Effective channel assignment is essential to optimising satellite communication networks. Although traditionally modelled as a graph colouring or disjunctive scheduling problem, such approaches fall short of addressing contemporary user demands and the increasing complexity of operations in congested electromagnetic environments. This paper extends the standard channel assignment problem by introducing cumulative interference constraints arising from overlapping frequency intervals with heterogeneous bandwidths and non-symmetric interference powers. The model represents a flexible, digitally channelised satellite communication network employing a single-channel-per-carrier waveform. To address the challenges posed by this extension, we integrate constraint programming and operations research techniques to develop matheuristic algorithms that exploit problem-specific relaxations and decompositions. Through experimental analysis, we evaluate the effectiveness of our algorithms and examine the relative strengths and limitations of each approach, providing a foundation for future research into resource allocation in large-scale, complex satellite communication constellations.
The conductance problem and its special cases—the Cheeger constant and graph expansion—are NP-hard graph partitioning problems. Hochbaum, Hochbaum (2024), recently introduced the Incremental Parametric Cut (IPC) algorithm, which solves a relaxation of the conductance problem, the conductance* problem, as well as other “monotone” ratio problems, in the complexity of a single minimum cut on a related graph. IPC is not only theoretically efficient but also very fast in practice, as demonstrated here and in a previous experimental study for the densest subgraph problem. A large number of other heuristic techniques have been proposed for the conductance problem and its special cases. These include spectral methods Fiedler Sweep, PR-Nibble Sweep, and ACL Sweep; flow-based refinement approaches such as MQI, Flow Improve, and the Simple Local algorithm; and graph partitioning methods that construct a partition with a small balanced cut value, such as the one provided by METIS. We present the first publicly available implementation of IPC for conductance*, together with an extensive experimental study comparing its performance against state-of-the-art techniques, including several spectral method implementations, several flow-based methods, and METIS. The study demonstrates that IPC achieves dramatically faster running times than any competing method, while also producing new best-known conductance values for many benchmark graphs.
We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the N largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within 1.7% of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.
In this study, we consider the problem of computing the Euclidean projection onto an ℓ _p quasi-norm ball with 0
Drowning is among the most prevalent causes of death from unintentional injuries worldwide. Because of the time-sensitive nature of swimming accidents and the shortage of lifeguard staff resulting in unsupervised swimming areas, interest in innovative supportive rescue methods increases. In this paper, we introduce an autonomous Unmanned Aircraft System (UAS) that can be employed by Emergency Medical Service (EMS) providers in swimmer rescue scenarios additionally to Standard Rescue Operation (SRO) equipment. The UAS consists of Unmanned Aerial Vehicles (UAVs) and purpose-built hangars located near the swimming area to store the UAVs. When receiving an alert, the UAVs autonomously navigate to the emergency site to conduct a Search and Rescue (S R) operation for the swimmer in distress. We introduce a Mixed-Integer Linear Programming (MILP) model to address the Facility Location-Allocation Problem (FALP), identifying optimal hangar locations and allocation of UAVs to hangars to serve the demand in the swimming area. Additionally, we present a MILP model to optimize the UAV flight trajectories in advance of the operation, allowing for efficient coordination of a heterogeneous UAV swarm. We apply the presented MILP models to a real-world scenario in the Lusatian Lake District, Eastern Germany using the state-of-the-art commercial solver CPLEX to solve the instances.
This special issue of Optimization and Engineering (OPTE) presents a selection of contributions arising from the Modeling and Optimization: Theory and Applications (MOPTA) 2024 Conference, which was hosted by the Industrial and Systems Engineering (ISE) Department at Lehigh University. The conference was held in Bethlehem, Pennsylvania, USA, from August 14 to 16, 2024, and continued the long-standing tradition, initiated in 2000, of bringing together a diverse group of researchers and practitioners working on both theoretical and applied aspects of continuous and discrete optimization. The fifteen papers collected in this issue cover a broad range of topics in optimization theory and its engineering applications, including stochastic and distributed optimization, tensor methods, variational inequalities, data assimilation, network flows, and game theory, with applications in energy systems, transportation, geophysical modeling, machine learning, and industrial processes.
