Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

In many engineered systems, optimization is used for decision making at time scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under tight latency requirements. We consider the problem of using the information available through this repeated solution process to learn important characteristics of the optimal solution as a function of the input parameters. Our proposed method is based on learning relevant sets of active constraints, from which the optimal solution can be obtained efficiently. Using active sets as features preserves information about the physics of the system, enables interpretable results, accounts for relevant safety constraints, and is easy to represent and encode. However, the total number of active sets is also very large, as it grows exponentially with system size. The key contribution of this paper is a streaming algorithm that learns the relevant active sets from training samples consisting of the input parameters and the corresponding optimal solution, without any restrictions on the problem type, problem structure or probability distribution of the input parameters. The algorithm comes with theoretical performance guarantees and is shown to converge fast for problem instances with a small number of relevant active sets. It can thus be used to establish simultaneously learn the relevant active sets and the practicability of the learning method. Through case studies in optimal power flow, supply chain planning, and shortest path routing, we demonstrate that often only a few active sets are relevant in practice, suggesting that active sets provide an appropriate level of abstraction for a learning algorithm to target.

Urban change as an untapped opportunity for climate adaptation

Urban social–ecological–technological systems (SETS) are dynamic and respond to climate pressures. Change involves alterations to land and resource management, social organization, infrastructure, and design. Research often focuses on how climate change impacts urban SETS or on the characteristics of urban SETS that promote climate resilience. Yet passive approaches to urban climate change adaptation may disregard active SETS change by urban residents, planners, and policymakers that could be opportunities for adaptation. Here, we use evidence of urban social, ecological, and technological change to address how SETS change opens windows of opportunity to improve climate change adaptation.

Optimization of Wind Driven RO Plant for Brackish Water Desalination during Wind Speed Fluctuation with and without Battery

This work aimed to carry out an optimal investigation of the design and operation of a large capacity reverse osmosis (RO) desalination plant powered by wind energy. Different scenarios involving two design options, such as using storage tanks or batteries, and operation options, such as using variable or fixed feed pressure, were analyzed and optimized. In addition, another operation option, of using a fixed number of RO vessels or a varying number of active RO vessels, was also considered. It was found that an optimized plant using storage tanks can provide a less expensive water cost and a less complicated plant structure. Moreover, the use of a variable feed pressure can help in attenuating the disturbances incurred in the form of wind intermittency. Conversely, the use of fixed feed pressure and constantly supplied power per vessel can run the RO units smoothly, leading to a predictable production rate. However, this requires operating the plant on different active sets of vessels each hour, which mandates additional automatic control systems. The water cost when storage tanks are utilized can be as low as 7.42 $/m3, while it is around 19.7 $/m3 when a battery is used.

The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical and Non-Surgical Interventions

Proprioception considered as the obtaining of information about one’s own action does not necessarily depend on proprioceptors. At the knee joint, perceptual systems are active sets of organs designed to reach equilibrium through synergies. Many surgical procedures, such as ACL reconstruction in personalized medicine, are often based on native anatomy, which may not accurately reflect the proprioception between native musculoskeletal tissues and biomechanical artifacts. Taking an affordance-based approach to this type of “design” brings valuable new insights to bear in advancing the area of “evidence-based medicine (EBM).” EBM has become incorporated into many health care disciplines, including occupational therapy, physiotherapy, nursing, dentistry, and complementary medicine, among many others. The design process can be viewed in terms of action possibilities provided by the (biological) environment. In anterior crucial ligament (ACL) reconstruction, the design goal is to avoid ligament impingement while optimizing the placement of the tibial tunnel. Although in the current rationale for tibial tunnel placement, roof impingement is minimized to avoid a negative affordance, we show that tibial tunnel placement can rather aim to constrain the target bounds with respect to a positive affordance. We describe the steps for identifying the measurable invariants in the knee proprioception system and provide a mathematical framework for the outcome measure within the knee.

Affordance-Based Assessment Cuts Across The Dichotomy Of Subjective-Objective Outcome Measure At The Knee Joint

There is increasing awareness of the need to include patient-reported outcome (PRO) instruments in evaluating the measurement of clinical outcomes, with an increasing focus placed on the patients’ perspective. Scientists have tried to link PROs with objective outcomes, providing unique information for managing patient care. Traditionally, objective and patient-reported outcomes (such as the Knee Injury and Osteoarthritis Outcome Score (KOOS)) are considered two distinct constructs, which cannot serve as a direct proxy for each other. Can Gibson´s affordance theory specify more about objective outcome measurements vs. subjective outcomes measurement and unify them? The present article develops a theoretical framework called entrainment of touch and posture that advocates the vis viva (living force) as the proper gauge for the dynamical action of a force, and that could explain “possibilities for action or affordance” during outcome measurement. We found that active touch and posture refer to what is ordinarily called touchingvariations in skin stimulation caused by surfaces are altered together by motor activity variations. This affordance of “walk-on-able” is worth noting because it is often neglected that locomotion and its surfaces form an inseparable pair. The assessment process can be viewed in terms of action possibilities provided by the active sets of organs residing that can obtain and utilize information about the tissue environments in which the grafts are to be located.