Applications – Science and Engineering

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

Published: 2026/08/21

Yaguang Yang

Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization arc-search, nonlinear optimization, obstacle avoidance, Path planning

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

Published: 2026/08/17

Nicole Cristina Cassimiro

(Mixed) Integer Linear Programming, Biomedical Applications, Multi-Criteria Optimization clustering, decision support, extended goal programming, goal programming, intensity modulated proton therapy, multi-criteria decision analysis, multi-objective optimization, multiobjective optimization, OR for medicine, Pareto set reduction, radiotherapy treatment planning, representative selection.

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

Published: 2026/08/14

(Mixed) Integer Linear Programming, Energy, Polyhedra District energy system, generalized benders decomposition, Mixed-integer subproblem, non-convex cut formulation, Subproblem monotonicity

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

Stochastic Heterogeneous Fleet Scheduling for Airport Ground Transportation under Passenger Spillover and Service Constraints

Published: 2026/08/10

(Mixed) Integer Linear Programming, Airline Optimization, Applications - OR and Management Sciences, Facility Planning and Design, Stochastic Programming airport management, Mobility, public transportation networks, stochastic optimization

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A Data-Assimilation-Augmented Optimization Framework for Parameter Estimation in Dynamical Systems

Published: 2026/07/29

Muhammad Jalil Ahmad

Control Applications, Nonlinear Optimization, Nonsmooth Optimization data assimilation, dynamical systems, inverse problems, nonlinear optimization, parameter estimation

Parameter estimation in nonlinear dynamical systems from observational data is a fundamental inverse problem with applications in many disciplines such as epidemiology, systems biology, climate science, and related fields. In practice, this is further complicated by the fact that observational data are often noisy, sparse, and available only for a subset of the state variables. … Read more

A new theorem of alternatives leading to sufficient conditions for the superiorization guarantee question of Dynamic String-Averaging in the inconsistent case

Published: 2026/07/29

Basic Sciences Applications, Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization

We study the Superiorization Methodology (SM) in the context of the General Dynamic String-Averaging (GDSA) method in the inconsistent case (that is, where the input operators don’t have a common fixed point) which primarily aims at achieving convex feasibility while simultaneously reducing an objective function. In many scientific and real-world problems modeled as constrained minimization … Read more

On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

Published: 2026/07/29

Basic Sciences Applications, Convex Optimization, Infinite Dimensional Optimization Affine subspace, boundedness, control, dynamic string-averaging, half-space, infinite product, innately regular, perturbation resilience, relaxed projection, strongly nonexpansive mapping

Very recently (2026), Bauschke and Tung extended from finite- to infinite-dimensional Hilbert spaces a result published by Meshulam in 1996 (following an earlier result of Aharoni-Duchet-Wajnryb from 1984) regarding the boundedness of infinite products of relaxed projections onto a finite family of closed affine subspaces. In the present note we extend in various ways the … Read more

Optimal Combinatorial Testing with Constraints: The Balancing Act

Published: 2026/07/20, Updated: 2026/07/22

(Mixed) Integer Linear Programming, Applications - Science and Engineering, Graphs and Matroids

Imagine that you are in front of a cockpit with several on–off buttons. If you were to thoroughly test it, you would need to try a prohibitive number of configurations. But since most bugs in practice can be isolated to interactions among few components, having tests that cover every possible pairwise configuration is a good … Read more

GPU-accelerated superiorization on constrained physical problems with SupPy

Published: 2026/07/03

Applications - OR and Management Sciences, Biomedical Applications, Constrained Nonlinear Optimization CT Image reconstruction, feasibility-seeking, Python SupPy, radiotherapy treatment planning, Seismic image reconstruction, superiorization method

The superiorization method (SM) is situated between feasibility-seeking and constrained optimization. Instead of aiming at the minimum of a given objective function over a constraint set, it seeks a feasible point at which the objective function value is reduced — though not necessarily minimal — compared to that reached by the feasibility-seeking algorithm alone. This … Read more

Spatial Optimization Models for Width-Constrained Wildlife Corridor Design

Published: 2026/07/01, Updated: 2026/07/13

(Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Applications - Science and Engineering algorithm, branch and cut algorithms, mixed-integer programming, network optimization

Human activities increasingly fragment natural habitats, placing many species at risk of population decline. This creates an urgent need to preserve biodiversity and maintain ecological connectivity through wildlife corridors. We present two spatial optimization models for corridor design that explicitly incorporate corridor width as a key ecological criterion. The first model minimizes total corridor cost … Read more