We address a three-dimensional packing problem encountered in the transportation of refrigerated pharmaceutical products. The input consists of a set of products, each comprising multiple boxes with specified dimensions (width, length, height), and a set of container types, each defined by internal dimensions (width, length, height), cost, and a maximum fraction of its internal volume that can be occupied by the products. The goal is to pack the boxes into containers while minimizing the total cost of the containers used, subject to several constraints. These constraints include: To solve this problem, we propose a heuristic approach that proceeds in two stages. First, dynamic programming is used to solve the mono-container and mono-product subproblem, inspired by similar existing pallet loading algorithms. This involves generating all feasible packing configurations for a single product within a single container. Subsequently, a backtracking-based procedure is employed to complete the assignment of the remaining boxes. Our intensive computational experiments for real-world scenarios show that this heuristic achieves acceptable solution times and delivers effective allocations.
Active Produced Water Management (APWM) in oil and gas production aims to optimize produced water (PW) disposal operations to reduce environmental impacts while handling economic trade-offs. This paper proposes the design of an APWM strategy based on Generalized Disjunctive Programming (GDP). The proposed approach is able to manage conflicting interests between distinct agents present in a PW re-injection (PWRI) operation by combining disjunctive sets with logic propositions, measurement feedback, and predictive capability, forming an optimization feedback loop in which decisions are both in the discrete as well as continuous domain. We demonstrate that the optimization feedback loop leads to feasibility of long-term discharging environmental constraint while effectively allocating pumping energy for PW re-injection at an offshore production facility. Finally, a tuning parameter is introduced to the proposed APWM enabling one to manipulate the conservativeness of the solution. The proposed methodology can be extended to other settings in which improvements of pumping operation as well as long-term control of pollutant discharges is required.
Despite the global surge in electric vehicle (EV) adoption and the recognized environmental, economic, and technical advantages of EVs, limited research addresses the location-allocation problem for EV charging stations (EVCSs) on directed and separated highway networks, especially considering both driving directions and single- or dual-access facilities. This study bridges that gap by addressing the capacitated fast-charging EVCS location-allocation problem on directed highways, incorporating path-based demands and the limited EV ranges. Unlike previous studies that assume a uniform number of chargers at each station, we allow the number of chargers at each EVCS to vary. In this study, we propose a novel model to optimize both the location of EVCSs and the number of chargers at each station. To overcome the computational challenges of identifying the optimal EVCS deployment, we develop a modified Bayesian optimization algorithm that leverages the expected improvement acquisition function. This approach balances demand maximization with the minimization of epistemic uncertainty in the surrogate model. The applicability of the proposed framework is validated through extensive experiments on the Pennsylvania Turnpike highway. Furthermore, a payback period analysis is conducted to enhance the practical relevance of the proposed model, providing insights into the economic feasibility of EVCS investments under different deployment scenarios. Sensitivity analyses are conducted to evaluate the effects of key factors, including the EV driving range, battery charge levels, and average traffic flow rates. Lastly, our solution approach achieves these results with significantly reduced computation times compared to baseline solutions, assuming a fixed number of chargers per EVCS.
Online portfolio selection is a decision-making process that involves dynamically adjusting asset positions based on historical price sequences. In the decision-making process, extreme market situations have a significant impact. Due to investors’ overreaction, asset prices often reverse after experiencing extreme market situations. However, existing online portfolio strategies seldom consider the significant impact of extreme market situations on investment decisions. In this paper, we construct a novel online portfolio strategy based on reversal signal and online gradient update algorithm. First, we identify reversal signal through a moving window, predict asset prices via the reversal signal, and construct a series of expert strategies based on predicted value of asset prices. Second, we aggregate the expert strategies through the online gradient update algorithm and propose our strategy. Then, we theoretically prove that the regret of our strategy has an upper bound, which guarantees the competitive performance of our strategy. Finally, we conduct extensive numerical experiments using real financial data from different markets. The results show that the proposed strategy performs well on cumulative wealth, risk-adjusted returns and transaction costs.
In costly engineering experiments, there is frequently a greater interest in regions potentially containing extreme values, including local extrema. This requires the selected samples to not only represent the global response but also focus on regions of interest. This paper proposes a novel adaptive exploration method for parallel optimization called Adaptive Sampling based on Local Penalization (ASLP). The adaptive exploration procedure comprises three stages. Initially, a space-filling design is employed to construct the surrogate model. Subsequently, the adaptive penalization term is incorporated to elevate the sampling priority in regions characterized by extreme values and rapid trend variations. Finally, adaptive sampling is implemented via the Minimum Energy Design (MED) approach. Through strategic parallel optimization, this methodology effectively concentrates on extremal regions while facilitating efficient evaluation of global performance. The effectiveness of the proposed method is verified by several numerical benchmark experiments and simulation experiments of radar anti-jamming performance evaluation.
