Feasible Region Research Articles

Monomial asymptotic polynomials and applications to polynomial optimization problems

The problem of polynomial optimization plays an important role in many fields such as physics, chemistry, and economics. This problem has received research attention from many mathematicians recently. In this paper, we study the polynomial optimization problem over a non-compact semi-algebraic set, for which its constraint set of polynomials G is asymptotic with a finite family of monomials. By changing variables via a suitable monomial mapping, we transform the problem under consideration into the polynomial optimization problem over a compact semi-algebraic feasible set. We then apply the well-known result that the optimal value of a polynomial over a compact semi-algebraic set can be approximated as closely as desired by solving a hierarchy of semi-definite programs and the convergence is finite generically, to obtain results in the general case when the cone C(G) is unimodular. In particular, in the case of polynomials in two variables, we solve the problem quite completely without requiring C(G) to be unimodular

Computational techniques to monitoring fractional order type-1 diabetes mellitus model for feedback design of artificial pancreas

Background and objectives:In this paper, we developed a significant class of control issues regulated by nonlinear fractal order systems with input and output signals, our goal is to design a direct transcription method with impulsive instant order. Recent advances in the artificial pancreas system provide an emerging treatment option for type 1 diabetes. The performance of the blood glucose regulation directly relies on the accuracy of the glucose-insulin modeling. This work leads to the monitoring and assessment of comprehensive type-1 diabetes mellitus for controller design of artificial panaceas for the precision of the glucose-insulin glucagon in finite time with Caputo fractional approach for three primary subsystems. Methods:For the proposed model, we admire the qualitative analysis with equilibrium points lying in the feasible region. Model satisfied the biological feasibility with the Lipschitz criteria and linear growth is examined, considering positive solutions, boundedness and uniqueness at equilibrium points with Leray–Schauder results under time scale ideas. Within each subsystem, the virtual control input laws are derived by the application of input to state theorems and Ulam Hyers Rassias. Results:Chaotic Relation of Glucose insulin glucagon compartmental in the feasible region and stable in finite time interval monitoring is derived through simulations that are stable and bounded in the feasible regions. Additionally, as blood glucose is the only measurable state variable, the unscented power-law kernel estimator appropriately takes into account the significant problem of estimating inaccessible state variables that are bound to significant values for the glucose-insulin system. The comparative results on the simulated patients suggest that the suggested controller strategy performs remarkably better than the compared methods. Conclusion:In the model under investigation, parametric uncertainties are identified since the glucose, insulin, and glucagon system’s parameters are accurately measured numerically at different fractional order values. In terms of algorithm resilience and Caputo tracking in the presence of glucagon and insulin intake disturbance to maintain the glucose level. A comprehensive analysis of numerous difficult test issues is conducted in order to offer a thorough justification of the planned strategy to control the type 1 diabetes mellitus with designed the artificial pancreas.

Features of planning and managing power flows in distribution grids of megalopolises

The study examines the root causes of disruptions of normal operation of power distribution grids in large cities and metropolitan areas. The existing principles of scheduling and maintaining power flows in power distribution grids as well as ways of ensuring the reliability of their operation are analyzed. The integration of fuel-fired distributed generation facilities and renewable generation plants into distribution networks is shown to affect the ability to ensure transient stability during emergency disturbances. We establish evaluation criteria and provide upward margin values to determine the feasibility of the planned power flows. The study reveals general patterns in the calculation of the upward margin for power distribution grids of large cities and metropolitan areas. Test power flow analysis is performed for a real-world segment of a metropolitan area power distribution grid to identify possible overloads of power grid equipment and develop and implement a list of measures for the power flow to achieve the feasible region. The developed approach makes it possible to minimize load shedding or rule out load shedding altogether, ensuring reliable power supply to consumers in large cities and metropolitan areas in the event of an unexpected load growth.

Linear programming with infinite, finite, and infinitesimal values in the right-hand side

The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints enlarges the class of linear programs, where those described by finite values only become a special case. To tackle optimization problems over such polyhedra, there is a need for an ad-hoc solving routine: this work proposes a generalization of the Simplex algorithm, which is able to solve common linear programs as corner cases. Finally, the study presents three relevant applications that can benefit from the use of these novel constraints, making the use of the extended Simplex algorithm essential. For each application, an exemplifying benchmark is solved, showing the effectiveness of the proposed routine.

