Economic Optimization Problem Research Articles

The coronavirus trade-off - Life vs. economy: Handling the trade-off rationally and optimally.

The recent coronavirus outbreak has made governments face an inconvenient trade-off choice, i.e. the choice between saving lives and saving the economy, forcing them to make immensely consequential decisions among alternative courses of actions without knowing what the ultimate results would be for the society as a whole. This paper attempts to frame the coronavirus trade-off problem as an economic optimization problem and proposes mathematical optimization methods to make rationally optimal decisions when faced with trade-off situations such as those involved in managing through the recent coronavirus pandemic. The framework introduced and the method proposed in this paper are on the basis of the theory of rational choice at a societal level, which assumes that the government is a rational, benevolent agent that systematically and purposefully takes into account the social marginal costs and social marginal benefits of its actions to its citizens and makes decisions that maximize the society's well-being as a whole. We approach solving this trade-off problem from a static as well as a dynamic point of view. Finally, we provide several numerical examples clarifying how the proposed framework and methods can be applied in the real-world context.

АЛГОРИТМ ОПТИМИЗАЦИИ ПАРАМЕТРОВ НЕФТЕПРОВОДОВ ПРИ ПРОЕКТИРОВАНИИ ОБОРУДОВАНИЯ НЕФТЕХИМИЧЕСКОЙ ПРОМЫШЛЕННОСТИ

The problem of technical and economic optimization of pipeline parameters for transportation of petroleum products exhibiting a viscosity anomaly is considered. The relations for determination of optimal pipeline diameter and pressure, providing pumping of the medium in the laminar, steady, isothermal regime on the pipeline from the condition of minimizing the total annual cost of its development and operation based on current prices and tariffs for the pipeline and energy topology of the pipeline, its working conditions, as well as anomalies of the viscosity of the transported medium.

New Method of Solving the Economic Complex Systems

In this study, the authors first develop a direct method used to solve the linear nonhomogeneous time-invariant difference equation with the same number for inputs and outputs. Economic cybernetics is the crystallization for the integration of economics and cybernetics. It analyzes the stability, controllability, and observability of the economic system by establishing a system model and enables people to better understand the characteristics of the economic system and solve economic optimization problems. The economic model generally applies the discrete recurrence difference equation. The significant analytic approach for the difference equation is the z-transformation technique. The z-transformation state of the economic cybernetics state-space difference equation generally is a rational function with the same power for the numerator and the denominator. The proposed approach will take the place of the traditional methods without all annoying procedures involving the long division of some complicated polynomials, the expanded multiplication of many polynomial factors, the differentiation of some complicated polynomials, and the complex derivations of all partial fraction parameters. To highlight the novelty of this research, this study especially applies the proposed theorems originally belonging to engineering to the field of economic applications.

Comparison of geostationary and low-orbit “round dance” satellite communication systems

Modern satellite navigations systems utilize high-orbit (mostly geostationary) and low-orbit satellites. Both satellite types have their advantages and disadvantages. A global communication system requires at least three or five GEO satellites with a life of 10 years, with each satellite costing around $200 million. Low-orbit global communication systems of the “round dance” type must have from hundreds to thousands of satellites. Their orbit life can range from 2 to 5 years; their cost must be between $1 million and $20 million. At this stage, there is a wide range of means for launching communications satellites into orbit, a large range of metal and composite structural materials. In addition, there are methods of designing, manufacturing, and testing communication satellites, as well as software and hardware for satellite control have been developed. So, the problem of economic optimization of communication satellite constellations becomes relevant. The paper presents the results of the comparative engineering and economic analysis of two types of satellite constellations.

Theoretical basis of selection of measurement measures in control of linear sizes

The important role of metrological support in machine-building production has been shown. It has been established that in connection with the introduction of quality systems and management systems for metrological support of measurements at machine-building enterprises and the need to assess the quality of measuring processes, it is necessary to develop methods for analyzing the effectiveness of the results of using one or another measuring instrument. The analysis of the existing methods of selection of measuring instruments for linear dimensions in the tolerance control of mechanical engineering products is carried out. It is proposed to solve the problem of economic optimization of measurement accuracy by taking into account both measurement costs and losses from measurement errors. An expression is obtained for calculating the theoretically optimal measurement error, which corresponds to the criterion of minimizing the amount of losses from the measurement error and the costs of the measuring process when organizing the control of a specific parameter by universal measuring instruments of linear dimensions.

