Mathematical Programming Optimization Research Articles

A novel combined fuzzy VIKOR and mathematical optimization programming for online advertising effectiveness

A novel combined fuzzy VIKOR and mathematical optimization programming for online advertising effectiveness

Addressing Carbon Storage in Forested Landscape Management Planning—An Optimization Approach and Application in Northwest Portugal

Climate change is driving worldwide efforts to mitigate and reverse the increasing anthropogenic emissions of greenhouse gases. Forests can uptake considerable amounts of carbon from the atmosphere, but management decisions and resultant silvicultural practices can largely influence these ecosystems’ carbon balance. This research presents an approach to help land managers cope with the need to ensure the provision of forest products and services while contributing to mitigating climate change via carbon sequestration. The emphasis is on combining a landscape-level resource capability model with a mathematical programming (LP) optimization method to model and solve a land management problem involving timber production, carbon sequestration, and resistance to wildfire targets. The results of an application on a forested landscape in Northwest Portugal showed that this approach may contribute to analyzing and discussing synergies and trade-offs between these targets. They revealed important trade-offs between carbon sequestration and both timber production and fire resistance.

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

Topology optimization (TO) has become increasingly popular as a useful tool for designers and engineers during the initial stages of design. TO aims to optimize the geometry of a design to achieve a specific objective, which can range from discrete grid-like structures to continuum structures. In essence, the geometry is parameterized pixel-by-pixel, with the material density of each element or mesh point serving as a design variable. After that, the optimization problem is addressed using mathematical programming and analytic gradient calculation-based optimization approaches. In this paper, we investigate the material distribution when performing topology optimization for an isotropic material with boundary conditions including fixed structures, supports, or external forces changing. In addition, we investigate more cases where there are material holes in the design domain, meaning that the density of the material is zero. In this study, the modified SIMP method and filter sensitivity are used for topology optimization. The results of the study are the optimized structural domains and the change in compliance according to the number of iterations. The results indicate that the compliance value of most structures reaches convergence after optimization up to the 20th iteration. Moreover, if the force applied to the design domain is symmetrical, the optimal structure also exhibits symmetry. Thus, the distribution of material is concentrated at the positions of the supports. Topology optimization produces designs that both meet boundary conditions while saving material and reducing their mass. The results obtained are important data for structural optimization design for isotropic elastomeric materials. From there, it can be applied to real objects with different requirements and conditions

Coordinated planning of charging swapping stations and active distribution network based on EV spatial‐temporal load forecasting

AbstractElectric vehicles (EVs) charging swapping stations (CSSs), as well as multi‐functional integrated charging and swapping facilities (CSFs), have become important to reduce the impact of e‐mobility on the electric power distribution system. This paper presents a coordinated planning optimization strategy for CSSs/CSFs and active distribution networks (AND) that includes distributed generation. The approach is based on the application of a specifically developed spatial‐temporal load forecasting method of both plug‐in EVs (PEVs) and swapping EVs (SEVs). The approach is formulated as a mathematical programming optimization model that provides the location and sizing of new CSSs, the best active distribution network topology, the required distributed generation, and substation capacities. The developed model is solved using CPLEX, and its characteristics and performances are evaluated through a realistic case study.

Optimal power flow in four-wire distribution networks: Formulation and benchmarking

In recent years, several applications have been proposed in the context of distribution networks. Many of these can be formulated as an optimal power flow problem, a mathematical optimization program which includes a model of the steady-state physics of the electricity network. If the network loading is balanced and the lines are transposed, the network model can be simplified to a single-phase equivalent model. However, these assumptions do not apply to low-voltage distribution networks, so the network model should model the effects of phase unbalance correctly. In many parts of the world, the low-voltage distribution network has four conductors, i.e. three phases and a neutral. This paper develops OPF formulations for such networks, including transformers, shunts and voltage-dependent loads, in two variable spaces, i.e. current–voltage and power–voltage, and compares them for robustness and scalability. A case study across 128 low-voltage networks also quantifies the modelling error introduced by Kron reductions and its impact on the solve time. This work highlights the advantages of formulations in current–voltage variables over power–voltage, for four-wire networks. • We develop two quadratic optimization formulations for unbalanced four-wire grids. • The current–voltage formulation is superior to the power–voltage formulation. • Four-wire optimization models require about 30% more time to solve than three-wire ones. • Numerical results support the proposed relaxation and approximation hierarchies.

