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In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order linear differential equation, makes it possible to systematically obtain these values in many situations. As an example, we address nine variants of the well-known secretary problem, including the classical one, that appear in the literature on the subject, as well as four other unpublished ones. [ABSTRACT FROM AUTHOR]

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has m identical copies. The case m = 2 has already been completely solved by several authors using different methods, but the case m > 2 had not been satisfactorily solved yet. Here, under the conjecture of certain (very likely true) uniform convergence results, we provide an efficient algorithm to compute the optimal threshold and the probability of success for every m. Moreover, we give a method to determine their asymptotic values based on the solution of a system of m ODEs. [ABSTRACT FROM AUTHOR]

We study a modified Lindemann mechanism, in which the second part of the reaction is 2 B → P instead of B → P . This model gives rise to a degenerate singularity in the associated system of ordinary differential equations. Using the blow-up technique, we describe this singularity qualitatively, showing that there is an invariant line, and that in the first quadrant (where the reaction takes place), it is stable. As a consequence, numerical methods for integrating differential equations can be used with confidence. Several examples are included. [ABSTRACT FROM AUTHOR]

In this work, the Homotopy Perturbation method is used for the first time to solve an irreversible linear pathway with enzyme kinetics. The enzymatic system has Michaelis–Menten kinetics and is modeled by a system of nonlinear ordinary differential equations. The analytical solution obtained with the method allow us to optimize several objectives: minimal time to reach a certain percent of final product, minimal amount of enzymes employed in the process, or even multiple objective optimization via Pareto front. We present an example to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper we consider the classic kinetic problem of the minimization of the operation time in which a substrate is transformed into a product in multi-step enzymatic reactions. We propose a realistic formulation that incorporates the enzyme dynamics, and present a method for obtaining the solution for an unbranched scheme and bi-linear kinetic model in an almost exclusively analytical way. The solution, which involves the exponential integral, is illustrated with several examples. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality. [ABSTRACT FROM AUTHOR]

Highlights • We analyze the dynamics of a multi-species fisheries system in the presence of harvesting. • We propose a rather general model for studying multi-species interactions which covers previous ones. • We solve a new problem: finding the optimal strategy for a mid-term horizon with a fixed final stock of each species. • The proposed method is not gravely influenced by the dimensionality of the problem or by the complexity of the model. Abstract In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. For its solution, we combine techniques derived from Pontryagin's Maximum Principle, cyclic coordinate descent and the shooting method. The algorithm we develop can solve problems both with inter-species competition and with predator–prey behaviors. Several numerical examples are presented to illustrate the different possibilities of the method and a study of the dependence of the behavior on some parameters is performed. [ABSTRACT FROM AUTHOR]

In this paper a general formulation for the kinetics of multi-step enzymatic reactions is presented. The optimal enzyme and metabolite concentrations are studied for the problem of minimizing the operation time in which the substrate is converted into the product. We give an analytic solution for three different kinetic models for both the unbranched and branched cases. Sufficient conditions for the optimality of the solution are studied. Several examples are presented. [ABSTRACT FROM AUTHOR]

