Applications – Science and Engineering

Two-stage approach for the predispatch problem with uncertain demand using splitting variables in interior-point methods

Categories Applications - Science and Engineering, Quadratic Programming, Stochastic Programming Tags , , ,

The stochastic predispatch optimal power flow problem aims to minimize generation costs and transmission losses subject to network constraints under demand uncertainty. We formulate it as a two-stage stochastic quadratic optimization problem with fixed recourse, in which hydroelectric generation constitutes the here-and-now decision, while thermal generation and transmission flows are recourse decisions. Using a splitting-variable … Read more

Two-Stage Stochastic Optimization for Capacitated Facility Location Under Demand Uncertainty

Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Stochastic Programming Tags , , , , ,

Facility location decisions are typically made before demand is fully known, yet most applied studies solve a single deterministic model using expected or nominal demand. This paper formulates and solves a capacitated facility location problem using a real academic benchmark instance, then extends it to a two-stage stochastic program in which facility-opening decisions are made … Read more

Twist Without Tangle: Flutter Suppression of Thin-Walled Wing-Engine Systems via Curvilinear Fiber Path Tailoring and Cross-Section Optimization

Categories Applications - Science and Engineering, Optimization of Simulated Systems, Optimization of Systems modeled by PDEs Tags , , ,

Flutter is traditionally delayed by modifying either a structure’s geometry or its stiffness distribution. Here, we show that allowing both to evolve simultaneously can unlock a fundamentally different route to aeroelastic stability. We concurrently optimize the cross-sectional geometry and fiber paths of a composite thin-walled wing–engine system to maximize flutter onset. The wing structure is … Read more

Rooting Out Self-Intersection: An Algebraic Shape-Optimization Barrier

Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Nonlinear Optimization Tags , , ,

Self-intersection is a fundamental feasibility constraint in shape optimization: a self-crossing boundary leaves its interior, normal field, and finite-element mesh ill-defined, yet most existing barriers rely on heuristic geometric-proximity measures rather than certifying self-intersection directly. We propose a self-intersection barrier grounded in algebraic detection. We derived two bivariate polynomials from a curve’s Fourier coefficients whose … Read more

An optimal orbit design for LISA

Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , ,

The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the … Read more

On the Equivalence of Monge and Kantarovich Problems in Discrete Optimal Transport

Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization of Systems modeled by PDEs

Consider a discrete optimal transport problem that has at least two consumers. We show that the Monge and Kantorovich versions of such a discrete optimal transport problem are equivalent for all cost functions if and only if the supply from all the suppliers are equal, and the demand from every consumer is an integral multiple … Read more

Combining Reinforcement Learning with Arc-search Interior-Point Method for Path Planning

Categories Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization Tags , , ,

Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more

A Decision-Support Framework for Structuring and Reducing Large Multi-Objective Solution Sets via Clustering: An Application to Proton Therapy

Categories (Mixed) Integer Linear Programming, Biomedical Applications, Multi-Criteria Optimization Tags , , , , , , , , , , ,

This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives. The methodology combines: (Phase 1) systematic solution generation through extended goal programming and structured preference exploration; (Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis; (Phase 3) filtering and dominance-based reduction … Read more

Indicator Cuts for Benders Decomposition with Mixed-Integer Subproblems

Categories (Mixed) Integer Linear Programming, Energy, Polyhedra Tags , , , ,

Classical Benders decomposition fails when the subproblem is a mixed-integer program, due to the absence of strong duality. We propose a novel class of dual-free indicator cuts that are applicable to all Benders-decomposable problems with a pure-integer master problem and mixed-integer linear programming (MILP) subproblems. These cuts are derived from the monotonicity property of the … Read more