Approach to optimizing charging infrastructure of autonomous trolleybuses for urban routes

P u r p o s e s. When designing a system of urban electric transport that charges while driving, including autonomous trolleybuses with batteries of increased capacity, it is important to optimize the charging infrastructure for a fleet of such vehicles. The charging infrastructure of the dedicated routes consists of overhead wire sections along the routes and stationary charging stations of a given type at the terminal stops of the routes. It is designed to ensure the movement of trolleybuses and restore the charge of their batteries, consumed in the sections of autonomous running.The aim of the study is to create models and methods for developing cost-effective solutions for charging infrastructure, ensuring the functioning of the autonomous trolleybus fleet, respecting a number of specific conditions. Conditions include ensuring a specified range of autonomous trolleybus running at a given rate of energy consumption on routes, a guaranteed service life of their batteries, as well as preventing the discharge of batteries below a critical level under various operating modes during their service life.M e t ho d s. Methods of set theory, graph theory and linear approximation are used.Re s u l t s. A mathematical model has been developed for the optimization problem of the charging infrastructure of the autonomous trolleybus fleet. The total reduced annual costs for the charging infrastructure are selected as the objective function. The model is formulated as a mathematical programming problem with a quadratic objective function and linear constraints.Co n c l u s i o n. To solve the formulated problem of mathematical programming, standard solvers such as IBM ILOG CPLEX can be used, as well as, taking into account its computational complexity, the heuristic method of "swarm of particles". The solution to the problem is to select the configuration of the location of the overhead wire sections on the routes and the durations of charging the trolleybuses at the terminal stops, which determine the corresponding number of stationary charging stations at these stops.

Distribution of financial resources by areas of investments in the human capital of the region

Introduction. The study has been conducted within the framework of the urgent scientific and practical task of accumulation and development of human capital of Russian regions. Under the conditions of risks and limited resources, the regional management faces the task of optimal distribution of financial resources invested in the development of human capital and improvement of the quality of life. The study aims to build and test the dynamic optimization model of financial resources distribution by areas of investment in human capital through the example of the Primorye Territory (Russian Federation). Materials and methods. The multi-period economic and mathematical model describes the influence of the volumes and structure of public and private investments on the regional human capital in the form of recurrent dependencies. The target function of the model is an integrated index of achieving the objectives for the development of human capital in the region. The model is a mathematical programming problem, the optimization variables are the shares of investment resources distributed by investment areas and years. Results. In a practical sense, the proposed model is a management tool for searching the optimal structure of investments in human capital by areas of investment and periods. Based on the annual results of modeling and numerical calculations through the example of the Primorye Territory (Russian Federation), the structure of the investments that allow advancing in the achievement of target values of strategic indicators in the field of human capital development is offered. Conclusion. In the long term, the achievement of target indicators will be facilitated by a more even structure of investments in the following areas: along with education and health care, it is advisable to increase investments in other areas, first of all, in the issues of national importance, national security, public order, and social policy.

Optimizing the allocation of technological resources of an air transport system in the presence of a schedule and fuzzy input data

The problem of optimal allocation of technological resources (operators) of a technical or organizational-technical system, designed to serve certain objects (operands) according to a given schedule, is considered. We take into account the necessity of incorporating, together with the main, preparatory and final operations, the possibility to select one or several operators for operand service into the service process, as well as the dependence of the operations duration on the factors characterized by uncertainty. Due to the supposed absence of statistics, expert-assigned indefinite values in the form of triangular fuzzy numbers are used. The optimization problem is formulated as a mathematical programming problem with a fuzzy criterion and clear-cut constraints, consisting in finding such a distribution of a given number of operators to serve each operand from a given set which minimizes the target function that takes into account deviations from the schedule (delay) with the service termination. Typical examples of systems for which the problem is relevant are the production complexes of air transport enterprises operating in conditions of uncertainty when it is necessary to ensure the regularity and safety of air transportation. A model example of solving the problem of allocating mobile refueling facilities at a hub airport, taking into account the peculiarities of its schedule, is presented. It is shown that the capabilities of standard personal computer software are sufficient for the solution.

Genetic Algorithms as Computational Methods for Finite-Dimensional Optimization

Introduction. As early as 1744, the great Leonhard Euler noted that nothing at all took place in the universe in which some rule of maximum or minimum did not appear [12]. Great many today’s scientific and engineering problems faced by humankind are of optimization nature. There exist many different methods developed to solve optimization problems, the number of these methods is estimated to be in the hundreds and continues to grow. A number of approaches to classify optimization methods based on various criteria (e.g. the type of optimization strategy or the type of solution obtained) are proposed, narrower classifications of methods solving specific types of optimization problems (e.g. combinatorial optimization problems or nonlinear programming problems) are also in use. Total number of known optimization method classes amounts to several hundreds. At the same time, methods falling into classes far from each other may often have many common properties and can be reduced to each other by rethinking certain characteristics. In view of the above, the pressing task of the modern science is to develop a general approach to classify optimization methods based on the disclosure of the involved search strategy basic principles, and to systematize existing optimization methods. The purpose is to show that genetic algorithms, usually classified as metaheuristic, population-based, simulation, etc., are inherently the stochastic numerical methods of direct search. Results. Alternative statements of optimization problem are given. An overview of existing classifications of optimization problems and basic methods to solve them is provided. The heart of optimization method classification into symbolic (analytical) and numerical ones is described. It is shown that a genetic algorithm scheme can be represented as a scheme of numerical method of direct search. A method to reduce a given optimization problem to a problem solvable by a genetic algorithm is described, and the class of problems that can be solved by genetic algorithms is outlined. Conclusions. Taking into account the existence of a great number of methods solving optimization problems and approaches to classify them it is necessary to work out a unified approach for optimization method classification and systematization. Reducing the class of genetic algorithms to numerical methods of direct search is the first step in this direction. Keywords: mathematical programming problem, unconstrained optimization problem, constrained optimization problem, multimodal optimization problem, numerical methods, genetic algorithms, metaheuristic algorithms.