As a nonconvex class of data envelopment analysis, free disposal hull (FDH) has become a commonly used method in productivity and efficiency analysis. However, existing FDH models often generate many efficient units, ignore the slacks of production variables, and compute efficiency and super-efficiency in separate steps. Meanwhile, FDH models typically lead to mixed-integer linear or nonlinear programming problems, which are more complicated to solve than conventional DEA models. To address these issues, we first propose two new slack-based FDH and feasible super-efficiency FDH models. The former explicitly accounts for variable slacks and thus yields more accurate efficiency measures, while the latter overcomes the challenges of numerous efficient units and infeasible solutions in conventional FDH super-efficiency evaluation. Then, an integrated slack-based FDH model is developed to simultaneously compute efficiency and super-efficiency in a one-stage approach. The proposed framework is applicable to performance measurement involving both desirable outputs and undesirable outputs, by incorporating their corresponding slacks in a unified formulation. Enumeration algorithms for the proposed models are theoretically derived, which transform the mixed-integer nonlinear programming problems into explicit enumeration procedures over a finite set of observed DMUs. The proposed measures satisfy several desirable properties, including feasibility, strict monotonicity, unit invariance, and invariance to alternate optima. The validation is conducted by assessing the performance of the Chinese thermal power industry.
A trust region gradient sampling algorithm that is applicable for solving nonsmooth unconstrained optimization problems in noisy environments is proposed, where a noisy environment is a scenario in which the function evaluation and gradient evaluation cannot be obtained precisely. The new algorithm constitutes a generalization of the basic trust region method. In the new approach, the subgradient used to formulate the trust region subproblem is computed through the gradient sampling approach. A novel reduction test is proposed to control the impact of noise on the performance of the developed algorithm. Under reasonable assumptions, the iterations of the algorithm ultimately enter one neighborhood and infinitely visit another neighborhood encompassed therein. The structures of these two neighborhoods are presented in this paper. Finally, the validity of the new algorithm is verified through numerical experiments.
Planning the optimal long-term generation of energy for hydro-thermal systems involves multistage stochastic programs in large dimensions. In Brazil, these problems are solved by stochastic dual dynamic programming (SDDP) techniques, considering that only water inflows into reservoirs are uncertain. The increasing growth of distributed generation has made net electricity consumption volatile, especially in the long term. To model accurately the impact of this phenomenon on the system load, the generation problem must consider not only the water inflows but also the net demand as stochastic input. We introduce probabilistic constraints into the considered multistage program, studying two different formulations. The first model ensures net demand satisfaction with a given probability, separately for each submarket in the power system. The resulting optimization problem remains solvable using the SDDP approach, without resorting to discretizing the probabilistic constraint. In the second model the probabilistic constraint holds jointly for all submarkets. This accounts for correlations unseen with the first model, but requires a sample-based discretization of the joint chance constraint. The corresponding discrete scenario representation leads to a multistage stochastic program with mixed integer variables, solved by stochastic dual integer dynamic programming. Results on real data for the Brazilian power system show the impact of the increasing penetration of distributed generation in the mix, and how the proposed probabilistic constrained models lead, not only to more stable profiles of thermal generation, but also to lower risk of deficit over the planning horizon.
This paper introduces a novel variational framework for image deblurring that leverages a spatially adaptive coupling of regularization terms. The proposed model integrates an edge-adaptive Total Variation (TV) with a non-convex L_1/L_2 gradient-based ratio through a unified spatio-structural mechanism. This hybrid approach enables a flexible diffusion process that effectively suppresses noise in homogeneous regions while mitigating over-smoothing near discontinuities. To solve the resulting non-convex and non-smooth optimization problem, we develop a high-performance numerical scheme based on the Alternating Direction Method of Multipliers (ADMM). Our solver integrates a Hybrid Conjugate Gradient with Anderson Acceleration (HCGAA) for primal updates and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) for non-smooth subproblems. Crucially, we establish a formal proof of global convergence to a stationary point by leveraging the Kurdyka-Łojasiewicz (KŁ) framework for semi-algebraic functions. Numerical experiments on blurred and noisy images demonstrate that the proposed ADMM–HCGAA–FISTA strategy consistently outperforms state-of-the-art methods, providing superior edge preservation and higher quantitative metrics.