The increasing penetration of photovoltaic technology in the electricity market requires the development of a methodology that facilitates the optimisation of photovoltaic plants with single-axis trackers. This paper presents an optimisation methodology that takes into account the most important design variables of single-axis photovoltaic plants, including irregular land shape, size and configuration of the mounting system, row spacing, and operating periods (for backtracking mode, limited range of motion, and normal tracking mode). Equations for the determination of the optimal row spacing and operating periods have been developed and is presented in detail. A packing algorithm that takes into account the irregular land shape and the possible configurations of the mounting systems is also presented. The objective function is the total area of the photovoltaic field and the optimisation is performed by a packing algorithm. As the economic aspect of energy generation also plays a key role in decision-making, the levelised cost of energy has been used to assess the economic viability of the optimal layout of the mounting systems. The results show that the proposed methodology and packing algorithm are able to optimise the photovoltaic plant with single-axis solar tracking and provide reliable results after a reasonable computation time. The methodology was demonstrated in detail for a Spanish photovoltaic plant (Granjera photovoltaic power plant), including the optimal layout of the mounting systems and the cost analysis for this layout. The optimal layout of the mounting systems could increase the amount of energy captured by 91.18% in relation to the current of Granjera photovoltaic power plant. The mounting system configuration used in the optimal layout is the one with the best levelised cost of energy efficiency, 1.09. The presented optimisation methodology can be utilised to facilitate the optimal design of commercial photovoltaic plants with single-axis trackers. Therefore, questions such as: what is the optimal distribution of mounting systems?, how much energy will this distribution produce?, and at what cost will it produce it?, can be answered by using the proposed methodology. • The optimal layout of single-axis solar trackers in large-scale PV plants. • A detailed analysis of the design of the inter-row spacing and operating periods. • The optimal layout of the mounting systems increases the amount of energy by 91%. • Also has the best levelised cost of energy efficiency, 1.09. [ABSTRACT FROM AUTHOR]

This paper presents the problem of finding the optimal harvesting strategy, maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. Combining the techniques of Pontryagin’s Maximum Principle and the shooting method, an algorithm has been developed that is not affected by the values of the parameter. The algorithm is able to solve conventional problems as well as cases in which the optimal solution is shown to be bang–bang with singular arcs. In addition, we present a result that characterizes the optimal steady-state in infinite-horizon, autonomous models (except in the discount factor) and does not require the solution of the dynamic optimization problem. We also present a result that, under certain additional conditions, allows us to know a priori the final state solution when the optimization interval is finite. Finally, several numerical examples are presented to illustrate the different possibilities of the method. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between two options for operating a wind park in combination with a pumped-storage hydro-plant. First, we analyze the behavior of a wind farm that goes to the electricity market having previously forecasted the wind speed, while accepting the deviation penalties these forecasts may incur. Second, we study the possibility of the wind farm not going to the market individually, but as part of a hydro-wind power plant. Considerations about the optimal size of the wind farm and the hydro-pumped storage plant have previously been analyzed in the literature. However, most of these papers do not analyze dynamic considerations. The dimensioning of the system is not studied in our paper; its main feature will instead be the consideration of the dynamic optimal control problem. The use of Pontryagin's Maximum Principle allows us to obtain a very efficient optimization algorithm. The hydro-plant is modelled in great detail, using a variable-head model for the pumped hydro-plant. Our study provides a useful tool for electricity companies. The algorithm is able to solve the problem of the day-ahead market, a problem that is not solved in other studies. [ABSTRACT FROM AUTHOR]

In this paper, an n-step, linear and unbranched pathway with Michaelis-Menten kinetics is solved in a quasi-analytical way. The method, based on the optimal control theory, calculates the optimal enzyme concentrations while minimizing the operation time. In the computation of the solution, the Lambert W-function plays a fundamental role, due to the presence of a non-linear kinetic model. Our method allows us to obtain the generalized solution and to perform the sensitivity analysis of the catalytic parameters. [ABSTRACT FROM AUTHOR]

The infimal convolution operation arises in mathematical economics in the analysis of several problems. In this paper we first present a survey and summarize two previous papers by the authors on the classic firm's cost-minimization problem. Moreover, we present a new application: the analytical solution of the utility maximization problem which we shall obtain applying the supremal convolution operation. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of optimal control problems inspired by the hydroelectric context. These problems model a continuous production process with several interrelated pre-set availability inputs in a finite time interval with production functions which are linear with respect to the consumption rate over time. It constitutes a bang–singular–bang control problem, which we solve using a cyclic coordinate descent strategy combined with a suitable adaptation of the shooting method. Finally, the proposed algorithm is implemented using the Mathematica package and applied to a hydraulic optimization problem in which the potential of the algorithm is evidenced. [ABSTRACT FROM AUTHOR]