State-of-the-Art of Optimal Active and Reactive Power Flow: A Comprehensive Review from Various Standpoints

Optimal power flow (OPF), a mathematical programming problem extending power flow relationships, is one of the essential tools in the operation and control of power grids. To name but a few, the primary goals of OPF are to meet system demand at minimum production cost, minimum emission, and minimum voltage deviation. Being at the heart of power system problems for half a century, the OPF can be split into two significant categories, namely optimal active power flow (OAPF) and optimal reactive power flow (ORPF). The OPF is spontaneously a complicated non-linear and non-convex problem; however, it becomes more complex by considering different constraints and restrictions having to do with real power grids. Furthermore, power system operators in the modern-day power networks implement new limitations to the problem. Consequently, the OPF problem becomes more and more complex which can exacerbate the situation from mathematical and computational standpoints. Thus, it is crucially important to decipher the most appropriate methods to solve different types of OPF problems. Although a copious number of mathematical-based methods have been employed to handle the problem over the years, there exist some counterpoints, which prevent them from being a universal solver for different versions of the OPF problem. To address such issues, innovative alternatives, namely heuristic algorithms, have been introduced by many researchers. Inasmuch as these state-of-the-art algorithms show a significant degree of convenience in dealing with a variety of optimization problems irrespective of their complexities, they have been under the spotlight for more than a decade. This paper provides an extensive review of the latest applications of heuristic-based optimization algorithms so as to solve different versions of the OPF problem. In addition, a comprehensive review of the available methods from various dimensions is presented. Reviewing about 200 works is the most significant characteristic of this paper that adds significant value to its exhaustiveness.

MATLAB Implementation of Direct and Indirect Shooting Methods to Solve an Optimal Control Problem With State Constraints

The paper presents a general procedure to solve numerically optimal control problems with state constraints. Itis used in the case, when the simple time discretization of the state equations and expressing the optimal control problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect.The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two Matlab codes are shown.

Formulating Intuitionistic Fuzzy Regression Models: A Mathematical Programming Approach

This study develops a mathematical programming approach to establish intuitionistic fuzzy regression models (IFRMs) by considering the randomness and fuzziness of intuitionistic fuzzy observations. In contrast to existing approaches, the IFRMs are established in terms of five ordinary regression models representing the components of the estimated triangular intuitionistic fuzzy response variable. The optimal parameters of the five ordinary regression models are determined by solving the proposed mathematical programming problem, which is linearized to make the resolution process efficient. Based on the concepts of randomness and fuzziness in the formulation processes, the proposed approach can improve on existing approaches’ weaknesses with establishing IFRMs, such as the limitation of symmetrical triangular membership (or non-membership) functions, the determination of parameter signs in the model, and the wide spread of the estimated responses. In addition, some numerical explanatory variables included in the intuitionistic fuzzy observations are also allowed in the proposed approach, even though it was developed for intuitionistic fuzzy observations. In contrast to existing approaches, the proposed approach is general and flexible in applications. Comparisons show that the proposed approach outperforms existing approaches in terms of similarity and distance measures.

Profit maximization in an inventory system with time-varying demand, partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.

Optimum Design of Reinforced Cylindrical Shells Under Combined Axial Compression and Internal Pressure

This paper discusses the use of the random search method for the optimal design of single-layered rib-reinforced cylindrical shells under combined axial compression and internal pressure with account taken of the elastic-plastic material behavior. The optimality criterion is the minimum shell volume. The search area for the optimal solution in the space of the parameters being optimized is limited by the strength and stability conditions of the shell. When assessing stability, the discrete rib arrangement is taken into account. In addition to the strength and stability conditions of the shell, the feasible space is subjected to the imposition of constraints on the geometric dimensions of the structural elements being optimized. The difficulty in formulating a mathematical programming problem is that the critical stresses arising in optimally-compressed rib-reinforced cylindrical shells are a function of not only the skin and reinforcement parameters, but also the number of half-waves in the circumferential and meridional directions that are formed due to buckling. In turn, the number of these half-waves depends on the variable shell parameters. Consequently, the search area becomes non-stationary, and when formulating a mathematical programming problem, it is necessary to provide for the need to minimize the critical stress function with respect to the integer wave formation parameters at each search procedure step. In this regard, a method is proposed for solving the problem of optimally designing rib-reinforced shells, using a random search algorithm whose learning is carried out not only depending on the objective function increment, but also on the increment of critical stresses at each extremum search step. The aim of this paper is to demonstrate a technique for optimizing this kind of shells, in which a special search-system learning algorithm is used, which consists in the fact that two problems of mathematical programming are simultaneously solved: that of minimizing the weight objective function and that of minimizing the critical stresses of shell buckling. The proposed technique is illustrated with a numerical example.