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Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets (...log(n) log(...)), iteration complexity bound for large-update methods with the special choice of its parameters. [ABSTRACT FROM AUTHOR]

In this paper, we use the dataset of a marine berthing structure per hour to construct the objective and linear constraint functions from the combination of a simple and non-preemptive queuing model, and we determine the optimal design of vessels and layout of quay through the solutions of quadratic programming problems. A methodology is proposed to formulate the quadratic programming problems from the input and output data of the mixed queuing model as the constraints on the characteristics of logistic demand, service time, waiting time, vessels, and layout of service quay for minimum utilization cost. This approach is applied to the port authority of Kribi in the south region of Cameroon to examine the more precise optimal solution with nonlinear complexities in the programs of discrete computer simulations. With adaptive experimental data of the modelling of berths as mixed models, the results provide the value of the most optimal solution projected in the port of Kribi compared to the solutions of integer and traditional linear programming problems. This study delivers the optimal number of vessel types and the associated layout in order of importance among the vessel types which can be safely moored for operations.

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This paper presents some novel theoretical results as well as practical algorithms and computational procedures on continuous fuzzy relational equations programming problems. The fuzzy relational programming problem is a minimization (maximization) problem with a linear objective function subject to fuzzy relational equalities or inequalities defined by certain algebraic operations. In the literature, the commonly seen frameworks for such optimization models are to assume that the operation takes minimum t-norm, strict continuous t-norms (e.g., product t-norm), nilpotent continuous t-norms (e.g., Lukasiewicz t-norm) or Archimedean continuous t-norms. Based on new concepts called partial solution sets, the current paper considers this problem in the most general case where the fuzzy relational equality constraints are defined by an arbitrary continuous t-norm and capture some special characteristics of its feasible domain and the optimal solutions. It is shown that the current generalized results are automatically reduced to (apparently) different ones that hold for special operators when continuous t-norm is replaced by strict, nilpotent or Archimedean continuous t-norm. Also, the relationship between the results derived here and those of previous publications regarding this subject is also discussed. Finally, the proposed algorithm is outlined and illustrated by a numerical example where the continuous fuzzy relational equations is defined by Mayor-Torrens operator that is not an Archimedean t-norm (and then, neither strict nor nilpotent). [ABSTRACT FROM AUTHOR]

The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems. Specifically, we are interested in problem instances requiring a known optimal solution, a known optimal partition, a specific interior solution, or all these together. In the proposed problem generators, different characteristics of optimization problems, including dimension, size, condition number, degeneracy, optimal partition, and sparsity, can be chosen to facilitate comprehensive computational experiments. We also develop procedures to generate instances with a maximally complementary optimal solution with a predetermined optimal partition to generate challenging semidefinite and second-order cone optimization problems. Generated instances enable us to evaluate efficient interior-point methods for conic optimization problems. [ABSTRACT FROM AUTHOR]

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially quantum interior point methods (QIPMs), to solve convex conic optimization problems. Most of them have applied a quantum linear system algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates in detail the use of quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point (II-QIPM) is developed to solve linear optimization problems. We also discuss how we can get an exact solution by iterative refinement (IR) without excessive time of quantum solvers. The proposed IR-II-QIPM shows exponential speed-up with respect to precision compared to previous II-QIPMs. Additionally, we present a quantum-inspired classical variant of the proposed IR-II-QIPM where QLSAs are replaced by conjugate gradient methods. This classic IR-II-IPM has some advantages compared to its quantum counterpart, as well as previous classic inexact infeasible IPMs. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are presented and analyzed. [ABSTRACT FROM AUTHOR]

Slope leveling is essential for the successful implementation of ground-mounted centralized photovoltaic (PV) plants, but currently, there is a lack of optimization methods available. To address this issue, a linear programming approach has been proposed to optimize PV slope leveling. This method involves dividing the field into blocks and grids and using hyperbolic paraboloids to simulate the design surface. By programming in MATLAB, the globally optimal solution for PV slope leveling can be calculated. Engineering case studies have demonstrated that this optimization method can achieve significant cut-and-fill volume savings ranging from 58% to 78%, when compared to the traditional segmented plane method. Additionally, the effectiveness of the optimization method improves with larger site areas and more complex terrains. A parameter analysis considering slope ratio, grid size, and block size reveals that grid size has a minimal impact on cut-and-fill volume, while slope ratio and block size have a significant influence. For typical PV projects, the recommended ranges of slope ratio, grid size, and block size are 3–7%, 5–20 m, and 30–50 m, respectively, for slope leveling design. In summary, the proposed linear optimization method provides an optimal slope leveling scheme for ground-mounted centralized PV plants, with convenient operation and fast computation. [ABSTRACT FROM AUTHOR]