In this paper, we present a quasi-analytical method to calculate the optimal enzyme concentrations in a chemical process, considering the minimization of the operation time. The resulting constrained optimal control problem is solved using Pontryagin's Minimum Principle. First, our method allows us to obtain the generalized solution of an $$n$$ -step system with an unbranched scheme and bilinear kinetic models and non-equal catalytic efficiencies of the enzymes. Second, we discuss the sensitivity analysis of these catalytic parameters in detail. [ABSTRACT FROM AUTHOR]

In this paper we present a method to solve a constrained optimal control problem to calculate the optimal enzyme concentrations in a chemical process by considering the minimization of the transition time. The method, based on Pontryagin's Minimum Principle, allows us to obtain the generalized solution of an $$n$$ -step system with an unbranched scheme and bilinear kinetic models in an almost exclusively analytical way. [ABSTRACT FROM AUTHOR]

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques. [ABSTRACT FROM PUBLISHER]

Renewable energies and, in particular, wind power have come to the forefront in the electricity market in recent years. The main drawback of wind power generation, however, is the major difficulty in forecasting its production. For this reason, when wind farms go to the market, they are very often made to pay penalties for the deviations between forecasting and actual production. In this paper we shall analyse whether real-time compensation of wind power plant deviation penalties is profitable by means of the coordinated optimization of the wind power plant with a large pumped-storage hydro-plant. We shall model the pumped storage plant in great detail and make use of optimal control techniques to carry out the optimization. We shall analyse the most relevant recent papers on the subject and compare them with our technique. We shall also analyse another possible solution based on compensation carried out a posteriori, instead of in real time. [ABSTRACT FROM PUBLISHER]

Abstract: The new Spanish regulations allow wind farms to go to the market to sell the energy generated by their facilities. In the case of over- or under-supply, other producers must reduce or increase their production to resolve the so-called deviation, thereby incurring financial losses. Faced with this situation, wind farms have several options. In this paper we consider one promising method: the combined optimization of a pumped-storage hydro-plant and a wind park. First, we are going to present the mathematical modelling of the resulting problem. Second, we shall solve the optimization problem using Optimal Control techniques and finally we shall present several examples of the combined optimization and analyse which strategy is the best one possible. [Copyright &y& Elsevier]

In this paper we present a new method for solving systems of ordinary nonlinear differential equations with initial conditions. The method is based on the transformation of the problem to an optimal control problem. We then solve it with a technique based on the use of an integral form of the Euler equation combined with the shooting method and the cyclic coordinate descent method. Our method substantially improves a previous approach that uses iterative dynamic programming to solve the associated optimal control problem. We consider the error functional instead of the classical global error, the error functional obtained by our method being lower than that obtained by classical methods. The method presented in this paper allows us to solve a wide range of nth order ordinary nonlinear differential equations with initial conditions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a generalization of the classic Firm’s Profit Maximization Problem, using the linear model for the production function, considering a decreasing price and maximum constraints for the inputs or, equivalently, considering inputs that are in turn outputs in economies of scale with quadratic concave cost functions. We formulate the problem by previously calculating the analytical minimum cost function in the quadratic concave case. This minimum cost function will be calculated for each production level via the infimal convolution of quadratic concave functions whose result is a piecewise quadratic concave function. [Copyright &y& Elsevier]

Abstract: In this paper we present an algorithm of quasi-linear complexity to exactly calculate the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint. [Copyright &y& Elsevier]

Abstract: The problem of economic dispatch with multiple fuel units has been widely addressed via different techniques using approximate methods due to the exponential complexity of full enumeration in the underlying combinatory problem. A method has recently been outlined by Min et al. (2008), that allows the problem to be solved in an exact way in polynomial time. In this paper, we present an alternative technique and take this idea further, studying and comparing two algorithms of polynomial complexity: basic recurrence and divide-and-conquer. Moreover, we provide the exact solution to the problem by Lin and Viviani (1984), that constitutes the traditional test for all approximate methods and present a comprehensive survey of several heuristic approaches. [Copyright &y& Elsevier]

