Constraints Of Problem Research Articles

A Review of Distribution Network Expansion Planning

Distribution Networks Expansion Planning (DNEP) is very complex and involves improving the system to meet the increasing demand using the most cost-effective strategy. Among the planned choices are the extension of substations, upgrade of distribution feeders, installation of additional Distributed Energy Resources (DERs), installation of Capacitor Banks (CBs) and many other methods. Distribution planners in contemporary networks must have faith in the reversibility of investments where Renewable Energy Resources (RERs) inject clean and cost-effective for DNEP to meet growing demand and environmental requirements. The comprehensive review of DNEP carried out in this paper covers all possible objective functions and problem constraints. With the rise of electric vehicles (EVs), there is a growing need to assess the impact of EV charging on distribution networks. Understanding how EV loads affect the network helps plan future expansions to efficiently accommodate the charging infrastructure. Integrating DERs, such as solar panels, wind turbines, and energy storage systems, is changing how electricity is generated, distributed, and consumed. Assessing the integration of DERs into distribution networks is crucial for optimal network planning and operation. In addition, CBs are essential for power factor correction and voltage regulation in distribution networks. Including CBs in expansion planning helps improve network efficiency, reliability, and overall power quality. By analyzing the impact of EV loads, DERs, and CBs in DNEP, researchers and planners can develop more accurate models and strategies for designing sustainable and resilient power systems to efficiently meet the growing energy demands.

Multipatch IGA for stress-constrained minimum weight structural topology optimization

In this article, an isogeometric analysis (IGA) formulation with various patches (multipatch approach) is proposed to solve the structural topology optimization (STO) problem. The multipatch formulation enables the solution of STO problems with geometries not equivalent to rectangles by using IGA. For this purpose, a minimum weight with stress constraints (MWSC) problem is stated. A quadratic B-splines basis defined for each patch is used to model the material distribution. The structural analysis is computed with IGA. The introduction of all of the stress constraints in the formulation of the problem is made with an overweight constraint (OC). Finally, the multipatch approach is validated with the solution of some benchmark problems.

Quantum distance approximation for persistence diagrams

Abstract Topological Data Analysis methods can be useful for classification and clustering
tasks in many different fields as they can provide two dimensional persistence dia-
grams that summarize important information about the shape of potentially complex
and high dimensional data sets. The space of persistence diagrams can be endowed
with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance.

However, computing the distance between two persistence diagrams involves finding an opti-
mal way to match the points of the two diagrams and may not always be an easy
task for classical computers. Recently, quantum algorithms have shown the po-
tential to speedup the process of obtaining the persistence information displayed on
persistence diagrams by estimating the spectra of persistent Dirac operators. So,
in this work we explore the potential of quantum computers to estimate the distance
between persistence diagrams as the next step in the design of a fully quantum frame-
work for TDA. In particular we propose variational quantum algorithms for the
Wasserstein distance as well as the dcp distance. Our implementation is a weighted
version of the Quantum Approximate Optimization Algorithm that relies on control
clauses to encode the constraints of the optimization problem.

Implicit Central Difference Approximations of Averaged Dynamics of Highly Oscillatory Systems With Applications to Direct Optimal Control

ABSTRACTTrajectory optimization of highly oscillatory systems can require huge computational efforts if the horizon of the problem is much larger than the duration of a single cycle. To alleviate this effort, stroboscopic averaging methods can be used, which utilize local single‐cycle simulations of the oscillatory dynamics to then approximate the average dynamics of the system and integrate them with integration steps much larger than a single cycle. Targeting especially the field of direct optimal control, where, after discretization, the simulation of the dynamics is often included implicitly in the equality constraints of the nonlinear programming problem, we introduce an implicit central difference scheme for the approximation of the average dynamics. In the introduced implicit central difference methods, we solve a nonlinear system of equations that connects single‐cycle simulations of the oscillatory dynamics in order to approximate the average dynamics from a linear combination of points in state‐space. We derive the accuracy order for this generalized ‐point central difference approximation of the average dynamics and confirm the claims in numerical experiments. Compared to existing explicit approaches, the introduced methods are up to twice as efficient while maintaining the same level of accuracy.