This article utilizes a simple univariate function to formulate the search direction for the full-Newton step and constructs a metric to estimate the distance between the iterative point and the central path. By doing so, it designs an infeasible interior point algorithm for linear optimization problems that employs only one kind of search step. As demonstrated in the complexity analysis, this straightforward univariate function proves to be highly beneficial in analyzing the algorithm. Additionally, we discuss the update parameters and threshold parameters of the algorithm, present three methods for parameter updates, and compare the efficiency of these three methods using numerical examples. [ABSTRACT FROM AUTHOR]

Background and Objectives: Red blood cell (RBC) transfusions pose a risk of alloantibody development in patients. For patients with increased alloimmunization risk, extended preventive matching is advised, encompassing not only the ABO‐D blood groups but also the most clinically relevant minor antigens: C, c, E, e, K, Fya, Fyb, Jka, Jkb, S and s. This study incorporates patient‐specific data and the clinical consequences of mismatching into the allocation process. Materials and Methods: We have redefined the MINimize Relative Alloimmunization Risks (MINRAR) model to include patient group preferences in selecting RBC units from a finite supply. A linear optimization approach was employed, considering both antigen immunogenicity and the clinical impact of mismatches for specific patient groups. We also explore the advantages of informing the blood bank about scheduled transfusions, allowing for a more strategic blood distribution. The model is evaluated using historical data from two Dutch hospitals, measuring shortages and minor antigen mismatches. Results: The updated model, emphasizing patient group‐specific considerations, achieves a similar number of mismatches as the original, yet shifts mismatches among patient groups and antigens, reducing expected alloimmunization consequences. Simultaneous matching for multiple hospitals at the distribution centre level, considering scheduled demands, led to a 30% decrease in mismatches and a 92% reduction in shortages. Conclusion: The reduction of expected alloimmunization consequences by incorporating patient group preferences demonstrates our strategy's effectiveness for patient health. Substantial reductions in mismatches and shortages with multi‐hospital collaboration highlights the importance of sharing information in the blood supply chain. [ABSTRACT FROM AUTHOR]

One of the main challenges of food bank warehouses in developing countries is to determine how to allocate perishable products to beneficiary agencies with different expiry dates while ensuring food safety, meeting nutritional requirements, and minimizing the shortage. The contribution of this research is to introduce a new multi-objective, multi-product, and multi-period perishable food allocation problem based on a single warehouse management system for a First Expired-First Out (FEFO) policy. Moreover, it incorporates the temporal aspect, guaranteeing the dispatch of only those perishable products that meet the prescribed minimum quality standards. A weighted sum approach converts the multi-objective problem of minimizing a vector of objective functions into a scalar problem by constructing a weighted sum of all the objectives. The problem can then be solved using a standard constrained optimization procedure. The proposed mixed integer linear model is solved by using the CPLEX solver. The solution obtained from the multi-objective problem allows us to identify days and products experiencing shortages. In such cases, when there is insufficient available inventory, the total quantity of product to be dispatched is redistributed among beneficiaries according to a pre-established prioritization. These redistributions are formulated as integer programming problems using a score-based criterion and solved by an exact method based on dynamic programming. Computational results demonstrate the applicability of the novel model for perishable items to a real-world study case.

Abstract Bidirectional charging allows energy from the electric vehicles (EV) to be fed back into the grid, offering the possibility of price-optimized charging. However, such strategies cause higher charging cycles, which affect the cyclic aging of the battery and reduce its service life, resulting in additional costs for the user. Various approaches are used to account for battery degradation in optimizations models of bidirectional charging use-cases. In this paper, a systematic literature review is carried out to identify existing battery degradation models and to determine the most suitable one. In the models under review, degradation is integrated into the optimization’s objective function. The review shows that there are mainly two strategies suitable for vehicle-to-grid (V2G) optimization problems: A weighted Ah-throughput model (wAh-model) with a constant degradation cost factor and a performance based model (pb-model) linking the degradation to measurable parameters such as capacity loss. Both models were implemented and analyzed. The results show that the wAh-model is the better optimization option, as in the pb-model the current state of health of the battery has an excessively large impact on the calculated degradation cost. It leads to excess costs due to a higher aging rate at the beginning of life which proves to be not ideal in the optimization. The sensitivity analysis reveals that altering the initial State of Health (SoH) from 95 % in the base scenario to 100 % leads to an increase in average degradation costs by factor 9.71 in the pb-model. From the evaluated base scenario the average degradation costs for the pb-model are 0.45 cent/kWh and for the wAh-model 0.23 cent/kWh.

