solving platforms.

Superhydrophobic heat exchangers delay frost formation and reduce defrost energy input of aircraft environmental control systems

Study on Ground-Test Simulation Method of the Ram Air for Commercial Airliners’ Environmental Control System

Combinatorial problems pose significant challenges, especially for large-scale instances. A promising approach to addressing these challenges involves quadratic unconstrained binary optimization (QUBO) models, a key framework in quantum computing. QUBO formulations require tailored approaches owing to their unique characteristics and the hardware constraints of quantum systems. This paper focuses on the QUBO formulations of the Hamiltonian cycle problem (HCP). We analyse three QUBO formulations for the HCP, including two inspired by Lagrangian relaxation techniques, where penalties may result in negative costs for certain solutions but are balanced within the model. A preprocessing methodology is also introduced. To evaluate these models, we employ D-Wave quantum annealers, which feature a fixed qubit topology and impose strict resource constraints. The mapping of QUBOs on to this architecture highlights the importance of efficient model design. Through experimental studies, we analyse the performance of the proposed QUBOs with and without preprocessing. This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 2)'.

Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training neural networks in this context. We first discuss QUBO problems that originate from translated instances of the traveling salesman problem (TSP): Analyzing this representation via autoencoders shows that there is way more information included than necessary to solve the original TSP. Then we show that neural networks can be used to solve TSP instances from both QUBO input and autoencoders' hidden state representation. We finally generalize the approach and successfully train neural networks to solve arbitrary QUBO problems, sketching means to use neuromorphic hardware as a simulator or an additional co-processor for quantum computing.

Quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts and has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy “flips” r binary variables to obtain a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for the implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy-embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, leading to very high-quality solutions within a short CPU time.

We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on a commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest.

The Ising model is defined by an objective function using a quadratic formula of qubit variables. The problem of an Ising model aims to determine the qubit values of the variables that minimize the objective function, and many optimization problems can be reduced to this problem. In this paper, we focus on optimization problems related to permutations, where the goal is to find the optimal permutation out of the n! possible permutations of n elements. To represent these problems as Ising models, a commonly employed approach is to use a kernel that applies one-hot encoding to find any one of the n! permutations as the optimal solution. However, this kernel contains a large number of quadratic terms and high absolute coefficient values. The main contribution of this paper is the introduction of a novel permutation encoding technique called the dual-matrix domain wall, which significantly reduces the number of quadratic terms and the maximum absolute coefficient values in the kernel. Surprisingly, our dual-matrix domain-wall encoding reduces the quadratic term count and maximum absolute coefficient values from n3−n2 and 2n−4 to 6n2−12n+4 and 2, respectively. We also demonstrate the applicability of our encoding technique to partial permutations and Quadratic Unconstrained Binary Optimization (QUBO) models. Furthermore, we discuss a family of permutation problems that can be efficiently implemented using Ising/QUBO models with our dual-matrix domain-wall encoding.

Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements.Among various approaches, quantum annealing methods effectively parallelize quadratic unconstrained binary optimization (QUBO) formulations of systems of linear equations.In this paper, we simplify these formulations by exploiting congruence of real symmetric matrices to diagonal matrices.We further exhibit computational merits of the proposed QUBO models, which can outperform classical algorithms such as QR and SVD decomposition.

Quantum Annealing is an algorithm for solving instances of quadratic unconstrained binary optimization (QUBO) that is implemented in hardware utilizing quantum effects to quickly find approximate solutions. However, QUBO can obviously also be solved by any classical optimization technique, for which various implementations exist. The UQ platform provides a unified interface to various means of solving QUBO that allows for a seamless switch between classical and quantum methods while implementing features such as load and user management.