Qualitative and Quantitative Performance Comparison of Recent Optimization Algorithms for Economic Optimization of the Heat Exchangers

Solving applied problem of economic optimization is considered as a real test for the optimization algorithms. The present work explores the qualitative and quantitative comparative analysis of nine recently developed optimization algorithms for the economic optimization of the heat exchangers. Passing vehicle search, Salp swarm algorithm, Artificial flora optimization, Grey wolf optimizer, Electro-search algorithm, Grasshopper optimisation algorithm, Symbiotic organisms search, Ant lion optimizer, and Heat transfer search algorithm are considered in the present work. Shell and tube, plate-fin, and fin-tube heat exchanger are considered for the optimization. Statistical analyses of the results are carried out to identify the significant between the results of comparative algorithms. The effect of various constraint handling techniques on the performance of the algorithms is identify and presented. Economically optimized geometry of each of the heat exchanger is presented in detail. Finally, the convergence of the considered algorithm in obtaining the minimum total cost solutions are also presented and discussed.

Worldwide geographical mapping and optimization of stand-alone and grid-connected hybrid renewable system techno-economic performance across Köppen-Geiger climates

In the last years, a significant interest in research in stand-alone (SA) and grid-connected (GC) photovoltaic (PV)-wind hybrid renewable energy systems (HRES) is observed for their complementary in the satisfaction of the electrical energy demand in many sectors. However, direct comparisons between the techno-economic performance of two system modes under the same operating conditions are rarely carried out. Additionally, most of the researches are limited to specific weather conditions.This work aims to bridge the lack of this type of investigations providing a worldwide techno-economic mapping and optimization of SA and GC PV-wind HRES to supply the electrical demand of an office building district. For this purpose, energy and economic optimization problems were formulated to find the optimal SA and GC systems worldwide among 343 HRES system power configurations located in 48 different localities, uniformly divided in the sub-group of the Koppen classification. The energy reliability and economic profitability of optimal systems were geographically mapped worldwide.In general, the energy or economic optimizations of SA HRES do not lead to highly profitable systems; instead, feed-in-tariff to sell the energy in excess assures viable GC HRES in many localities. However, economically optimal SA and GC HRES, respectively, do not everywhere comply with the threshold value of 70% of the satisfied energy required by the load and are characterized by a high level of energy exchanged with the grid.The study highlighted that the most suitable climate conditions to install a SA HRES are: (i) Toamasina (Madagascar) from an energy point of view, with 76% of load satisfied and 76% of the energy generated utilized to supply the load; (ii) Cambridge Bay (Canada) from an economic point of view, with 11.1% of the capital cost recovered each year; instead, the most suitable climate conditions to install a GC HRES are: (iii) New Delhi (India) from an energy point of view, with 48% of energy exchanged with the grid per each kWh required by the load; (iv) Lihue (Hawaii, United States) from an economic point of view, with 24.3% of the capital cost recovered each year.

Hybrid method for achieving Pareto front on economic emission dispatch

In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-objective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.

Economic Performance Optimization by Set Point and Weighting Parameter Tuning based on LQG Controller Design

Several researches have formulated economic performance optimization problems taking account of a trade-off relation between process input and output variance. The present work introduces theoretical formulations that relate the weighting parameter with each input and output variance on the condition that the Linear Quadratic Gaussian (LQG) controllers are implemented as lower layer controllers. The proposed approach is applied to a two-input, two-output separation process model, and solves optimal weighting parameter based on LQG control. The numerical example also shows that the obtained optimal weighting parameter is effective for a MPC based learning algorithm.

Impact of the Weather on the Combined Economic and Emission Optimization Problem of MG

The high integration of renewable energy resources and utilizing of storage devices with possible exchange power with the utility grid make the optimization problem of microgrid (MG) significantly difficult comparing with the conventional systems. This paper quantifies the impact of weather conditions on the combined economic and emission optimal operation of the MG. The optimization problem is formulated as mixed integer quadratic program (MIQP), where the unit commitment (UC) is taken into consideration in the optimization problem. In addition, realistic constraints are taken into account to make the problem close to the real scenario. The proposed optimization approach is applied to the low voltage MG, which includes distributed generators (DGs), renewable energy sources (wind, solar) and storage battery. The results reveal that the abundant of wind and solar energies leads to reduce the operation and emission cost.

Determining the Optimal Operating Point of CHP Units with Nonconvex Characteristics in the Context of Combined Heat and Power Scheduling Problem

ABSTRACTDetermining the optimal operating point of generating units in the optimal combined heat and power scheduling is an economic optimization problem aimed at minimizing the total operating costs. The generation cost would nonlinearly increase with the increase in the power generation of fossil fuel thermal units. On the other hand, in combined heat and power (CHP) units, the amounts of power and heat generation are highly mutually dependent. Therefore, the determination of the optimal operating points of such units would be much more difficult compared to electric power or heat-only generating units. Obviously, the aim beyond implementing the day-ahead generation scheduling (GS) problem is to determine the optimal operating points of generating units. In this regard, the power outputs of the units are specified such that the total operating costs of the system are minimized taking into consideration the technical and economic constraints. This paper solves the GS problem in the presence of CHP units with nonconvex feasible operating regions (FORs). This paper investigates the problem of optimal operating point determination of CHP units along with electrical and heat-only units.