Abstract: In this paper we study the profit-maximization problem, considering maximum constraints for the general case of m-inputs and using the Cobb–Douglas model for the production function. To do so, we previously study the firm’s cost minimization problem, proposing an equivalent infimal convolution problem for exponential-type functions. This study provides an analytical expression of the production cost function, which is found to be a piece-wise potential. Moreover, we prove that this solution belongs to class C 1. Using this cost function, we obtain the explicit expression of maximum profit. Finally, we illustrate the results obtained in this paper with an example. [Copyright &y& Elsevier]

This paper deals with the optimal control (OC) problem that arise when a hydraulic system with fixed-head hydroplants is considered. In the frame of a deregulated electricity market, the resulting Hamiltonian for such OC problems is linear in the control variable and results in an optimal singular/bang-bang control policy. To avoid difficulties associated with the computation of optimal singular/bang-bang controls, an efficient and simple optimization algorithm is proposed. The computational technique is illustrated on one example. [ABSTRACT FROM AUTHOR]

We consider the problem of the optimization of the functioning of a pumped-storage hydroplant. The problem can be mathematically formulated as an optimal control problem, and when the considered hydromodel is of the fixed-head type, an added complication arises: the solution is of the bangsingular-bang type. In this paper, we propose a simple and efficient optimization algorithm to find the solution. [ABSTRACT FROM AUTHOR]

Numerical methods and software packages for solving dynamic optimization or optimal control problems require a suitable initial estimation of the solution. This paper focuses on problems that arise in chemical processes described by complex dynamics. We present a very simple method, based on Pontryagin’s Minimum Principle, to obtain an initial guess for the solution. Our method presents numerous advantages: it is very easy to programme, it allows a wide range of problems to be addressed, the computation time is very short, the initial guess is very close to the solution and is attracted to a global minimum. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new method for addressing the short-term optimal operation of a generation company, fully adapted to represent the characteristics of the new competitive markets. We propose an efficient and highly accurate novel method for next-day price forecasting. We model the functional time series with a linear autoregressive functional model which formulates the relationships between each daily function of prices and the functions of previous days. For the optimization problem (formulated within the framework of nonsmooth analysis using Pontryagin’s Maximum Principle), we propose a new method that uses diverse mathematical techniques (the Shooting Method, Euler’s Method, the Cyclic Coordinate Descent Method). These techniques are well known for the case of functions, but are adapted here to the case of functionals and are efficiently combined to provide a novel contribution. Finally, the paper presents the results of applying our method to a price-taker company in the Spanish electricity market. [Copyright &y& Elsevier]

Abstract: This paper addresses a hydrothermal problem that simultaneously considers non-regular Lagrangian and non-holonomic inequality constraints, obtaining a necessary minimum condition. It is further shown that the discontinuity of the lagrangian does not translate as discontinuity in the derivative of the solution. Finally, a solution algorithm is developed and applied to an example. [Copyright &y& Elsevier]

In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and an optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke's) gradient and the Nonsmooth maximum principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented. [ABSTRACT FROM AUTHOR]