Simulation-based emergency department staffing and scheduling optimization considering part-time work shifts

Emergency department (ED) physicians have long been in short supply, which causes serious overcrowding and the excessive waiting of patients in many countries. ED managers are under great pressure to make staffing and scheduling decisions. To address this problem, this paper introduces part-time work shifts with fixed starting times and durations in peak hours to increase the flexibility and reduce patients’ waiting times. Then, a two-stage framework is proposed to optimize the weekly staffing and scheduling decisions with both fixed and part-time work shifts. Stage I is a weekly staffing problem to determine the number of physicians for both types of work shifts. The weekly staffing problem is decomposed and then solved using a simulation optimization method. Specifically, an adaptive partitioning empirical stochastic branch and bound (ESB&B-AP) algorithm is proposed by employing adaptive cut-generation methods in the process of feasible region partitioning, which significantly improves the searching efficiency of the algorithm. Stage II is a scheduling problem to determine the work schedules of physicians based on a predetermined set of work patterns. Numerical experiments validate the advantages of part-time work shifts, as well as the effectiveness of the two-stage optimization framework and the ESB&B-AP algorithm.

Manifold-assisted coevolutionary algorithm for constrained multi-objective optimization

In constrained multi-objective optimization problems (CMOPs), constraints often fragment the Pareto solution space into multiple feasible and infeasible regions. This fragmentation presents a challenge for evolutionary optimization methods as feasible regions can be discrete and isolated by infeasible areas, making exploration difficult and leading to populations getting trapped in local optima. To address these issues, this paper introduces a manifold assisted coevolutionary algorithm for solving CMOPs. Firstly, a guided feasible search strategy is proposed to explore feasible regions, especially those isolated by infeasible barriers. This is achieved by estimating directions to the Constrained Pareto Set (CPS). Secondly, a manifold learning-based exploration strategy is employed to spread the population along the Pareto Set (PS) manifold by estimating the manifold distribution. Moreover, two populations are exploited, where the first population serves as the primary population, considering both constraints and objectives to explore the feasible region and search along the CPS. The second population, on the other hand, does not consider constraints and serves as an auxiliary population to explore the Unconstrained PS. By cooperating, these two populations effectively approach and cover separated CPS segments. The proposed algorithm is evaluated against seven state-of-the-art algorithms on 37 CMOP test functions and 5 CMOPs with fraudulent constraints. The experimental results clearly demonstrate that our algorithm can reliably locate multiple CPSs and is considered state-of-the-art in handling CMOPs.

Capturing opportunity costs of peer-to-peer energy transactions in microgrids via virtual state-of-charge bids

Since the prosumers can absorb or generate power in the P2P energy market, we equivalently model the prosumers as virtual energy storages (VESs) and employ the latest state-of-charge (SOC)-dependent bids to depict the prosumers’ bidding strategies. We first model the P2P market participants’ trading behaviors considering their loads, batteries, and distributed energy resources (DERs). To derive the equivalent VESs, we develop an algorithm to estimate the prosumers’ virtual capacities. We analyze the market operator’s model to guarantee energy delivery in the distribution network. Then, we project the operator’s network constraints to the prosumers’ feasible regions for privacy preservation and iteration reduction. Based on the virtual capacities, we develop VSOCs to depict the prosumers’ different trading states during market operation. We finally convexify the market-clearing problem and modify the alternating direction method of multipliers (ADMM) to calculate the optimal trading results with VSOC-dependent bids. Two cases are employed to verify that the VSOC-dependent bids can accommodate the prosumers’ parameter changes and trading preferences. The opportunity costs are reduced by 41.2% when allowing prosumers to bid differently in various VSOCs.

Identification of feasible regions for managed aquifer recharge in the Republic of Cyprus using a co-participative multi-criteria decision analysis

This study proposes an integrated approach that aims at finding locations which are eligible for Managed Aquifer Recharge (MAR) installation in Cyprus via the active involvement of key stakeholders of MAR-related sectors during all stages of the decision process to ensure the validity of the outcomes. The MAR problem is jointly formulated with the key stakeholders according to the site needs by introducing the so-called "MAR typology" concept, consisting of the recharge objective, the recharge method, and the available water sources. Tertiary-treated wastewater is adapted as the water source, which is recharged in aquifers via recharge ponds for irrigation. Various sources of information have been considered for assessing the degree of feasibility, aggregated in three thematic clusters (feasibility components), namely intrinsic site-suitability, the availability of water resources for MAR purposes, and water demand. Twelve criteria have been selected jointly with key stakeholders to evaluate the feasibility components via a GIS-MCDA process. Seven of these criteria are associated with the intrinsic suitability of a region (aquifer, land-use, and topographical properties), and five criteria are associated with the amount of water available for MAR (characteristics of the water source and evapotranspiration) and the crop irrigation needs. Stakeholder meetings were conducted to determine weights for each criterion and thematic cluster, leading to thematic and feasibility maps. The results demonstrate large discrepancies among the feasibility components in terms of their spatial variation and the location where the most favourable regions are present. Smoother profiles are observed for intrinsic suitability compared to the other thematic layers, partly attributed to the use of a larger number of criteria. Sensitivity analysis demonstrates that the MAR-favourable regions are weakly influenced by the variation of the relevant importance among the thematic layers, being mostly present in the vicinity of the southern and south-eastern coastlines.