Study on the Electrical and Mechanical Properties of TiC Particle-Reinforced Copper Matrix Composites Regulated by Different Rare Earth Elements.

Copper matrix composites (CMCs) synergistically reinforced with rare earth oxides (Re2O3) and TiC were prepared using a powder metallurgy process with vacuum hot-pressing and sintering technology, aiming to explore new ways to optimize the properties of composites. Through this innovative approach, we propose a new solution strategy and idea for the difficult problem of mutual constraints between electrical and mechanical properties faced by traditional dual-phase reinforced Cu-matrix composites. Meanwhile, the modulation mechanism of Re2O3 in CMCs and the electrical and mechanical properties of the composites were investigated. The compressive yield strength was improved from pure Cu (50 MPa) to TiC/Cu (159 MPa). The yield strength of Eu2O3-TiC/Cu obtained after biphasic strengthening is 213 MPa, which is 326% higher than that of pure Cu, and the ultimate compressive strength reaches 790 MPa. The conductivity was enhanced from TiC/Cu (81.4% IACS) to La2O3-TiC/Cu (87.3% IACS).

Floorplanning with I/O Assignment via Feasibility-Seeking and Superiorization Methods.

The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee convergence in such situations, which are also heavily influenced by the initialization. We present a quantitative property about the choice of the initial point that helps good initialization and analyze the occurrence of the oscillation phenomena for bad initialization. In implementation, we introduce a resetting strategy aimed at effectively reducing the problem of algorithmic divergence in the projection-based method used for the feasibility-seeking formulation. Furthermore, we introduce the novel application of the superiorization method (SM) to floorplanning, which bridges the gap between feasibility-seeking and constrained optimization. The SM employs perturbations to steer the iterations of the feasibility-seeking algorithm towards feasible solutions with reduced (not necessarily minimal) total wirelength. Notably, the proposed algorithmic flow is adaptable to handle various constraints and variations of floorplanning problems, such as those involving I/O assignment. To evaluate the performance of Per-RMAP, we conduct comprehensive experiments on the MCNC benchmarks and GSRC benchmarks. The results demonstrate that we can obtain legal floorplanning results 166× faster than the branch-and-bound (B&B) method while incurring only a 5% wirelength increase compared to the optimal results. Furthermore, we evaluate the effectiveness of the algorithmic flow that considers the I/O assignment constraints, which achieves an 6% improvement in wirelength. Besides, considering the soft modules with a larger feasible solution space, we obtain 15% improved runtime compared with PeF, the state-of-the-art analytical method. Moreover, we compared our method with Parquet-4 and Fast-SA on GSRC benchmarks which include larger-scale instances. The results highlight the ability of our approach to maintain a balance between floorplanning quality and efficiency.

The vehicle routing problem as applied to residential solid waste collection operations: Systematic literature review

The accelerated growth of cities, population increase and economic development have leveraged waste generation globally. This trend is expected to continue, with a significant increase projected in the coming years. Therefore, efficient waste management has become a crucial concern for local, national and international authorities. Transportation plays a key role in waste collection and disposal, being directly related to traffic congestion, fuel consumption and environmental pollution. Despite the existing studies on household waste collection, there is a gap in the literature regarding routing for residential waste collection in medium-sized cities, especially in emerging and frontier developing countries. Therefore, this study seeks through the science tree metaphor and PRISMA methodology, to find studies focused on the vehicle routing problem in waste collection operations, considering aspects such as Modeling approaches and solution techniques, applied Vehicle Routing Problems variants, objective functions, decision variables and constraints, applications in real environments, applied algorithms, and studies considering uncertainty and real conditions. A methodological outline of Vehicle Routing Problems in waste collection operations is presented, where central research topics are identified such as processes developed with Geographic Information System and their integration with exact methods, time windows, multi-objective capacitated vehicle routing problems, the application of stochastic models consider the uncertainty in waste collection, which has allowed including future prediction and optimization as prediction models, based on neural networks, to foresee uncertain conditions of the operations. This article analyzes the evolution in the optimization of municipal solid waste collection routes since 1964, highlighting the transition from iterative models to advanced technologies and multi-objective approaches. The importance of tools such as 3D Geographic Information System and heuristic/metaheuristic algorithms in improving planning and efficiency, despite limitations in the face of uncertainty, is emphasized. The systematic review shows a trend towards sustainable and efficient solutions, indicating future directions for research in urban waste management.