This paper presents an environmentally constrained economic dispatch algorithm for a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of a firm in a competitive market is described, the objective function of which can be defined as profit maximization, and we consider that thermal plants are constrained to technical and environmental restrictions. An optimal control technique is applied and Pontryagin's theorem is employed. The proposed algorithm is implemented using the Mathematica© package and is applied to a sample system. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the optimization of large-scale hydrothermal power systems. For the general problem with n hydro-plants, we present an algorithm using a particular strategy related to the Gauss–Southwell method of nonlinear optimization. The algorithm offers a constructive method for producing sequences of problems with one hydro-plant. For this simple problem we use Pontryagin’s minimum principle to prove a condition for the extremals of the functional. We set out our problem in terms of optimal control in continuous time, with the Bolza-type functional. Finally, we present one example employing a program developed with the “Mathematica” package and analyze the convergence of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper the authors present a necessary condition for minimum of a functional in the case in which the function L is continuous but not of class . This situation arises in problems of optimization of hydrothermal systems with pumped-storage plants. In such problems, the function is discontinuous in , which is the borderline point between the power generation zone and the pumping zone . The problem can be naturally formulated in the framework of nonsmooth analysis, using the generalized (or Clarke''s) gradient. [Copyright &y& Elsevier]

Abstract: In this paper we revise the classical formulation of the problem of the optimization of hydrothermal systems. First we demonstrate that a number of thermal plants can be substituted by a single one that behaves equivalently to the entire set. We then calculate the equivalent plant in the case where the cost functions are general (nonquadratic). We prove that the equivalent thermal plant is a second-order polynomial with piece-wise constant coefficients. Moreover, it belongs to the class . Next we calculate the equivalent plant in the case of imposing constraints of minimum or maximum thermal power. Finally, we present an example and execute the proposed algorithm using Mathematica package. [Copyright &y& Elsevier]

We present a comparative study of the different racking systems used in photovoltaic power systems, with a new methodology for determining the total energy produced by each one under usual weather conditions (not clear-skies). In systems without solar tracker, the tilt angle is a major factor contributing to the energy production, and its optimization is essential. We study the effect of tilt update frequency (daily, monthly, or constant) on the total irradiation received by a plane surface, and present a method for computing the optimal tilt angle, which we validate using previous studies. This method is easily implemented, accurate, and valid for any location. We compare all the systems with the most energy-productive one, the dual-axis tracker, in two ways: with respect to energy production, and to levelized cost of energy, both in 39 cities around the World. The results provide a new insight on the relative and objective value of trackerless systems, and some remarkable properties arise, which may be relevant in budgetary consideration. • We study the effect of tilt angle update frequency (daily, monthly, or constant). • We present a method for computing the optimal tilt angle (not clear-skies). • We compare all the racking PV systems with respect to energy production, and LCOE. • We provide a new insight on the value of trackerless systems. • Energy diff. Between daily and monthly tilt angle adjustment is less than 0.14%. [ABSTRACT FROM AUTHOR]

Certain advantages of using mountainous terrain for the installation of solar plants are well known, such as lower temperature, higher solar irradiance present at high altitudes, and economic aspects related to the lower cost of land. This paper highlights another one: the higher annual solar irradiation incident of single-axis N-S trackers installed on sloping terrain, as compared to horizontal ones. After a theoretical study in which the relevant formulas are derived, numerical simulations are presented. Then we showcase the results of a year-long experiment in which a N-S aligned single-axis tracker prototype was used, at the location of our Department (Gijón, Spain). The experimental results confirm the trends in the formulas and simulations. Finally, theoretical values for the energy gain for different slopes, at locations over the northern hemisphere between latitudes of 6 ° and 60 ° are provided. These gains can reach values up to 13.5%. • N-S oriented solar trackers in sloped terrain receive higher solar irradiation. • Formulas and simulations are included for irradiation in sloped terrains. • Results of a year-long experiment are included for a location in Gijón (Spain). • Experiment confirms the theoretical and numerical ones. Gains can be up to 10%. • Numerical estimations for latitudes between 6° and 60° are provided. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the wind effects, wind velocity and wind direction, on heat losses from a receiver with the longitudinal tilt angle of small-scale linear Fresnel reflectors for urban applications. In urban applications, the area required to install a solar collector is a critical parameter, therefore the parameter given by the energy-to-area ratio must reach its maximum value. Different combinations of longitudinal tilt angles are analyzed and compared with the typical configuration of a large scale linear Fresnel reflector (C1 configuration). The analysis is performed by SolidWorks Flow Simulation for different wind velocities and wind directions. Heat losses from the receiver have been estimated using a 3-D computational fluid dynamics model. Based on the numerical simulation of the receiver, the heat loss analysis has been calculated for several wind velocities, wind directions, and maximum energy-to-area ratio configurations. The effect of wind direction on heat losses is almost negligible. Although, heat losses are slightly higher in the North wind direction in most simulations. It will be demonstrated that the heat losses dramatically increase with a maximum energy-to-area ratio configuration, with the increase in longitudinal angle and, obviously, with the wind velocity. On the other hand, heat losses are higher at those locations with greater maximum energy-to-area ratio configuration. The heat losses, for wind velocity of 10 (m / s) and North direction, are, approximately, 120 % of C 1 , 131 % of C 1 , 143 % of C 1 , 165 % of C 1 and 174 % of C 1 , in Almeria, Rome, Budapest, Berlin and Helsinki, respectively. The longitudinal inclination of the receiver has positive effects on the performance of small scale linear Fresnel reflectors for urban applications. • An analysis of the wind effects, wind velocity and wind direction, on heat losses. • The effect of wind direction on heat losses is almost negligible. • The heat losses increase with the increase in longitudinal angle. • The longitudinal inclination of the receiver has positive effects. [ABSTRACT FROM AUTHOR]