On the strength of Lagrangian duality in multiobjective integer programming

AbstractThis paper investigates the potential of Lagrangian relaxations to generate quality bounds on non-dominated images of multiobjective integer programs (MOIPs). Under some conditions on the relaxed constraints, we show that a set of Lagrangian relaxations can provide bounds that coincide with every bound generated by the convex hull relaxation. We also provide a guarantee of the relative quality of the Lagrangian bound at unsupported solutions. These results imply that, if the relaxed feasible region is bounded, some Lagrangian bounds will be strictly better than some convex hull bounds. We demonstrate that there exist Lagrangian multipliers which are sparse, satisfy a complementary slackness property, and generate tight relaxations at supported solutions. However, if all constraints are dualized, a relaxation can never be tight at an unsupported solution. These results characterize the strength of the Lagrangian dual at efficient solutions of an MOIP.

Convergence error analysis of reflected gradient Langevin dynamics for non-convex constrained optimization

AbstractGradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex constrained non-convex problems. In the present work, we extend those frameworks to non-convex problems on a non-convex feasible region with a global optimization algorithm built upon reflected gradient Langevin dynamics and derive its convergence rates. By effectively making use of its reflection at the boundary in combination with the probabilistic representation for the Poisson equation with the Neumann boundary condition, we present promising convergence rates, particularly faster than the existing one for convex constrained non-convex problems.

Patient safety in the Innovation Fund - Characterization, results and evaluation of completed projects: Results of a scoping review

The German Innovation Fund has funded various studies on patient safety. Their thematic spectrum, methodological quality, results and recommendations of the Innovation committee were to be systematically investigated in order to derive proposals for optimizing transfer success. As part of a scoping review, all Innovation Fund projects funded in the period 2016-02/2023 with a focus on patient safety were analyzed. Each included study document was critically reviewed by two independent persons. The 16 included projects addressed a wide range of populations, indications and interventions. The study quality was mostly good. The results ranged from feasible indicator sets and the prevention of adverse drug reactions to the optimization of error management. For seven projects, the Innovation Committee recommended forwarding the results to healthcare institutions with the request that they take note and/or examine the feasibility of implementation in standard care. Implementation, however, has not yet taken place. In order to facilitate implementation, the joint development of an implementation strategy by the recipients of the Innovation Committee's recommendations is necessary.

Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

This paper proposes a distributed consensus algorithm in predefined time of time‐varying optimization with inequality constrains for multi‐agent systems (MASs) with external disturbances over an undirected graph. Firstly, by utilizing exponential function, a novel criterion with respect to the stability in predefined time is developed for the nonlinear systems. Secondly, a new distributed switching control protocol, which can inhibit the external unbounded disturbances, is piecewise designed to drive the states of agents to the sliding mode surface via the predefined‐time set by users. Subsequently, under the designed event‐triggered controller (ETC), the states of agents achieve consensus in predefined time on the sliding mode surface. Meanwhile, with the help of log barrier function, the consensus states of agents reach the feasible region and converge to the optimal solution in predefined time. Finally, the correctness and availability of the proposed optimization control algorithm are verified by a simulation example.

Optimal aggregation and disaggregation for coordinated operation of virtual power plant with distribution network operator

Virtual power plants (VPPs) offer an effective approach for managing distributed energy resources (DERs), including microturbines, distributed generators, demand response aggregators, and energy storage systems. This technology significantly enhances the economic efficiency and flexibility of distribution network systems. This study aims to facilitate a flexible power exchange between the distribution network system and the upper-level grid by aggregating the power flexibility of heterogeneous DERs via a VPP. Additionally, it introduces a methodology for optimal aggregation and disaggregation within a coordinated operation framework between the VPP and distribution network operator (DNO). On one hand, the VPP can determine its day-ahead feasible region and real-time flexible regulation power based on operational constraints of DERs and representative data provided by the DNO, circumventing the need for detailed network information. On the other hand, day-ahead and real-time correction procedures for the DER cost functions are proposed, effectively neutralizing the impact of network operational constraints on these cost functions. Consequently, precise cost functions for both the active power and the flexible regulation power aggregated by the VPP are derived. Employing this aggregated cost function enables the determination of a cost-minimized optimal scheduling solution in real-time by solving a fundamental economic dispatch problem, significantly alleviating computational demands. Finally, case studies demonstrate that the proposed method achieves an error in aggregated power of only 0.77%, compared to the precise computation method that requires comprehensive system information. The proposed optimal VPP disaggregation scheme exhibits power discrepancies of 0.63% and cost discrepancies of 0.91% relative to the precise method. Additionally, when implementing the most cost-effective demand response plan based on the proposed cost function, the average costs for aggregators are reduced by 19.7%.