Least costly energy management for extended-range electric vehicles: An economic optimization framework

In this work, the energy management strategy problem for extended-range electric vehicles is tackled by considering all the factors affecting the system costs and performance, ranging from traditional fuel consumption to noise emissions up to battery aging and engine start-up costs. To solve the resulting economic optimization problem, a control-oriented model of the powertrain is first derived focusing on power generation, thermal dynamics and noise emissions. Then, the energy management strategy problem is formally stated as a mixed-integer convex program involving all the costs of interest and solved with state-of-the-art optimization tools. The optimal strategy can be used as a benchmark for real-time controls, to understand whether to purchase a range extender is economically effective, or to assess the cost of operating the vehicle. An electric bus case-study is illustrated in detail to show the potential of the proposed approach.

Economic Reliability-Aware MPC-LPV for Operational Management of Flow-Based Water Networks Including Chance-Constraints Programming

This paper presents an economic reliability-aware model predictive control (MPC) for the management of drinking water transport networks (DWNs). The proposed controller includes a new goal to increase the system and components reliability based on a finite horizon stochastic optimization problem with joint probabilistic (chance) constraints. The proposed approach is based on a single-layer economic optimization problem with dynamic constraints. The inclusion of components and system reliability in the MPC model using an Linear Parameter Varying (LPV) modeling approach aims to maximize the availability of the system by estimating system reliability. On the other hand, the use of a LPV-MPC control approach allows the controller to consider nonlinearities in the model in a linear like way. Moreover, the resulting MPC optimization problem can be formulated as a Quadratic Programming (QP) problem at each sampling time reducing the computational burden/time compared to solving a nonlinear programming problem. The use of chance-constraint programming allows the computation of an optimal strategy with a pre-established risk acceptability levels to cope with the uncertainty of the demand forecast. Finally, the proposed approach is applied to a part of the water transport network of Barcelona for demonstrating its performance. The obtained results show that the system reliability of the DWN is maximized compared with the other approaches.

Application of the stochastic fractal search algorithm and compromise programming to combined heat and power economic–emission dispatch

Combined heat and power (CHP) generation is a competent configuration for simultaneous production of thermal and electric energy. The interdependency of heat and power outputs of CHP units presents complications and non-convexities in modelling and optimization. The nonlinear constrained economic dispatch optimization problem becomes more complex when one considers the pollution produced by generating units, transmission losses and valve-point effects of thermal units. This article uses the stochastic fractal search algorithm to solve the bi-objective combined heat and power economic dispatch (CHPED) problem. The CHPED problem has bounded feasible operating regions and many local minima. The compromise programming method is used to transform the two objective functions into an aggregated objective function. The results are compared with previous results obtained by many different methods reported in the literature. The results reveal that the proposed algorithm achieves a better near-global solution and compares favourably with other commonly used global optimization techniques.

Distributed Cooperative Economic Optimization Strategy of a Regional Energy Network Based on Energy Cell–Tissue Architecture

The conventional centralized control method can effectively solve the influence of system power imbalance on the optimal dispatching of a power network and stabilize the power fluctuation of tie lines when the control precision is relatively high. However, when there are disturbances and uncertainties in the system, the robustness is insufficient. The distributed control method in economic optimization scheduling has the advantages of simple communication and high reliability and is well adapted to the energy dispersion characteristics of a distributed generator within the regional energy network. However, the control accuracy is slightly less than that of the centralized control method, and when the distributed power encounters a random input or exit, the corresponding sparse network matrix needs to be updated every time, complicating the use of this system for economic operation. In addition, when message loss or communication noise occurs in the communication path, the robustness of distributed control is greatly reduced. To address these issues, this paper proposes a novel power allocation framework to solve the economic optimization problem of a regional energy network that requires only local information exchange among neighboring energy cells and tissues. Correspondingly, to meet the supply–demand balance, a distributed cooperative approach based on the equal incremental principle is used to impart decentralized autonomy to the whole system. In addition, the concept of virtual consistency variables is introduced to manage topological change caused by power excursions in the energy cell and to implement plug-and-play capabilities. Relative to the conventional collaborative control method, the case studies demonstrate the scalability, plug-and-play capability, and robustness of decentralized autonomous control strategies in terms of communication delay, communication failure, and message loss, among other aspects.