Solar tracking systems are an indispensable requirement for optimal efficiency in small-scale linear Fresnel reflector systems. A thorough study of the influence of solar tracking errors on energy production is, therefore, required. The power produced by each mirror at any moment is also explicitly computed, as well as its variation under error. We study the large effect that the distance between the mirror and the absorber tube, solar time, and the day of the year have on the variation of power. Our results provide the foundations for the analysis of small-scale solar tracking systems. Solar tracking errors of less than 0.09 ∘ are acceptable (they cause power losses less than 1 %), whereas errors larger than 0.36 ∘ start being noticeable (power losses greater than 3 %). • A novel formula for the length illuminated under solar tracking error is proposed. • The power loss ratio is greater for the mirrors near the borders of the reflector. • Errors of less than 0.09° are acceptable: power losses less than 1%. • Errors larger than 0.36° start being noticeable: power losses greater than 3%. • High non-linearity in the influence of the solar tracking error on the power loss. [ABSTRACT FROM AUTHOR]

A new method for obtaining very accurate models to predict the Beam and Diffuse Horizontal Irradiance is proposed, using two sources of data: satellite irradiation estimations and two clear-sky models (one for Beam and one for Diffuse Irradiance). By means of a Fourier Series approximation, we correct the clear-sky models and adapt them to the climatological conditions of a specific location. Applying it to six cities in latitudes ranging from 36 ∘ to 60 ∘ degrees North, we compare our predictions with real ground-level data obtained (in this work) from the WRDC database. Results show that the proposed model is both accurate and applicable to different climates. • New method for predicting Beam and Diffuse Horizontal Irradiance in cloudy sky. • Easy implementation and very few data required thanks to Fourier series. • Validation using ground-level measured data. • Monthly and daily error measures confirm goodness of fit. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology for determining the geometrical parameters and the optimal distribution of small-scale linear Fresnel reflectors on flat roofs of urban buildings. This engineering problem is highly complex as it involves 21 variables; in contrast to present-day studies available in the literature, our method provides a global solution. The algorithm involves several stages, in which it uses multiple objective functionals: maximization of the used area of the roof, minimization of the cost, minimization of losses. The solution found by this method combines all the relevant aspects from the technical and/or economic point of views and obtains, as the final objective, the maximization of the absorbed annual energy for the stated problem. • A new methodology to determine the optimal geometrical parameters and distribution. • It maximizes the energy obtained on the roofs of urban buildings. • It maximizes the total mirror field area. • Parameters: the length, width and orientation of the available flat roof area. [ABSTRACT FROM AUTHOR]