Optimization and Engineering最新文献

Many design optimization problems include constraints to prevent intersection of the geometric shape being optimized with other objects or with domain boundaries. When applying gradient-based optimization to such problems, the constraint function must provide an accurate representation of the domain boundary and be smooth, amenable to numerical differentiation, and fast-to-evaluate for a large number of points. We propose the use of tensor-product B-splines to construct an efficient-to-evaluate level set function that locally approximates the signed distance function for representing geometric non-interference constraints. Adapting ideas from the surface reconstruction methods, we formulate an energy minimization problem to compute the B-spline control points that define the level set function given an oriented point cloud sampled over a geometric shape. Unlike previous explicit non-interference constraint formulations, our method requires an initial setup operation, but results in a more efficient-to-evaluate and scalable representation of geometric non-interference constraints. This paper presents the results of accuracy and scaling studies performed on our formulation. We demonstrate our method by solving a medical robot design optimization problem with non-interference constraints. We achieve constraint evaluation times on the order of (10^{-6}) seconds per point on a modern desktop workstation, and a maximum on-surface error of less than 1.0% of the minimum bounding box diagonal for all examples studied. Overall, our method provides an effective formulation for non-interference constraint enforcement with high computational efficiency for gradient-based design optimization problems whose solutions require at least hundreds of evaluations of constraints and their derivatives.

Optimization problems with discrete–continuous decisions are traditionally modeled in algebraic form via (non)linear mixed-integer programming. A more systematic approach to modeling such systems is to use generalized disjunctive programming (GDP), which extends the disjunctive programming paradigm proposed by Egon Balas to allow modeling systems from a logic-based level of abstraction that captures the fundamental rules governing such systems via algebraic constraints and logic. Although GDP provides a more general way of modeling systems, it warrants further generalization to encompass systems presenting a hierarchical structure. This work extends the GDP literature to address two major alternatives for modeling and solving systems with nested (hierarchical) disjunctions: explicit nested disjunctions and equivalent single-level disjunctions. We also provide theoretical proofs on the relaxation tightness of such alternatives, showing that explicitly modeling nested disjunctions is superior to the traditional approach discussed in literature for dealing with nested disjunctions.

This paper develops an optimization model for determining the placement of switches, tie lines, and underground cables in order to enhance the reliability of an electric power distribution system. A central novelty in the model is the inclusion of nodal reliability constraints, which consider network topology and are important in practice. The model can be reformulated either as a mixed-integer exponential conic optimization problem or as a mixed-integer linear program. We demonstrate both theoretically and empirically that the judicious application of partial linearization is key to rendering a practically tractable formulation. Computational studies indicate that realistic instances can indeed be solved in a reasonable amount of time on standard hardware.

Many real-world application problems encountered in industry have no analytical formulation, that is they are blackbox optimization problems, and often make use of expensive numerical simulations. We propose a new blackbox optimization algorithm named BOA to solve mixed-variable constrained blackbox optimization problems where the evaluations of the blackbox functions are computationally expensive. The algorithm is two-phased: in the first phase it looks for a feasible solution and in the second phase it tries to find other feasible solutions with better objective values. Our implementation of the algorithm constructs surrogates approximating the blackbox functions and defines subproblems based on these models. The open-source blackbox optimization solver NOMAD is used for the resolution of the subproblems. Experiments performed on instances stemming from the literature and two automotive applications encountered at Stellantis show promising results of BOA in particular with cubic RBF models. The latter generally outperforms two surrogate-assisted NOMAD variants on the considered problems.

Long-term block scheduling is a challenging problem that involves determining the best extraction period for blocks to maximize the net present value of the open-pit mining business. This process involves multiple constraints, mainly ensuring safe pit walls and imposing maximum limits on operational resource consumption. However, most of the models proposed in the literature do not sufficiently consider geometric constraints that ensure a minimum space for mining equipment to operate safely. These models overlook practical and operational constraints and generate solutions that are difficult to implement. Consequently, the promised net present value cannot be achieved. In this paper, we propose an integer linear programming model that considers minimum mining width requirements along with a decomposition heuristic method to solve it.The proposed model determines which blocks should be mined and when to maximize net present value while ensuring safe pit walls and respecting limits on operational resources and geometric constraints. Geometric constraints require that the minimum operational distance be considered within each extraction period. Because the incorporation of geometric constraints in the proposed model makes it harder to solve, a time-space decomposition heuristic is implemented. This heuristic consists of successive time and space aggregation/disaggregation to generate simpler subproblems to be solved. This approach was applied on two case studies. The results show that the proposed methodology generates practical production plans that are more realistic to implement in mining operations, lowering the gap between factual and promised net present value.

The primal-dual interior-point method is widely recognized as one of the most effective approaches for solving the linear complementarity problem. As an extension of the linear complementarity problem, the study of the weighted linear complementarity problem is more necessary. In this paper, a new full-Newton step primal-dual interior-point algorithm is proposed for the special weighted linear complementarity problem. At each iteration, the search directions of the method are determined via a positive-asymptotic kernel function. The iteration complexity of the algorithm is analyzed, and the result is the same as the currently best known complexity bound of the similar methods. Finally, the validity of the algorithm is verified by some numerical results.

This editorial article discusses recent findings in the optimization and engineering for sustainable development. The current Special Issue (SI) of the Optimization and Engineering journal stems from the 2022 Sustainable Development of Energy, Water and Environment Systems Conferences. These events included the 5th South East European, 3rd Latin American, and 17th SDEWES Conferences. Being selected from conference presentations, the papers in SI represent the main topics in optimization approaches that integrate various life-supporting systems discussed during these three events. After careful selection, the current SI accepted ten excellent papers summarized here. These contributions use differentiated modeling approaches and supporting tools, such as P-graph and network-flow modeling, computational fluid dynamics, pinch analysis (PA), and the Geographic Information System. The range of optimization methods includes mixed-integer linear and mixed-integer nonlinear programming (MILP and MINLP), dynamic programming, stochastic optimization, and PA and P-graph extensions.

This paper studies the dual relation between risk-sensitive control and large deviation control of maximizing the probability for out-performing a target for Markov Decision Processes. To derive the desired duality, we apply a non-linear extension of the Krein-Rutman Theorem to characterize the optimal risk-sensitive value and prove that an optimal policy exists which is stationary and deterministic. The right-hand side derivative of this value function is used to characterize the specific targets which make the duality to hold. It is proved that the optimal policy for the “out-performing” probability can be approximated by the optimal one for the risk-sensitive control. The range of the (right-hand, left-hand side) derivative of the optimal risk-sensitive value function plays an important role. Some essential differences between these two types of optimal control problems are presented.

Spreading processes on networks (graphs) have become ubiquitous in modern society with prominent examples such as infections, rumors, excitations, contaminations, or disturbances. Finding the source of such processes based on observations is important and difficult. We abstract the problem mathematically as an optimization problem on graphs. For the deterministic setting we make connections to the metric dimension of a graph and introduce the concept of spread resolving sets. For the stochastic setting we propose a new algorithm combining parameter estimation and experimental design. We discuss well-posedness of the algorithm and show encouraging numerical results on a benchmark library.