An individualized adaptive distributed approach for fast energy-carbon coordination in transactive multi-community integrated energy systems considering power transformer loading capacity

The optimization of multi-community integrated energy systems (MCIES), as a proficient means of integrating distributed energy resources and diverse loads, poses a compelling challenge. This challenge revolves around strategically harnessing the energy-carbon synergy advantages within these systems, while factoring in the heterogeneity among different communities and the constraints imposed by electrical connectivity devices. Facing the challenge, this paper proposes an individualized adaptive distributed approach for energy-carbon coordination in MCIES with power transformers (PT-MCIES). Firstly, a feasible region is constructed based on current and temperature limits to assess the loading capacity of power transformers. Based on this, a transactive energy (TE) based co-optimization model for PT-MCIES considering energy sharing and carbon trading is developed, where rolling horizon optimization is adopted to cope with the randomness from renewable energy and loads. For the TE problem, the alternating direction method of multipliers (ADMM) algorithm is employed to achieve distributed optimization. Uncertain renewable energy and loads, along with variable rolling horizons, make it difficult for the traditional ADMM to ensure convergence speed in the co-optimization of PT-MCIES. Accordingly, an individualized adaptive ADMM (IAADMM) embedded a spectral penalty parameter selection rule is adopted. Simulation results show that the proposed scheduling model can effectively guarantee the safe operation of power transformers with the suggestion of a feasible region, and achieve higher economic and environmental benefits than the reference one that ignores energy-carbon coordination. Furthermore, the proposed IAADMM exhibits superior performance in terms of convergence speed and robustness to the initial penalty parameter when compared to ADMM and its various variants.

Transient synchronization stability of a weak‐grid connected VSC considering the interaction of outer control loops and PLL dynamics

AbstractSince these large‐scale renewable power generation (RPGs) stations are always located far away from load centres, voltage source converters (VSCs) always operate in weak‐grid connected conditions, due to the long distance of transmission line and increasing capacity of RPGs. Large power disturbance of RPGs easily causes weak‐grid connected VSCs (WG‐VSCs) suffering from transient synchronization instability issue, which is lack of theoretical and quantitative analysis. This paper is motivated to fill this gap. By considering the dynamic interaction of outer DC voltage control, reactive power loop, and phase‐locked loop (PLL), an equivalent synchronization model of a WG‐VSC system is established first. Then, the mechanism of transient synchronization instability is revealed by the combination of equal area criterion and numerical integration method. Furthermore, the concept of feasible region of active power disturbance (FR‐APD) is introduced for the first time. With the constructed FR‐APD, the transient stability of the WG‐VSC system can be confirmed. Finally, experimental results based on the RT‐BOX hardware‐in‐the‐loop platform are presented to verify the theoretical analysis.

Riemann Problem for the Isentropic Euler Equations of Mixed Type in the Dark Energy Fluid

We are concerned with the Riemann problem for the isentropic Euler equations of mixed type in the dark energy fluid. This system is non-strictly hyperbolic on the boundary curve of elliptic and hyperbolic regions. We obtain the unique admissible shock waves by utilizing the viscosity criterion. Assuming fixed left states are in the elliptic and hyperbolic regions, respectively, we construct the unique Riemann solution for the mixed-type models with the initial right state in some feasible regions. Finally, we present numerical simulations which are consistent with our theoretical results.

