Optimization and Engineering最新文献

Mine planners utilize production schedules to determine when activities should be executed, e.g., blocks of ore should be extracted; a medium-term schedule maximizes net present value associated with activity execution while a short-term schedule reacts to unforeseen events. Both types of schedules conform to spatial precedence and resource restrictions. As a result of executing activities, heat accumulates and activities must be curtailed. Airflow flushes heat from the mining areas, but is limited to the capacity of the ventilation system and operational setup. We propose two large-scale production scheduling models: (i) that which prescribes the start dates of activities in a medium-term schedule while considering airspeed, in conjunction with ventilation and refrigeration; and, (ii) that which minimizes deviation between both medium- and short-term schedules, and production goals. We correspondingly present novel techniques to improve model tractability, and demonstrate the efficacy of these techniques on cases that yield short-term schedules congruent with medium-term plans while ensuring the safety of the work environment. We solve otherwise-intractable medium-term instances using an enumeration technique if the gaps are greater than 10%. Our short-term instances solve in 1,800 seconds, on average, to a 0.1% optimality gap, and suggest varying optimal airspeeds based on the maximum heat load on each level.

As climate change provides impetus for investing in smart cities, with electrified public transit systems, we consider electric public transportation buses in an urban area, which play a role in the power system operations in addition to their typical function of serving public transit demand. Our model considers a social planner, such that the transit authority and the operator of the electricity system co-optimize the power system to minimize the total operational cost of the grid, while satisfying additional transportation constraints on buses. We provide deterministic and stochastic formulations to co-optimize the system. Each stochastic formulation provides a different set of recourse actions to manage the variable renewable energy uncertainty: ramping up/down of the conventional generators, or charging/discharging of the transit fleet. We demonstrate the capabilities of the model and the benefit obtained via a coordinated strategy. We compare the efficacies of these recourse actions to provide additional managerial insights. We analyze the effect of different pricing strategies on the co-optimization. Noting the stress growing electrified fleets with greater battery capacities will eventually impose on a power network, we provide theoretical insights on coupled investment strategies for expansion planning in order to reduce greenhouse gas (GH) emissions. Given the recent momentum towards building smarter cities and electrifying transit systems, our results provide policy directions towards a sustainable future. We test our models using modified MATPOWER case files and verify our results with different sized power networks. This study is motivated by a project with a large transit authority in California.

This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a multi-dimensional function along a one-dimensional line segment of interest. The method does not rely on derivative information and the function to be learned can be a computationally-expensive “black box” function that must be queried via simulation or other means. It is assumed that the underlying function is noise-free and smooth, although the algorithm can still be effective when the underlying function is piecewise smooth. The method constructs a smooth surrogate on a set of equally-spaced grid points by evaluating the true function at a sparse set of judiciously chosen grid points. At each iteration, the surrogate’s non-tabu local minima and maxima are identified as candidates for sampling. Tabu search constructs are also used to promote diversification. If no non-tabu extrema are identified, a simple exploration step is taken by sampling the midpoint of the largest unexplored interval. The algorithm continues until a user-defined function evaluation limit is reached. Numerous examples are shown to illustrate the algorithm’s efficacy and superiority relative to state-of-the-art methods, including Bayesian optimization and NOMAD, on primarily nonconvex test functions.

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.