A comparative study on BCTW-GIA and T-DW deposition processes

ABSTRACT To address the problem of mutual constraints between heat input and efficiency in arc additive manufacturing, a BCTW-GIA process is proposed. In this paper, components are manufactured using the BCTW-GIA and T-DW methods. The macroscopic morphology, cooling process, microstructure and properties of the components are analysed. According to the results, the BCTW-GIA method achieves a deposition efficiency of 15.46 kg/h, which is a 123% improvement compared to the T-DW method. The addition of the main wire in the BCTW-GIA method consumed some of the heat, resulting in less heat being applied to the member, and the maximum and average temperatures were reduced by 26% and 13%, respectively, compared to the T-DW method. The BCTW-GIA components have a finer grain size and an average microhardness of 197.17 HV. The BCTW-GIA specimens had higher transverse and longitudinal tensile strengths, which increased by 7% and 10% respectively over the T-DW specimens.

Predicting multi-parametric dynamics of an externally forced oscillator using reservoir computing and minimal data

AbstractMechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the external forcing seen during training, but it also provides qualitatively accurate and robust system response predictions for completely unknown multi-parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework correctly predicts higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.

Optimal Design of Pile Caps considering Soil Structures Iteration

This study presents a formulation for the optimum design of pile caps considering the soil structure interaction. To solve the optimization problem, the Bonobo algorithm is used. This algorithm was developed based on the social behavior of bonobos and is implemented for the design of the pile caps and the piles. The objective function considers the CO2 emissions and the pile cap final costs related to the materials used for its execution. The Brazilian standard impositions, and the criteria for determining the optimal dimensions of piles are the considered problem constraints. Comparative analyses are developed between the optimal solution against the proposed by structural design offices, and results proposed in the literature.

Distributionally robust CVaR optimization for refinery integrated production–maintenance scheduling under uncertainty

In the petroleum refining industry, efficient production planning and maintenance scheduling are crucial for economic performance and operational efficiency. Moreover, the production processes face significant uncertainties stemming from market fluctuations and equipment failures. However, traditional optimization methods often treat production and maintenance independently and neglect the risk management associated with uncertainties in the production process, leading to unreliable plans and suboptimal execution. To address these issues, this paper proposes an innovative data-driven distributionally robust conditional value-at-risk (DRCVaR) method to tackle the integrated production–maintenance optimization problem under crude oil price uncertainty. By constructing confidence sets with L2 norm constraints based on historical data, our approach directly links the model’s conservatism to the amount of available data, effectively managing risk. In addition, we propose robust linear transformation to simplify the min–max nonlinear problem into a conic constraint problem, enhancing solution efficiency and ensuring better operational stability. Refinery case studies demonstrate that the proposed DRCVaR consistently achieves a practical and acceptable solution, significantly outperforming state-of-the-art approaches.

REHAS: Robust and Efficient Hyperelliptic Curve‐Based Authentication Scheme for Internet of Drones

ABSTRACTInternet of Drones (IoD) is one of the most beneficial and has many versatile applications like Surveillance and Security, Delivery and Logistics, Environmental Monitoring, Agriculture, and so forth. The IoD network is crucial for collecting sensitive data like geo‐coordinates, vehicle traffic data, and property details while surveying the various deployment locations in smart cities. The communication between users and drones can be compromised over insecure wireless channels by multiple attacks such as Man‐in‐the‐middle‐attack, Denial of Service, and so forth. Many schemes have already been propounded in the field of IoD. Still, many of them cannot address the resource constraints problem of drones, and existing protocols have higher computation and communication costs. Therefore, this paper has proposed a robust and efficient Hyper‐Elliptic Curve‐based authentication scheme (REHAS), which provides a session key for secure communication. Artificial Identities are generated using a hash function and random numbers. Fuzzy Extractor is used for user biometric authentication, which makes the smart device secure when lost. HECC is used with a smaller bit size of 80 bits rather than ECC of 160 bits. The security of the REHAS has been ensured using Scyther simulation. Furthermore, the resilience, safety, and robustness of REHAS are ensured by Informal security analysis. Lastly, a comparative study of the REHAS has been performed with other related Authentication and key agreement (AKA) protocols regarding communication cost, Computation cost, and security features, demonstrating that REHAS incurred less computation cost (6.7171 ms), communication overhead (1696 bits), and energy consumption (22.5 mJ) than other existing AKA schemes.