Exploring pathways for transitioning to clean energy to achieve climate change mitigation goals is essential. Addressing the economic impact of decarbonization options requires strategic planning to determine cost-effective CO2 mitigation strategies. The assessment of marginal CO2 abatement cost curves (MACC) is commonly used to link costs and emission reduction of decarbonization measures, with the cumulative CO2 abatement potential and associated costs.This study aims to calculate a step-wise MACC to identify the most cost-effective order of investments in decarbonization measures for the German sector-coupled energy system from 2030 to 2045. It provides in-depth insights into the techno-economic, intertemporal, and intersectoral interactions of decarbonization options by applying a linear optimization model to determine the minimal cost of CO2 abatement.The results show that the optimal strategy for decarbonization includes expanding wind and solar power capacity, and increasing demand-side flexibility, by integrating battery electric vehicles, power-to-heat, and power-to-gas. Results indicate that the interaction between the decarbonization measures is significant and that the integration of surplus electricity through sector-coupling can significantly reduce curtailment. Overall, the presented step-wise MACC approach can support policymakers in determining the most cost-efficient energy strategy by identifying the optimal technology mix to meet specific climate goals.

Versatile video coding (VVC) aims to achieve high compression but also issues like varying content/network conditions. Existing rate control (RC) methods struggle to achieve optimal quality under these complex scenarios. This paper proposes a novel RC scheme for VVC based on a linear model. The Lagrange minimization multiplier is introduced under bit budget constraints, allowing optimized bit allocation. RC optimization is formulated as a convex solution, and is derived into the optimal quantization parameter (QP) for RC. Experimental analysis demonstrates the proposed linear model-based RC algorithm performances are better compared to other state-of-the-art methods due to their use of a linear model and optimal QP determination. [ABSTRACT FROM AUTHOR]

This paper proposes a secure data access control framework that utilizes the attribute values and the user specific usage details to provide secure and fine-grained data access. It aims to minimize the data leakage during data retrieval which is a critical challenge for handling health data. No standard data retrieval policies are in place for preserving the privacy of medical data though any data breach may have a disastrous effect on society. In our proposed framework data is divided into different segments based on data sensitivity and data utility and users are authorized based on attribute details. An Integer Linear Programming (ILP) based solution is designed here to optimize the amount of information a user can retrieve from the application while minimizing the data leakage. The data storage technique and the user authorization technique complement each other to decide upon access to the portion of the information available to that particular user. An experimental result shows the sensitivity score calculation of the data items, ILP based privilege value assignment of the users and data retrieval strategy to minimize data leakage. The technique is validated on the benchmark datasets. The results show the utility of the sensitivity score of the data items and user privilege values while ensuring faster data retrieval time as compared to state-of-the-art works. [ABSTRACT FROM AUTHOR]

We consider a decomposition approach to the problem of finding the orthogonal projection of a given point onto a convex polyhedral cone represented by a finite set of its generators. The reducibility of an arbitrary linear optimization problem to such projection problem potentially makes this approach one of the possible new ways to solve large-scale linear programming problems. Such an approach can be based on the idea of a recurrent dichotomy that splits the original large-scale problem into a binary tree of conical projections corresponding to a successive decomposition of the initial cone into the sum of lesser subcones. The key operation of this approach consists in solving the problem of projecting a certain point onto a cone represented as the sum of two subcones with the smallest possible modification of these subcones and their arbitrary selection. Three iterative algorithms implementing this basic operation are proposed, their convergence is proved, and numerical experiments demonstrating both the computational efficiency of the algorithms and certain challenges in their application are performed. [ABSTRACT FROM AUTHOR]

Slope leveling is essential for the successful implementation of ground-mounted centralized photovoltaic (PV) plants, but currently, there is a lack of optimization methods available. To address this issue, a linear programming approach has been proposed to optimize PV slope leveling. This method involves dividing the field into blocks and grids and using hyperbolic paraboloids to simulate the design surface. By programming in MATLAB, the globally optimal solution for PV slope leveling can be calculated. Engineering case studies have demonstrated that this optimization method can achieve significant cut-and-fill volume savings ranging from 58% to 78%, when compared to the traditional segmented plane method. Additionally, the effectiveness of the optimization method improves with larger site areas and more complex terrains. A parameter analysis considering slope ratio, grid size, and block size reveals that grid size has a minimal impact on cut-and-fill volume, while slope ratio and block size have a significant influence. For typical PV projects, the recommended ranges of slope ratio, grid size, and block size are 3–7%, 5–20 m, and 30–50 m, respectively, for slope leveling design. In summary, the proposed linear optimization method provides an optimal slope leveling scheme for ground-mounted centralized PV plants, with convenient operation and fast computation.

Our aim in this work is to extend the primal-dual interior point method based on a kernel function for linear fractional problem. We apply the techniques of kernel function-based interior point methods to solve a standard linear fractional program. By relying on the method of Charnes and Cooper [3], we transform the standard linear fractional problem into a linear program. This transformation will allow us to define the associated linear program and solve it efficiently using an appropriate kernel function. To show the efficiency of our approach, we apply our algorithm on the standard linear fractional programming found in numerical tests in the paper of A. Bennani et al. [4], we introduce the linear programming associated with this problem. We give three interior point conditions on this example, which depend on the dimension of the problem. We give the optimal solution for each linear program and each linear fractional program. We also obtain, using the new algorithm, the optimal solutions for the previous two problems. Moreover, some numerical results are illustrated to show the effectiveness of the method.