Dynamic grey relational analysis-based supplier selection in a health-care unit

Purpose In the present-day highly customer-conscious service environment, supply chain management has become a critical component of health-care industry, helping in fulfilling patient expectation, optimizing inventory and automating departmental activities. Supplier selection is one of the crucial elements of health-care supplier chain, establishing mutually beneficial relationships with the reliable suppliers that provide the most value of money. Health-care supplier selection with feasible sets of alternatives and conflicting criteria can be treated as a multi-criteria decision making (MCDM) problem. Among the MCDM methods, grey relational analysis (GRA) appears as a potent tool due to its simple computational steps and ability to deal with imprecise data. The purpose of this paper is to explore the applicability of a newly developed MCDM tool for solving a health-care supplier selection problem. Design/methodology/approach In GRA, the distinguishing coefficient (ξ) plays a contributive role in final ranking of the alternative suppliers and almost all the past researchers have considered its value as 0.5. In this paper, a newly developed MCDM tool, i.e. dynamic GRA (DGRA), is adopted to evaluate the relative performance of 25 leading pharmaceutical suppliers for a health-care unit based on nine important financial metrics. Instead of static value of ξ, DGRA treats it as a dynamic variable dependent on grey relational variator and ranks the health-care suppliers using their computed rank product scores. Findings Based on rank product scores and developed exponential curve, DGRA classifies all the suppliers into reliable, moderately reliable and unreliable clusters, helping the health-care unit in identifying the best performing suppliers for subsequent order allocation. Among the reliable suppliers, alternatives A2 and A11 occupy the top two positions having almost the same performance with respect to the considered financial metrics. Originality/value Application of DGRA along with determination of the most reliable suppliers would help in effectively adopting multi-sourcing strategy to increase resilience while diversifying the supply portfolio, thereby enabling the health-care unit to minimize chances of sudden disruption in the supply chain. It can act as an intelligent decision-making framework aiding in solving health-care supplier selection problems considering perceived risks and dynamic input data.

Flexibility enhancement of urban energy systems through coordinated space heating aggregation of numerous buildings

Due to the intrinsic flexibility of thermal energy in buildings, collective space heating can potentially offer significant benefits to urban energy systems. In this context, this study introduces a novel thermal energy normalisation approach to capturing the collective indoor temperature dynamics of clustered buildings. The feasible operational region of the normalised equivalent building thermal energy model is derived from individual building parameters and temperature requirements through the constraint-tightening technique. By employing the thermal energy normalisation approach, the aggregate flexibility of building populations is quantified and integrated into the energy management optimisation problem for the urban energy system operator. To associate the response of the normalised equivalent building model and individual building models, a deadbeat controller is designed to synchronise the energy levels and realise robust operation for buildings. Through a series of case studies, the simulation results demonstrate that the proposed preheating coordination strategy can facilitate energy savings for energy system operation, cost-effectively perform congestion management to ensure no local network is overloaded, and ensure the satisfaction of indoor temperature requirements.

ATM-R: An Adaptive Tradeoff Model With Reference Points for Constrained Multiobjective Evolutionary Optimization.

The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and well-distributed feasible solutions. To achieve this goal, a delicate tradeoff must be struck among feasibility, diversity, and convergence. However, balancing these three elements simultaneously through a single tradeoff model is nontrivial, mainly because the significance of each element varies in different evolutionary phases. As an alternative approach, we adapt distinct tradeoff models in various phases and introduce a novel algorithm named adaptive tradeoff model with reference points (ATM-R). In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence." This transition is instrumental in discovering an adequate number of feasible regions and accelerating the search for feasible Pareto optima in succession. In the feasible phase, ATM-R places an emphasis on balancing diversity and convergence to obtain a set of feasible solutions that are both well-converged and well-distributed. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a diverse set of benchmark test functions and real-world problems demonstrate that ATM-R is effective. When compared to eight state-of-the-art constrained multiobjective optimization evolutionary algorithms, ATM-R consistently demonstrates its competitive performance.

Nearby allocation of emergency repair resources for multiple faults in distribution networks based on parallel CNN algorithm

In order to improve the efficiency of emergency repair for multiple faults in distribution networks, a method for allocating emergency repair resources for multiple faults in distribution networks based on parallel convolutional neural network (CNN) algorithm is studied. This method uses a matrix operation based multiple fault detection method for distribution networks. After determining the location of multiple faults based on the direction of fault power, the principle is to allocate emergency repair resources nearby for multiple faults, with the goal of minimizing economic losses caused by the fault point and minimizing fault repair time. The objective function for allocating emergency repair resources nearby is constructed, and parallel CNN algorithm is used to solve the problem by classification, to find the feasible solution with the minimum mean square error between the objective function and the feasible solution set for nearby allocation of emergency repair resources, and it is used as the optimal solution for nearby allocation of repair resources. The experimental results show that when the proposed method is used to allocate emergency repair resources for multiple faults in the distribution network, the optimal time for setting the repair plan is 0.53 and 0.96 s, respectively, with an average allocation accuracy of 91%. It has been confirmed that this method can achieve the optimal decision of resource allocation plan in a short period of time, improving the efficiency of emergency repair.