Пути повышения эффективности логистического обеспечения деятельности международной транспортной системы «Агроэкспресс» на основе инструментария однокритериальной оптимизации

Purpose: To develop technology variants to provide for necessary level of cargo traffic for trains “Agroexpress” and mathematical model proposal for these purposes. Methods: System analysis, operation mathematical optimization and linear programming. Results: Work flows on provision of agricultural cargos of the being considered train are analyzed. Mathematical model of provision of agro-production of “Agroexpress” trains in Uzbekistan is developed. With the help of the model, there is a possibility to improve work technology on provision of cargo traffic of “Agroexpress” in sufficient quantity by minimal expenditure criterion. Practical importance: The proposed model creates favorable conditions for increasing foreign cargo traffic of Russia and Uzbekistan. With the help of the model it is possible to improve the technology of work to ensure the cargo traffic in a sufficient number of “Agroexpress” on the criterion of minimum costs.

No More Unimplementable Nurse Workforce Planning

Objective This paper aims to spur thought-provoking practical debates on current nurse workforce staffing and scheduling systems in relation to a critical review of Ang and colleagues’ (2018) article entitled “Nurse workforce scheduling in the emergency department: A sequential decision support system considering multiple objectives.” Design Discussion paper on a practical discourse in connection with the aforementioned published article. Discussion Mathematical Programming (optimization) (MP)-based nursing research has been published for nearly thirty years almost exclusively in industrial engineering or health business administration journals, demonstrating a widening gap between nursing research and practice. Nurse scientists’ knowledge and skill of MP is insufficient, as are their interdisciplinary collaborations, setting back the advancement of nursing science. Above all, nurse scientists skilled in decision science are desperately needed for that analytic intellection which is rooted in the ‘intrinsic nature and value of nursing care.’ It is imperative that nurse scientists be well-prepared for the new age of the Fourth Industrial Revolution through both an education in MP and interdisciplinary collaboration with decision science experts in order to prevent potential stereotyped MP-based algorithm-driven destructive influences. Conclusions The current global nursing shortage makes optimal nursing workforce staffing and scheduling more important. MP helps nurse executives and leaders to ensure the most efficient number of nurses with the most effective composition of nurse staffing at the right time for a reasonable cost. Nurse scientists urgently need to produce a new nursing knowledge base that is directly implementable in nursing practice.

Linear and nonlinear shelf space allocation problemswith vertical and horizontal bands

Aim/purpose – Shelf space is one of the most important tools for attracting customers’ attention in a retail store. This paper aims to develop a practical shelf space allocation model with visible vertical and horizontal categories. and formulate it in linear and non- -linear forms. Design/methodology/approach – The research is mainly based on operational research. Simulation, mathematical optimization, and linear and nonlinear programming methods are mainly used. Special attention is given to the decision variables and constraints. Changing the dimensioning of the decision variables results in an improvement in the formulation of the problem, which in turn allows for obtaining an optimal solution. Findings – A comparison of the developed shelf space allocation models with visible vertical and horizontal categories in linear and nonlinear forms is presented. The compu- tational experiments were performed with the help of CPLEX solver, which shows that the optimal solution of the linear problem formulation was obtained within a couple of seconds. However, a nonlinear form of this problem found the optimal solution only in 19 out of 45 instances. An increase in the time limits slightly improves the performance of the solutions of the nonlinear form. Research implications/limitations – The main implication of research results for sci- ence is related to the possibility of determining an optimal solution to the initially formu- lated nonlinear shelf space allocation problem. The main implication for practice is to take into consideration the practical constraints based on customers’ requirements. The main limitations are the lack of storage conditions and holding time constraints. Originality/value/contribution – The main contribution is related to developing math- ematical models that consider simultaneous categorization of products vertically, based on one characteristic, and horizontally, based on another characteristic. Contribution is also related to extending the shelf space allocation theory with the shelf space allocation problem model in relation to four sets of constraints: shelf constraints, product con- straints, orientation constraints, and band constraints. Keywords: Retailing, decision making/process, merchandising, shelf space allocation, planogram. JEL Classification: C61, L81.

An Energy-Efficient Internet of Things Relaying System for Delay-Constrained Applications

The emerging Internet-of-things (IoT) systems contain a large number of small wireless devices with limited energy, communication, and computational capabilities. In such systems, a helping station located between the IoT devices and backhaul servers can be deployed to broadcast the IoT devices to the backhaul networks. This paper investigates a hybrid energy-efficient framework using multiple energy harvested relays with data buffering capabilities. The relays are powered by a hybrid energy supply consisting of a traditional electric grid and renewable energy grid. We propose an energy efficient novel approach aiming to support the wireless uplink transmission from IoT devices to backhaul servers with an acceptable delay threshold or transmission deadline. A mathematical mixed-integer linear programming (MILP) optimization problem is formulated to optimize the relays’ placement and energy consumption considering the association between relays and devices, instantaneous relays’ battery level, and transmit power budget. Due to the non-convex nature of the formulated optimization problem, we propose two heuristic low-complexity solutions to solve this problem. Finally, we compare the performance of the proposed algorithms with exhaustive search solutions as a benchmark.

