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.

All-composite integrated 3D-Kagome lattice cores sandwich structure with flexible mortise-tenon joints

Composite lattice cores sandwich structures have shown obvious advantages in specific mechanical property and potential multifunctional integration. 3D-Kagome lattice core is regarded as a classic core configuration with relative optimal theoretical performance. However, it is still unavailable due to preparation problem of the overlap joint-node of composite cores. In this paper, a self-locking mortise-tenon joint method is presented to sucessfully fabricate the integrated 3D-Kagome cores with the expected mechanical properties. The out-of-plane compressive behaviour and energy absorption characteristics are experimentally studied. For the composite structures with various relative densities, three kinds of compressive curves are observed, following by different failure modes. An obvious bearing reinforcement emerges for the lattice cores with high relative density. As the length-to-thickness ratio of the core-rods increases, the initial peak strength and modulus of structures both decrease with a slowing rate. Though the mortises weaken the load-bearing capacity of core-rods, the active constraint of mortise-tenon joint suppresses an obvious degradation. The dominated failure more depends on the core-height than rod-thickness. The composite 3D-Kagome cores show more excellent mechanical properties than other similar structures, especially for the elastic strain before the initial peak stress. The semi-rigid power-wasting mortise-tenon joint and load-bearing characteristics of Kagome core together provide a large deformation tolerance at a relatively high stress level. All suggest that the presented 3D-Kagome lattice cores could be considered as a potential energy absorbing material.

Design optimization of water distribution networks: real-world case study with penalty-free multi-objective genetic algorithm using pressure-driven simulation

Water distribution systems are an integral part of the economic infrastructure of modern-day societies. However, previous research on the design optimization of water distribution systems generally involved few decision variables and consequently small solution spaces; piecemeal-solution methods based on pre-processing and search space reduction; and/or combinations of techniques working in concert. The present investigation was motivated by the desire to address the above-mentioned issues including those associated with the lack of high-performance computing (HPC) expertise and limited access in developing countries. More specifically, the article’s aims are, firstly, to solve a practical water distribution network design optimization problem and, secondly, to develop and demonstrate a generic multi-objective genetic algorithm capable of achieving optimal and near-optimal solutions on complex real-world design optimization problems reliably and quickly. A multi-objective genetic algorithm was developed that applies sustained and extensive exploration of the active constraint boundaries. The computational efficiency was demonstrated by the small fraction of 10-245 function evaluations relative to the size of the solution space. Highly competitive solutions were achieved consistently, including a new best solution. The water utility’s detailed distribution network model in EPANET 2 was used for the hydraulic simulations. Therefore, with some additional improvements, the optimization algorithm developed could assist practitioners in day-to-day planning and design.