Multiple-Input Multiple-Output Synthetic Aperture Radar Waveform and Filter Design in the Presence of Uncertain Interference Environment

Multiple-input multiple-output synthetic aperture radar (MIMO-SAR) anti-jamming waveform design relies on accurate prior information about the interference. However, it is difficult to obtain accurate prior knowledge about uncertain intermittent sampling repeater jamming (ISRJ), leading to a severe decline in the detection performance of MIMO-SAR systems. Therefore, this article studies the robust joint design problem of MIMO radar transmit waveform and filter against uncertain ISRJ. We characterize two categories of uncertain interference, including sample length uncertainty and sample-time uncertainty, modeled as Gaussian distribution in different range bins. Based on the uncertain interference model, we formulate the maximizing SINR as a figure of merit, which is a non-convex quadratic optimization problem under specific waveform constraints. Based on the alternating direction method of multipliers (ADMM) framework, a novel joint design algorithm of waveform and filter is proposed. In order to improve the convergence performance of ADMM, the difference in convex functions (DC) programming is applied to the ADMM iterations framework to solve the problem of waveform energy inequality constraint. Finally, numerical results demonstrate the effectiveness and robustness of the proposed method, compared to the existing methods that utilize deterministic interference models in the uncertain ISRJ environment. Moreover, the spaceborne SAR real scene imaging simulations are conducted to evaluate the anti-ISRJ performance.

A Case Study on the Application of Evolutionary Algorithms for Solving Non-linear Programming Problems in Water Resource Management

Evolutionary algorithms have been proposed and used in this case study for the solution to non-linear programming problems related to water resources. Heuristic, a type of optimization algorithm characterized by population-based search as well as using the genetic algorithms, are used to model and determine the optimal distribution and utilization of aquatic resources based on environmental and demand factors. These materials include examples based on water distribution networks, managing a reservoir, and forecasting demands of customers, demonstrating the effectiveness of the aforementioned algorithms in solving non-linear constraint problems and in dealing with multiple objectives. The comparative analysis is based on a number of simulation experiments to examine the efficiency of such microevolutionary algorithms as Genetic Algorithm, Particle Swarm Optimization, and Differential Evolution in contrast to the traditional optimization algorithms. These results show that there is significant value in using evolutionary algorithms as a basis for managing and modelling water resources as it offers a pragmatic approach and has the potential to meet the demands of the water industry in terms of sustainability, cost and resource requirements. There seems to be considerable scope for extension of these algorithms to a wide range of natural resources management and administration.

Robust Semi-Infinite Interval Equilibrium Problem Involving Data Uncertainty: Optimality Conditions and Duality

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from the literature. We introduce the dual robust version of the above problem, prove the Mond–Weir-type weak and strong duality theorems, and illustrate our results with an example.

Data-driven prediction of relevant scenarios for robust combinatorial optimization

We study iterative constraint and variable generation methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. The goal of this work is to find a set of starting scenarios that provides strong lower bounds early in the process. To this end we define the Relevant Scenario Recognition Problem (RSRP) which finds the optimal choice of scenarios which maximizes the corresponding objective value. We show for classical and two-stage robust optimization that this problem can be solved in polynomial time if the number of selected scenarios is constant and NP-hard if it is part of the input. Furthermore, we derive a linear mixed-integer programming formulation for the problem in both cases.Since solving the RSRP is not possible in reasonable time, we propose a machine-learning-based heuristic to determine a good set of starting scenarios. To this end, we design a set of dimension-independent features, and train a Random Forest Classifier on already solved small-dimensional instances of the problem. Our experiments show that our method is able to improve the solution process even for larger instances than contained in the training set, and that predicting even a small number of good starting scenarios can considerably reduce the optimality gap. Additionally, our method provides a feature importance score which can give new insights into the role of scenario properties in robust optimization.