Optimization of quality, safety and health aspects in personal care product preservative design

Personal care products (PCPs) are structured products that are constituted by numerous chemicals ingredients. However, there are several hazardous ingredients in PCPs that may cause exposure to consumers and lead to adverse health impacts. The main contribution of this study is the development of a comprehensive framework for the PCP ingredient design that integrates the safety and health aspects as well as performance aspects simultaneously into computer-aided molecular design (CAMD). Mathematical optimization programming is utilized in this study to generate a list of high quality, poses good safety and health-performance PCP preservative candidates. Furthermore, an index-based safety and health effect assessment is presented in this study. In addition, the exposure assessment of the selected molecule is performed by applying Margin of Exposure. A case study on PCP preservative design is presented. Laboratory experiment is carried out to verify the feasibility of the addition of safer and healthier preservative into the eye cream formulation.

Optimization of a multi-generation power, desalination, refrigeration and heating system

The optimization of a multi-generation system which represents the integrated dual-purpose desalination plant and a low-scale absorption refrigeration system is addressed. A nonlinear mathematical programming optimization model that integrates a natural gas combined-cycle, a multi-effect distillation desalination plant, a series flow double-effect water-lithium bromide absorption refrigeration system, and a water heater, is developed based on first-principle models. The model is implemented in General Algebraic Modelling System and a generalized gradient-based optimization algorithm is used.Given design specifications for electricity generation (around 37 MW), freshwater production (100 kg/s), refrigeration capacity (2 MW), and thermal load for heating (around 0.7 MW of hot water), the integrated system is optimized by minimizing two objective functions by single-objective optimization: total heat transfer area and total annual cost. As a result, minimum total heat transfer area values of 39148 m2, 36002 m2, and 35161 m2 are obtained when 4, 5, and 6 distillation effects were considered in the multi-effect distillation system, respectively. Also, a minimum annual cost of around 24 MM$/yr. is obtained for 5 distillation effects.The influence of the number of effects in the multi-effect distillation subsystem on the optimal solutions is analyzed. Cost-effective optimal solutions are developed for the studied multi-generation system.

Solving Hydropower Unit Commitment Problem Using a Novel Sequential Mixed Integer Linear Programming Approach

Hydro Unit Commitment (HUC) is an important problem of power systems and when it is dealt with via a mathematical programming approach and optimization, it leads to the complicated class of mixed-integer nonlinear programming (MINLP). Many attempts have been made to solve the problem efficiently, while there is still ongoing research to come up with better solution schemes in terms of runtime and optimality. Highly nonlinear nature of the relationships and constraints in the optimization problem have forced the researchers to deal with the HUC problem in simplified manners which may result in impractical and unreliable solutions, i.e. schedules. Here in this paper we proposed a new method based on sequential mixed-integer linear programming (MILP) for solving a more realistic version of the HUC problem efficiently. We applied the proposed method to a cascade of two hydropower plants, Karun-3 and Karun-4, located in the Southwest of Iran. The sequential MILP approach was compared with several MINLP solvers of the GAMS optimization package. The results indicated that the proposed methodology outperformed the MINLP solvers in terms of efficiency, with solution time of less than 30 s, compared to 10 min that were given to the solvers, and in terms of optimality with more than 20 thousand cubic meters per day in water release. Additionally, we have explored the effect of penalizing the total number of startups on the total release, convergence of the algorithm, and the computation time. In all of the cases the total number of startups was reduced more than three times.

A Review on Data Reconciliation and Gross Error Detection for Process Plant Energy Management

Process plant is essential for energy management, especially for analysis that requires steady state data, such as Pinch Analysis. The data from the distributed control system (DCS) often recorded with fluctuations. Data processing is needed to obtain representable data for energy management related analysis. Data error occurs in several forms such as gross error, random error, bias error, and systemic error. This error affects the reliability of energy management studies. Data reconciliation (DR) and gross error detection (GED) come in place for the data processing required before the energy management analysis could be done. GED detects measurement variable error which works with DR technique for a new estimate or reconciled value will be gather and use for further data analysis. DR and GED are commonly used in mathematical programming optimization, such as model predictive control (MPC), which has proved its effectiveness in providing good data for further analysis. This means that DR and GED affect energy data manipulation and studies. In this paper, DR and GED on energy data for plant energy enhancement are reviewed. The specific method for DR and GED are classified and discussed in this paper.