Bidirectional charging allows energy from the electric vehicles (EV) to be fed back into the grid, offering the possibility of price-optimized charging. However, such strategies cause higher charging cycles, which affect the cyclic aging of the battery and reduce its service life, resulting in additional costs for the user. Various approaches are used to account for battery degradation in optimizations models of bidirectional charging use-cases. In this paper, a systematic literature review is carried out to identify existing battery degradation models and to determine the most suitable one. In the models under review, degradation is integrated into the optimization's objective function. The review shows that there are mainly two strategies suitable for vehicle-to-grid (V2G) optimization problems: A weighted Ah-throughput model (wAh-model) with a constant degradation cost factor and a performance based model (pb-model) linking the degradation to measurable parameters such as capacity loss. Both models were implemented and analyzed. The results show that the wAh-model is the better optimization option, as in the pb-model the current state of health of the battery has an excessively large impact on the calculated degradation cost. It leads to excess costs due to a higher aging rate at the beginning of life which proves to be not ideal in the optimization. The sensitivity analysis reveals that altering the initial State of Health (SoH) from 95 % in the base scenario to 100 % leads to an increase in average degradation costs by factor 9.71 in the pb-model. From the evaluated base scenario the average degradation costs for the pb-model are 0.45 cent/kWh and for the wAh-model 0.23 cent/kWh. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step size, interior point algorithms can be divided into two main groups, short-step, and long-step methods. In practice, long-step variants perform better, but usually, a better theoretical complexity can be achieved for the short-step methods. One of the exceptions is the large-update algorithm of Ai and Zhang. The new wide neighborhood and the main characteristics of the presented algorithm are based on their approach. In addition, we use the algebraic equivalent transformation technique of Darvay to determine new modified search directions for our method. We show that the new long-step algorithm is convergent and has the best known iteration complexity of short-step variants. We present our numerical results and compare the performance of our algorithm with two previously introduced Ai-Zhang type interior point algorithms on a set of linear programming test problems from the Netlib library. [ABSTRACT FROM AUTHOR]

Low-inertia, isolated power systems face the problem of resiliency to active power variations. The integration of variable renewable energy sources, such as wind and solar photovoltaic, pushes the boundaries of this issue further. Higher shares of renewables requires better evaluations of electrical system stability, to avoid severe safety and economic consequences. Accounting for frequency stability requirements and allocating proper spinning reserves, therefore becomes a topic of pivotal importance in the planning and operational management of power systems. In this paper, dynamic frequency constraints are proposed to ensure resiliency during short-term power variations due to, for example, wind gusts or cloud passage. The use of the proposed constraints is exemplified in a case study, the constraints being integrated into a mixed-integer linear programming algorithm for sizing the optimal capacities of solar photovoltaic and battery energy storage resources in an isolated industrial plant. Outcomes of this case study show that reductions in the levelized cost of energy and carbon emissions can be overestimated by 8.0% and 10.8% respectively, where frequency constraints are neglected. The proposed optimal sizing is validated using time-domain simulations of the case study. The results indicate that this optimal system is frequency stable under the worst-case contingency.

In this work, we investigate a full Newton step infeasible interior-point method for linear optimization based on a new search direction which is obtained from an algebraic equivalent transformation of the central path system. Furthermore, we prove that the proposed method obtains an ε-optimal solution to the original problem in polynomial time.

This paper introduces a framework aimed at analyzing the water-energy-food nexus (WEF) within the context of sustainable farming practices utilizing renewable energy sources, specifically Solar PV, to optimize water management efficiency. The focus lies on investigating the interplay between the water-energy-food nexus and both technical and institutional factors. The study particularly delves into the utilization of distributed energy systems and microgrids for electricity distribution. To achieve the objectives outlined, the framework is applied to a case study involving an off-grid farm in Morocco, aligned with the country's "Green Morocco Plan" of 2008. The study employs the AnyMOD open-source modeling framework in combination with the publicly available decision support tool CropWat (Version 8.0). Through this coupling, a linear optimization model is created to assess various irrigation practices, thus evaluating the energy and water supply variations across different crop growth stages. By employing scenario analysis, the study reveals that the integration of a smart microgrid alongside storage technologies proves beneficial in terms of reducing overall system costs. This integration presents cost-effective solutions and enables the establishment of a sustainable energy supply driven by renewable energy resources. Furthermore, the investigation highlights that constraining irrigation to specific hours of the day results in increased storage requirements and higher associated costs. In conclusion, the study underscores that enhancing the water-energy-food nexus through the integration of a renewable-based microgrid is a complex task. However, it significantly contributes to the development of sustainable farming solutions. This research sheds light on the challenges and opportunities associated with aligning renewable energy, water management, and agricultural practices, ultimately facilitating the pursuit of environmentally conscious and efficient farming methodologies. [ABSTRACT FROM AUTHOR]