Constructing ambiguity sets in distributionally robust optimization is difficult and currently receives increased attention. In this paper, we focus on mixture models with finitely many reference distributions. We present two different solution concepts for robust joint chance-constrained optimization problems with these ambiguity sets and non-convex constraint functions. Both concepts rely on solving an approximation problem that is based on well-known smoothing and penalization techniques. On the one side, we consider a classical bundle method together with an approach for finding good starting points. On the other side, we integrate the Continuous Stochastic Gradient method, a variant of the stochastic gradient descent that is able to exploit regularity in the data. On the example of gas networks, we compare the two algorithmic concepts for different topologies and two types of mixture ambiguity sets with Gaussian reference distributions and polyhedral and ϕ -divergence based feasible sets for the mixing coefficients. The results show that both solution approaches are well-suited to solve this difficult problem class. Based on the numerical results, we provide some general advice for choosing the more efficient algorithm depending on the main challenges of the considered optimization problem. We give an outlook for the applicability of the method in a wider context.
Power generation from renewable energy sources is the key to a sustainable future. However, the efficiency in energy conversion is driven by the precision of the control system. A common problem in this kind of applicationis the voltage sags in the DC link,which can disturb the operation ofthe machine-side converter. In thissense, this work presents a methodfor tuning applied proportional-integral controllers with cross-coupling feed forward compensation terms and an integral clamping strategy used to control direct drive non-salientpoles permanent magnet synchronous generator-based wind turbines under voltage sags. Thismethod is grounded in the black-winged kite optimization algorithm enhanced with chaoticinitialization using Chebyshevmap, and takes into consideration the minimization of the current tracking errors while concerns with system stability. Wind speed profile is emulated with a log-normal distribution model during the controller tuning and test. Anin-depth discussion on how to use the parametrization procedure is provided, discussing 45experiments (controller tuning andclosed-loop system performance using optimized controllers). Theresults indicate the feasibility of using this sophisticated control design, where all obtained sets ofgains provide fast tracking response and system stability,even when an unpredicted voltagesag occurs. Besides, a comparison with well-established meta-heuristic optimizers shows that the chaotic black-winged kite optimizer can provide a controller that provides smaller meanabsolute tracking errors incomparison to bat optimizer,artificial bee colony algorithm,and krill herd optimizer.
By sequencing the cells in several samples of a cancer mass, we can obtain the frequency of mutations occurring in the samples genomes. The variant allele frequencies factorization problem which leads to finding a phylogenetic tree showing the ancestral relationships between clones has attracted many researchers. Since real data are obtained from sequencing cells, they are prone to errors and suffer from uncertainty. In this paper, the robust mathematical formulations of this problem are proposed with different uncertainty sets. The robust model is defined under the uncertainty sets proposed by Bertsimas and Sim, the ellipsoidal, the interval, and the intersection of the ellipsoidal and interval uncertainty sets, then the results are compared. Since the interval uncertainty set is more conservative than the ellipsoidal and the intersection of the ellipsoidal and interval, it demonstrates greater robustness against data uncertainty. Consequently, in such problems, the resulting phylogenetic tree that illustrates the progression of cancer is more reliable. In the robust model under ellipsoidal and interval uncertainty sets, adjusting the parameters to increase model robustness yields a more reliable output.
This Special Issue of Optimization and Engineering presents four papers selected from the 2024 Sustainable Development of Energy, Water and Environment Systems (SDEWES) conference series after rigorous peer review. The contributions address (i) spatially explicit MILP optimisation of an offshore-wind-driven hydrogen supply chain, (ii) a game-theoretic coalition-formation framework for municipal waste-to-energy networks, (iii) dynamic-programming-based feedforward control of electric motor speed in four-wheel-drive electric vehicles, and (iv) an AC optimal-power-flow-driven prioritisation methodology for Dynamic Line Rating deployment. Together, the papers illustrate current trends in mixed-integer programming, cooperative game theory, optimal control and data-driven decision support for sustainable energy–water–environment systems, offering insights for researchers and practitioners working toward more resilient and resource-efficient engineered infrastructures.