Short-term underground mine planning: a review

This paper reviews the state-of-the-art in short-term underground mine planning, which is critical for future mining activities. According to the literature, the research is conducted in the categories of mathematical programming optimisation and discrete event simulation. Mathematical programming aims at minimising an objective with the functionality of cost, makespan, deviation from a specific target such as tonnage and fleet management and scheduling. Mining simulation is widely applied in case of short-term mine planning, mostly based on modelling the internal mining process and parameters and on implementing a model for different case studies. A comprehensive review is provided for the aforementioned issues, commercial software packages and programming languages. Finally, research limitations and future area investigation are discussed. The studies reveal a deficiency of research based on the type of mining methods and incorporation of uncertainties.

New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization

In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.

Closed-Loop Two-Stage Stochastic Optimization of Offshore Wind Farm Collection System

A two-stage stochastic optimization model for the design of the closed-loop cable layout of an Offshore Wind Farm (OWF) is presented. The model consists on a Mixed Integer Linear Program (MILP) with scenario numeration incorporation to account for both wind power and cable failure stochasticity. The objective function supports simultaneous optimization of: (i) Initial investment (network topology and cable sizing), (ii) Total electrical power losses costs, and (iii) Reliability costs due to energy curtailment from cables failures. The mathematical optimization program is embedded in an iterative framework called PCI (Progressive Contingency Incorporation), in order to simplify the full problem while still including its global optimum. The applicability of the method is demonstrated by application to a real-world instance. The results show the functionality of the model in quantifying the economic profitability when applying stochastic optimization compared to a deterministic approach, given certain values of cables failure parameters.

Vehicle Routing Problem with Simultaneous Pickup and Delivery

This paper focuses on the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) issue. VRPSPD is one of the extended problems related to the usual Vehicle Routing Problem (VRP). VRPSPD consists of both linehaul customers and backhaul customers with a known demand. In VPRSPD, only a single depot can receive and supply the loads. The vehicles can only visit each customer once and can serve all customers simultaneously by delivering or picking up the loads within a limited capacity. VPRSPD is a NP-hard problem. The huge data size has increased the difficulty for it to be solved by using mathematical programming or combinatorial optimisation. A heuristic approach based on the Variable Neighbourhood Search (VNS) is proposed. Heuristic based solutions offer feasible solutions that are approximately accurate to the exact solution. It is one of the most popular solutions to solve a complex problem. In this research, the algorithm solution consists of two main phases. A simple heuristic is used to generate the initial solution in the first phase. Then, the feasible solution obtained in the first phase will become the initial input for the improvement phase which applied the VNS algorithm. The proposed algorithm is tested using a list of benchmark dataset. The result obtained is compared with the best solution that can be found from the literature research. The comparison result shows that the heuristic algorithm is favourable to be used for this kind of vehicle routing problem.

Analysis of the effect of alternative agri-environmental policy instruments on production performance and nitrogen surplus of representative dairy farms

Nitrogen (N) surplus is an important environmental problem on the island of Ireland (Northern Ireland and the Republic of Ireland), and the dairy sector has been identified as contributing more to this problem compared to other agricultural sectors. As a result, there has been increased demand for efficient policy measures to improve the economic and environmental performance of dairy farms in the region. In this study, we employed the positive mathematical programming (PMP) optimization modelling framework to simulate the economic and environmental impact of two alternative agri-environmental policy instruments on different dairy farm types. Specifically, the study considers the effects of an N surplus tax and an agri-environmental nutrient application standard on the production performance and N surplus of representative dairy farms using scenario analyses. The results of the analyses showed that the effects of the agri-environmental policy instruments vary across the two countries and clusters of dairy farms, resulting in clear differential effects on farm structure and N surpluses. The study concluded that in situations where the nutrient surplus is already high, as with the large farms clusters in this study, the use of manure application standards will be more effective in limiting nutrient surplus to soils compared to the use of nutrient surplus tax.

The method of a primary design of a scientifically grounded scheme for optimization an energy saving system on the basis of the steamgas power plant and an absorption lithium bromide refrigerating machine

The selection of the scheme for optimization of a complex energy saving system was grounded. The method of creation and implementation of the methodology of obtaining necessary data to develop a simulation mathematical model necessary for solving the optimization problem was studied. Using the DataFit 9.0 mathematical analysis program the necessary dependences were obtained in a wide range of operation parameters, which later were assumed as a basis of the mathematical model and optimization program.

Control System Loop-Shaping as a Mathematical Optimization Problem: An Ensemble of Models

This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.