One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup. [ABSTRACT FROM AUTHOR]

In this paper, we propose a full-Newton step infeasible interior-point algorithm (IPA) for solving linear optimization problems based on a new kernel function (KF). The latter belongs to the newly introduced hyperbolic type (Guerdouh et al. in An efficient primal-dual interior point algorithm for linear optimization problems based on a novel parameterized kernel function with a hyperbolic barrier term, 2021; Touil and Chikouche in Acta Math Appl Sin Engl Ser 38:44–67, 2022; Touil and Chikouche in Filomat 34:3957–3969, 2020). Unlike feasible IPAs, our algorithm doesn't require a feasible starting point. In each iteration, the new feasibility search directions are computed using the newly introduced hyperbolic KF whereas the centering search directions are obtained using the classical KF. A simple analysis for the primal-dual infeasible interior-point method (IIPM) based on the new KF shows that the iteration bound of the algorithm matches the currently best iteration bound for IIPMs. We consolidate these theoretical results by performing some numerical experiments in which we compare our algorithm with the famous SeDuMi solver. To our knowledge, this is the first full-Newton step IIPM based on a KF with a hyperbolic barrier term. [ABSTRACT FROM AUTHOR]

To limit climate change, decarbonization of the transportation sector is necessary. The change from conventional combustion vehicles to vehicles with electric drives is already taking place. In the long term, it can be assumed that a large proportion of passenger cars will be battery–electric. On the one hand, this conversion will result in higher energy and power requirements for the electricity network; on the other hand, it also offers the potential for vehicles to provide energy for various systems in the future. Battery–electric vehicles can be used to shift grid purchases, optimize the operation of other components and increase the self-consumption rate of photovoltaic systems. An LP model for the optimal energy management of the neighborhood consisting of buildings with electricity and heat demand, a PV system, a BEV fleet, a heat pump and thermal storage was formulated. The potential of the BEV fleet to provide energy via V2B in the neighborhood was investigated, considering electricity tariff models and individual charging/discharging efficiencies of vehicles and stochastic mobility profiles. The vehicle fleet provides between 4.8 kWh −1 sqm −1 a (flat-fee) and 25.3 kWh −1 sqm −1 a (dynamic tariff) per year, corresponding to 6.7, 9.5% and 35.7% of the annual energy demand of the neighborhood. All tariff models lead to optimization of self-consumption in summer. Dynamic pricing also leads to arbitrage during winter, and a power price tariff avoids peaks in grid draw. Due to individual charging efficiencies, the power supplied by the fleet is distributed unevenly among the vehicles, and setting limits for additional equivalent full cycles distributes the energy more evenly across the fleet. The limits affect the V2B potential, especially below the limits of 20 yearly cycles for flat and power tariffs and below 80 cycles for a dynamic tariff. [ABSTRACT FROM AUTHOR]

In order to explore the flow characteristics at tip clearance and the coupling deformation of the blade during running on the centrifugal air compressor, based on the fluid-structure coupling heat transfer theory, the hydrodynamic and structural mechanics numerical calculation models of the impeller were established. Considering centrifugal force, aerodynamic force and thermal stress, the stress and deformation distribution at the blade tip under different tip clearances were analyzed. The results show that tip clearance can generate inlet separation vortex and tip leakage flow, which together disturb the flow in the main flow zone and increase the flow loss. Under the combined action of centrifugal force, air pressure load and thermal load, the maximum deformation of the blade occurs at about 0. 3 chord length of the blade tip. The maximum deformation of the suction surface is 3. 7% larger than that of the pressure surface. With the decrease of the blade height, deformation decreases gradually. The stress value at the leading edge of blade tip is small, and the maximum stress value at the pressure surface and suction surface is not in the same axial position. With the increase of clearance value, the overall stress value at the top gradually decreases. Through the flow field and structure analysis, the optimum clearance size was determined, and the blade was optimized. The aerodynamic performance and safety of the blade were significantly improved after optimization. [ABSTRACT FROM AUTHOR]

The infinite time reachable set of a strictly stable linear control system is the Hausdorff limit of the finite time reachable set of the origin as time tends to infinity. By definition, it encodes useful information on the long-term behavior of the control system. Its characterization as a limit set gives rise to numerical methods for its computation that are based on forward iteration of approximate finite time reachable sets. These methods tend to be computationally expensive, because they essentially perform a Minkowski sum in every single forward step. We develop a new approach to computing the infinite time reachable set that is based on the invariance properties of the control system and the desired set. These allow us to characterize a polyhedral outer approximation as the unique solution to a linear program with constraints that incorporate the system dynamics. In particular, this approach does not rely on forward iteration of finite time reachable sets. [ABSTRACT FROM AUTHOR]

Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets ..., iteration complexity bound for large-update methods with the special choice of its parameters. [ABSTRACT FROM AUTHOR]

Investments in the development of the district heating system require a thorough analysis of the technical, economic, and legal aspects. Regarding the technical and economic context, a mathematical model of the district heating system has been proposed. It optimizes both the technical and economic aspects of the function and development of a district heating system. To deal with non-linearities, the developed linear programming model is divided into three phases: flow, thermal, and pressure. Therein, non-linear dependencies are calculated between the linear optimization phases. This paper presents the main assumptions and equations that were used to calculate the parameters of the heating system, along with the optimal level of heat production, the flow rate of the heating medium in the heat nodes and edges of the network graph, the heat, power, and temperature losses at each edge, and the purchase costs of heat and its transmission. The operation of the model was tested on a real-world district heating system. The case study results confirm that the model is effective and can be used in decision support. The economic results of the model, before the calibration process, were 3.6% different from historical values. After the calibration process, they were very similar to the real data—all percentage deviations were within 1%. [ABSTRACT FROM AUTHOR]

A large number of researchers have addressed social aspects in hierarchical production planning. This article responds to research gaps identified in our previous literature review. Accordingly, consideration of social aspects and the economic implications of social improvements are required in a longer term planning approach. For this, we integrate work intensity as employee utilization in a general mixed-integer programming model for master production scheduling. Following existing fatigue functions, we represent the relationship between work intensity and exhaustion through an employee-utilization-dependent exhaustion function. We account for the economic implications through exhaustion-dependent capacity load factors. We solve our model with a CPLEX standard solver and analyze a case study based on a realistic production system and numerical data. We demonstrate that the consideration of economic implications is necessary to evaluate social improvements. Otherwise, monetary disadvantages are overestimated, and social improvements are, thus, negatively affected. Moreover, from a certain level of work-intensity reduction, demand peaks are smoothed more by pre-production, which requires more core employees, while temporary employment is reduced. Further potential may arise from considering and quantifying other interdependencies, such as employee exhaustion and employee days off. In addition, the relationship between social working conditions and employee turnover can be integrated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new optimization problem with respect to a generalized form of fuzzy relational equations (FRE) in which fuzzy equality replaces ordinary equality in the constraints (FRE-FC). Fuzzy constraints enable us to attain optimal points (called super-optima in this paper) that are better solutions than those resulted from the resolution of the similar problems with ordinary equality constraints. Some structural properties of the FRE-FC problems are studied and a new formulation is presented in which the fuzzy constraints (equations) are precisely modeled. Subsequently, a new PSO-based algorithm is proposed to solve the FRE-FC problems defined by arbitrary continuous t-norms. The proposed algorithm is tested with different test problems generated by ten well-known continuous t-norms used in the literature. Moreover, the generated solutions for these problems, are also compared with some well-known meta-heuristic methods which have been applied to many practical optimization problems. It is shown that the optimal intensity of electromagnetic radiation problem can be formed as a special case of FRE-FC problems in which fuzzy composition is defied by max-product composition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a comparative numerical study between the minorant functions and line search methods in computing the step size in the penalty method for linear optimization. The minorant functions were confirmed by many interesting numerical experimentations to be more beneficial than the classical line search methods. [ABSTRACT FROM AUTHOR]

A planar PCC graph is a simple connected planar graph with everywhere positive combinatorial curvature which is not a prism or an antiprism and with all vertices of degree at least 3. We prove that every planar PCC graph has at most 208 vertices, thus answering completely a question raised by DeVos and Mohar. The proof is based on a refined discharging technique and on an accurate low-scale combinatorical description of such graphs. We also prove that all faces in a planar PCC graph have at most 41 sides, and this result is sharp as well. [ABSTRACT FROM AUTHOR]

In this paper, we propose a primal–dual interior point method for Linear Complementarity Problem (LCP) based on a new parameterized kernel function. The investigation according to it yields the best-known iteration bound O (n log ⁡ (n) log ⁡ (n ϵ)) for large-update algorithm and thus improves the iteration bound obtained in Bai et al. (SIAM J Optim. 2004;15:101–128) for large-update algorithm. Finally, we present few numerical results to demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The paper considers the possibility of joint optimization of the control of a low-thrust spacecraft and the layout of nodes approximating the control function using a modified linearization method. [ABSTRACT FROM AUTHOR]

Due to the physical restriction of current CMOS technology, the study of majority based nanotechnologies has been progressing steadily. In this paper, we present a new exact synthesis algorithm for majority-of-three and majority-of-five boolean functions. Key in our approach is the formulation of constraints that encodes majority logic problems into linear optimization models. The proposed algorithm is able to generate optimal results for both depth and size minimization, while also minimizing the number of inverters and literals in the output function. With this new approach, we can decrease the total production cost of a circuit in technologies where inverters and literals are expensive to build, without losing optimal results for depth and size minimization. To evaluate our method, a comparison was made with two exact synthesis algorithms that can generate optimal results when considering depth and size as cost criteria, for majority-of-three and majority-of-five boolean functions. Since our method considers two additional cost criteria, the goal is to generate functions that are also optimal in relation to depth and size, but with less inverters and literals. The obtained results have shown that the proposed algorithm was able to further optimize 64% of all 220,376 compared functions, while also achieving equal cost results for the remaining 36%.