Adaptive Range Genetic Algorithm: A hybrid optimization approach and its application in the design and economic optimization of Shell-and-Tube Heat Exchanger

Several optimization algorithms have been developed in the past for application in a variety of complex real world problems. Herein, a new hybrid variant of Genetic Algorithm (GA), utilizing the sample space reduction technique of Cohort Intelligence (CI) Algorithm, referred to as Adaptive Range Genetic Algorithm (ARGA) is presented and discussed. The correctness of the proposed algorithm is established by solving 50 standard test functions. Also, the practical applicability of the proposed algorithm is demonstrated by applying it to the design and economic optimization problem of a Shell and Tube Heat Exchanger. Heat exchangers are critical industrial components used in a wide range of industrial applications. Owing to their high manufacturing costs and complicated design criteria, their economic efficiency of operation depends heavily on optimization of their design. A relative assessment, comparing the performance of the proposed method of solution to other existing algorithmic methods, is conducted. The quality and robustness of the proposed solution method highlights its adeptness in solving real world computational problems in core mechanical engineering applications.

The solution of optimization problems in the economy by overlaying integer lattices: applied aspect

The results of generalization of scientific approaches to the solution of modern economic optimization tasks have shown the need for a new vision of their solution based on the improvement of existing mathematical tools. It is established that the peculiarities of the practical use of existing mathematical tools for solving economic optimization problems are caused by the problems of enterprise management in the presence of nonlinear processes in the economy, which also require consideration of the corresponding characteristics of nonlinear dynamic processes. The approach to solving the problem of integer (discrete) programming associated with the difficulties that arise when applying precise methods (methods of separation and combinatorial methods) is proposed, namely: a fractional Gomorrhic algorithm – for solving entirely integer problems (by gradual "narrowing" areas of admissible solutions of the problem under consideration); the method of branches and borders - which involves replacing the complete overview of all plans by their partial directional over. Illustrative examples of schemes of geometric programming, fractional-linear programming, nonlinear programming with a non-convex region, fractional-nonlinear programming with a non-convex domain, and research on the optimum model of Cobb-Douglas model are given. The advanced mathematical tools on the basis of the method of overlaying integer grids (OIG), which will solve problems of purely discrete, and not only integer optimization, as an individual case, are presented in the context of solving optimization tasks of an applied nature and are more effective at the expense of reducing the complexity and duration of their solving. It is proved that appropriate analytical support should be used as an economic and mathematical tool at the stage of solving tasks of an economic nature, in particular optimization of the parameters of the processes of organization and preparation of production of new products of the enterprises of the real sector of the economy.

Optimization of Network-Load Interaction With Multi-Time Period Flexible Random Fuzzy Uncertain Demand Response

This paper represents a network-load interaction optimization framework integrated multi-time period flexible random fuzzy uncertain demand response (DR) model, which involved shifting of loads’ operation time and uncertain response to the price signal. The network-load interaction is to optimize load profile and network topology under the guidance of electricity price at the aim of achieving the economic and secure operation of the distribution network and at the same time satisfying the consumers’ satisfaction. This framework is a two-level framework, which includes the price-based DR level to minimize the daily load variance and maximize the customers’ satisfaction, and the reconfiguration level to minimize the network reconfiguration cost and power unbalancing. Firstly, the price-based DR level determines the price and the load profile subject to the multi-time period flexibility and uncertainties of the DR. Then, the reconfiguration level optimizes the network configuration topology according to the load profile and feeds the results back to the price-based DR level. This network-load interaction optimization model is tackled by the proposed multi-objective self-adaptive particle swarm (SAPSO) optimization algorithm. The proposed network-load interaction optimization model is applied to the IEEE33-bus distribution system and a real system. The results show that this model is efficient to solve the network economic operation and load profile optimization problem simultaneously.

Application of Differential Evolution with Selective Pressure to Economic Dispatch Optimization Problems

Differential evolution is an evolutionary algorithm for continuous optimization problems, known for its robustness and quick convergence. In this paper, differential evolution with a modified mutation strategy and a parameter adaptation scheme is applied to several economic dispatch optimization problems. The modification of differential evolution involves the application of selective pressure to the archive set and the ordering of vectors by fitness values. The proposed algorithm is used to solve static economic load dispatch, dynamic economic dispatch and the hydrothermal scheduling problem.

Efficient nested modifier-adaptation methodology for dealing with process constraints in real-time optimization

Real-time optimization (RTO) is not always able to achieve optimal process operation due to the presence of significant uncertainty in the plant models that are used to make decisions. Modifier adaptation (MA) overcomes these issues by modifying the cost and constraint functions of the economic optimization problem solved at the RTO level to drive the process to optimality. This paper proposes an alternative MA methodology for dealing with process-dependent constraints without increasing the number of modifiers. The key feature consists in computing the modifiers from the gradient of the Lagrangian function, thereby requiring a single gradient modifier per process input. The approach is illustrated in simulation via the nested modifier-adaptation (NMA) scheme implemented on a depropanizer distillation column that is characterized by a significant amount of uncertainty. The convergence of the proposed Lagrangian-based NMA scheme is significantly faster than that of standard NMA.