Modified Noise-Immune Fuzzy Neural Network for Solving the Quadratic Programming With Equality Constraint Problem.

Quadratic programming with equality constraint (QPEC) problems have extensive applicability in many industries as a versatile nonlinear programming modeling tool. However, noise interference is inevitable when solving QPEC problems in complex environments, so research on noise interference suppression or elimination methods is of great interest. This article proposes a modified noise-immune fuzzy neural network (MNIFNN) model and use it to solve QPEC problems. Compared with the traditional gradient recurrent neural network (TGRNN) and traditional zeroing recurrent neural network (TZRNN) models, the MNIFNN model has the advantage of inherent noise tolerance ability and stronger robustness, which is achieved by combining proportional, integral, and differential elements. Furthermore, the design parameters of the MNIFNN model adopt two disparate fuzzy parameters generated by two fuzzy logic systems (FLSs) related to the residual and residual integral term, which can improve the adaptability of the MNIFNN model. Numerical simulations demonstrate the effectiveness of the MNIFNN model in noise tolerance.

Sustainable Water Management Solutions for Urban Areas

The management of water resources is a serious concern in urban areas because of the effects of climate change, aging infrastructure, and rapid population increase. This essay examines the vital significance of sustainable water management in urban settings, emphasizing cutting-edge frameworks for policy and technology that can improve water resilience and efficiency. Successful strategies, such as demand management and diversification of the water supply, are demonstrated by case studies like Windhoek, Namibia. In order to solve the intricate and interrelated problems of urban water scarcity, infrastructure constraints, and environmental repercussions, the essay emphasizes integrated water resources management (IWRM) as a crucial technique that incorporates multidisciplinary viewpoints. In order to guarantee a sustainable urban water future, the importance of inclusive policies and governance is also covered, highlighting the necessity of cooperative and flexible problemsolving techniques.

Multi-Static Radar System Deployment Within a Non-Connected Region Utilising Particle Swarm Optimization

This paper is mainly devoted to studying the deployment problem of a multi-static radar system (MSRS) within a non-connected deployment region using multi-objective particle swarm optimization (MOPSO). By modeling and reformulating the problem, it can be represented as a multi-objective mixed integer programming (MOMIP), which eliminates the need for additional constraints. To enhance the algorithm performance, integer variables and continuous ones are treated separately employing multiple velocity formulas. The velocity formulas for integer variables are modified using the sigmoid function and genetic operation, leading to the proposal of two MSRS deployment algorithms, namely MOPSO-Sigmoid and MOPSO-Gene. To evaluate the performance of the proposed algorithms, they are compared with two existing MOPSO-based algorithms. The first algorithm is the MSRS deployment algorithm for the non-connected deployment region that addresses the additional constraint problem model. The second algorithm is based on an existing conventional MOPSO algorithm and addresses the equivalent MOMIP problem model. A numerical study demonstrates that MOPSO-Sigmoid and MOPSO-Gene exhibit promising efficiency and effectiveness.

Optical circuit switched three-stage twisted-folded Clos-network design model guaranteeing admissible blocking probability

Some data center networks have already started to use optical circuit switching (OCS) with potential performance benefits, including high capacity, low latency, and energy efficiency. This paper addresses a switching network design to maximize the network radix, i.e., the number of terminals connected to the network under the condition that a specified number of identical switches with the size N×N and the maximum admissible blocking probability are given. Previous work presented a two-stage twisted and folded Clos network (TF-Clos) with a blocking probability guarantee for OCS, which has a larger network radix than TF-Clos with a strict-sense non-blocking condition. Expanding the number of stages allows for enhancing the network radix. This paper proposes a model designing an OCS three-stage TF-Clos structure with a blocking probability guarantee to increase the network radix compared to the two-stage TF-Clos. We formulate the problem of obtaining the network configuration that maximizes the network radix as an optimization problem. We conduct an algorithm based on an exhaustive search to obtain a feasible solution satisfying the constraints of the optimization problem. This algorithm identifies the structure with the largest network radix in non-increasing order to avoid unnecessary searches. Numerical results show that the proposed model achieves a larger network radix than the two-stage model.