Compared with the standard staggered-grid finite-difference (FD) methods, equivalent staggered-grid (ESG) ones can significantly reduce the computational memory for acoustic wave modelling in the variable-density media. To further enhance the simulation efficiency and accuracy, one way is to optimize the FD coefficients, another way is to design new FD stencils. In this paper, we propose a modified ESG (M-ESG) scheme which can significantly accelerate the wavefield simulation process while preserving or even improving the modelling accuracy. We calculate the FD coefficients by approximating the temporal and spatial derivatives simultaneously based on time–space domain (TS-D) dispersion relation of the discrete wave equation. Our M-ESG scheme in the TS-D can maintain basically the same accuracy as the conventional ESG (C-ESG) one when the FD coefficients are derived by the Taylor-series expansion (TE) approach. Note that the TS-D dispersion relation is nonlinear with respect to the FD coefficients of the C-ESG scheme, so it is difficult to obtain the optimized FD coefficients for the discrete wave equation. However, we can minimize the L2-norm error of the dispersion relation based on our M-ESG scheme to implement a linear FD coefficients optimization strategy, which is easy and efficient. Comparisons with TE- and optimization-based C-ESG schemes demonstrate the accuracy, stability, and efficiency superiorities of our TE- and optimization-based M-ESG ones. [ABSTRACT FROM AUTHOR]

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model—a decision forest—is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms—one based on column generation and one based on random sampling—for estimating such models from data. Using synthetic data and real transaction data exhibiting nonrational behavior, we show that the model outperforms both rational and nonrational benchmark models in out-of-sample predictive ability. This paper was accepted by Chung Piaw Teo, optimization. [ABSTRACT FROM AUTHOR]

The paper describes linear optimization of process conditions for condensation of tert-butanol with aqueous formaldehyde in the presence of synthetic zeolites (CA-Y, NaA-Y, CaA-Y, NaX, and CaX) and phosphoric acid as catalysts. The process was carried out in an autoclave at 100–150°C, 0.5–0.6 MPa, and a stirring speed of 60 rpm. The selectivity towards 4,4-dimethyl-1,3-dioxane (DMD) as a target product in the Prins reaction involving tert-butanol was investigated as a function of optimization parameters such as reaction time, temperature, reactant ratio, phosphoric acid content, and synthetic zeolite type. For each "parameter vs. DMD selectivity" function, an extremum point corresponding to the optimal parameter value was found. In the presence of NaA-Y, the DMD selectivity reached 98%. [ABSTRACT FROM AUTHOR]

Local Energy Markets (LEMs) were recently proposed as a measure to coordinate an increasing amount of distributed energy resources on a distribution grid level. A variety of market models for LEMs are currently being discussed; however, a consistent analysis of various proposed grid tariff designs is missing. We address this gap by formulating a linear optimization-based market matching algorithm capable of modeling a variation of grid tariff designs. A comprehensive simulative study is performed for yearly simulations of a rural, semiurban, and urban grids in Germany, focusing on electric vehicles, heat pumps, battery storage, and photovoltaics in residential and commercial buildings. We compare energy-based grid tariffs with constant, topology-dependent and time-variable cost components and power-based tariffs to a benchmark case. The results show that grid tariffs with power fees show a significantly higher potential for the reduction of peak demand and feed-in (30–64%) than energy fee-based tariffs (8–49%). Additionally, we show that energy-based grid tariffs do not value the flexibility of assets such as electric vehicles compared to inflexible loads. A postprocessing of market results valuing the reduction of power peaks is proposed, enabling a compensation for the usage of asset flexibility. [ABSTRACT FROM AUTHOR]

This study internalizes carbon pricing and other regulatory policy tools for decarbonizing the electricity generation mix of Sri Lanka. Carbon Pricing is shifted to the supply side as a decision-making tool. We consider $10/tCO2, $20/tCO2, $30/tCO2, $44/tCO2, $130/tCO2, and $297/tCO2 as potential carbon prices. Other regulatory policy tools, such as mandatory renewable energy (RE) development, fuel switching, fossil fuel phasing out, fossil fuel development moratoriums, and mandatory RE utilization, are included as possible supporting tools. Three capacity-development scenarios and three optimization models with three objective functions are designed and implemented in the General Algebraic Modeling System (GAMS). Six policy options are presented for the Sri Lankan context considering cost, emission, and diversification. Results suggest a carbon price that falls between $10/tCO2-$44/tCO2 as suitable for Sri Lanka. The study contributes to the ongoing debate on the effectiveness of carbon pricing by empirically testing the effectiveness of carbon prices in the electricity generation planning of a developing country. The findings support the emerging consensus of adopting other regulatory policy tools along with carbon prices to achieve deep decarbonization. The study also assesses the role LNG could play in a developing country’s electricity generation mix. We recommend transitioning from coal to LNG as an intermediate decarbonization policy option until the RE capacities are developed to make the near-zero emission mix a reality.

This paper studies the linear optimization problem subject to a system of bipolar fuzzy relation equations with the max-product composition operator. Its feasible domain is briefly characterized by its lower and upper bound, and its consistency is considered. Also, some sufficient conditions are proposed to reduce the size of the search domain of the optimal solution to the problem. Under these conditions, some equations can be deleted to compute the minimum objective value. Some sufficient conditions are then proposed which under them, one of the optimal solutions of the problem is explicitly determined and the uniqueness conditions of the optimal solution are expressed. Moreover, a modified branch-and-bound method based on a value matrix is proposed to solve the reduced problem. A new algorithm is finally designed to solve the problem based on the conditions and modified branch-and-bound method. The algorithm is compared to the methods in other papers to show its efficiency.

This paper proposes a new linear program for finding a relative interior point of a polyhedral set. Based on characterizing the relative interior of a polyhedral set through its polyhedral representing sets, two main contributions are made. First, we complete the existing results in the literature that require the non-negativity of the given polyhedral set. Then, we deal with the general case where this requirement may not be met.

Between 2015 and 2021, the World Food Programme (WFP) carried out "Fill the Nutrient Gap" (FNG) analyses in 37 countries. Apart from a few early FNG analyses, each analysis calculated the cost of energy-sufficient diets, staple-adjusted nutrient-adequate diets, and the non-affordability of the latter at the subnational level during a specific period decided by in-country stakeholders and data availability. In 2021–2022, all FNG output data were compiled into one dataset, which is provided as an online supplement to this paper. Here, we describe the parameters and data used in these FNG analyses and the process for standardizing diet costs for time (to January 2020) and in currency (PPP USD and MER USD). The objective of this paper was to provide the dataset utilized in the other papers in this GFS special issue on diet cost and affordability analyses conducted as part of FNG analyses by WFP and partners, and to provide a description of the considerations and methods employed for compiling this dataset. • The paper presents a novel dataset on the cost and non-affordability of diets for sex- and age-specific individuals from subnational FNG analyses (2015 to 2021). • This paper is a methodological foundation for papers in this GFS special issue on FNG diet cost and affordability analyses. • When analysing diet costs, the choice to use either market exchange rates or purchasing power parities greatly impacts estimates. • Different household combinations of individuals will produce varying per capita household averages. [ABSTRACT FROM AUTHOR]

We introduce a new variant of Chubanov's method for solving linear homogeneous systems with positive variables. In the Basic Procedure we use a recently introduced cut in combination with Nemirovski's Mirror-Prox method. We show that the cut requires at most O (n 3) time, just as Chubanov's cut. In an earlier paper it was shown that the new cuts are at least as sharp as those of Chubanov. Our Modified Main Algorithm is in essence the same as Chubanov's Main Algorithm, except that it uses the new Basic Procedure as a subroutine. The new method has O (n 3.5 log 2 ⁡ (1 / δ A)) time complexity, where δ A is a suitably defined condition number. As we show, a simplified version of the new Basic Procedure competes well with the Smooth Perceptron Scheme of Peña and Soheili and, when combined with Rescaling, also with two commercial codes for linear optimization. [ABSTRACT FROM AUTHOR]

This study presents an optimal framework for the operation of integrated energy systems using demand response programs. The main goal of integrated energy systems is to optimally supply various demands using different energy carriers such as electricity, heating, and cooling. Considering the power market price, this work investigates the effects of multiple energy storage devices and demand response programs, including the time of use pricing, real-time pricing, and integrated demand response on optimal operation of energy hub. Moreover, impacts of different optimization methods are evaluated on the optimal scheduling of multi-carrier energy systems. Maximizing profits of selling electrical energy and minimizing the purchasing cost of input carrier energies are considered as objective functions to indicate bidirectional interchanges of energy hub systems with the power grid. To minimize the generation cost of energy carriers, a new quadratic objective function is also optimized using genetic algorithm. In this study, optimal operation of the energy hub based on the proposed quadratic objective function is an economic dispatch problem where the purchasing electrical power by the energy hub is considered as a load of the upstream grid. The optimization problem is implemented in the sample energy hub to indicate the effectiveness of different energy storage roles and applied demand response programs in the optimal operation of energy hub systems.