Elia Daniele

Equilibrium strategies via GA to stackelberg games under multiple follower's best reply

In this paper, we study a two‐person game between one leader and one follower, called the Stackelberg game. The leader player enounces a decision before the others, and the follower takes into account this decision and solves an optimization problem that may have multiple solutions. Then, the leader optimizes his objective by assuming a given followers reaction depending on his behavior. We consider in this paper a hierarchical equilibrium solution for a two‐level game, particularly the strong Stackelberg solutions that corresponds to an optimistic leaders point of view and we give a numerical procedure based on a genetic algorithm (GA) evolution process to compute them. The use of a multimodal genetic algorithm allows us to approach the possible multiple solutions to the lower level problem. The algorithm convergence is illustrated by means of some test cases.

A Hierarchical MultiModal Hybrid Stackelberg–Nash GA for a Leader with Multiple Followers Game

In this paper a numerical procedure based on a genetic algorithm (GA) evolution process is given to compute a Stackelberg solution for a hierarchical n + 1-person game. There is a leader player who enounces a decision before the others, and the rest of players (followers) take into account this decision and solve a Nash equilibrium problem. So there is a two-level game between the leader and the followers, called Stackelberg–Nash problem. The idea of the Stackelberg-GA is to bring together genetic algorithms and Stackelberg strategy in order to process a genetic algorithm to build the Stackelberg strategy. In the lower level, the followers make their decisions simultaneously at each step of the evolutionary process, playing a so called Nash game between themselves. The use of a multimodal genetic algorithm allows to find multiple Stackelberg strategies at the upper level. In this model the uniqueness of the Nash equilibrium at the lower-level problem has been supposed. The algorithm convergence is illustrated by means of several test cases.

Conceptual adaptive wing-tip design for pollution reductions

Most of the commercial long-range aircraft are equipped with winglet to decrease the induced drag thus saving more fuel; this feature can also be found on birds, but in conventional aircraft, the winglet device is fixed. Recent projects point toward advanced smart materials and telescopic wing-tip devices to obtain an adaptive morphing shape that gives, through performances improvement, a fuel consumption and so a pollutant reduction. In order to obtain pollution reductions via high aerodynamic efficiency, the design of a telescopic inflatable variable height wing-tip device has been addressed. The span variation is pursued toward a telescopic device that is linked to an inflatable system distributed in chord and along the base of tip, ready to be extruded according to flight conditions. The performance analysis has been conducted especially to evaluate range performance, which mainly provides the relation to fuel consumption. The hinged telescopic device gives the chance of obtaining variation in winglet span according to flight condition requirements in terms of stability and aerodynamic efficiency. The solution of the inflatable system would guarantee a more comfortable arrangement of deployment system and just minor surplus of weight compared to classical winglet solutions, with all the subsequent advantages.

Development and application of a grid generation tool for aerodynamic simulations of wind turbines

This manuscript presents an effort towards the introduction of a new grid generation tool for computational fluid dynamics (CFD) simulations of wind turbines. The tool was developed and designed to considerably reduce the duration and complexity of the grid generation process and, moreover, to enable users to perform an efficient CFD simulation for a complete wind turbine rotor. Furthermore, the tool is fully automatized, thus enabling the user to refine the grid along the desired direction. For the purpose of validation, the quality of the generated grid was checked via a grid independence test. Finally, the grid generator tool was evaluated by means of a series of simulations of the NREL phase VI rotor using a three-dimensional CFD Reynolds averaged Navier–Stokes method. The capability of CFD simulations based on the generated grid in capturing aerodynamic performances (such as the power) and the detailed flow characteristics (e.g. the surface pressure distributions) were investigated under various conditions. The obtained results demonstrate the quality and reliability of the developed grid generation tool.

A Planar Location-Allocation Problem with Waiting Time Costs

We study a location-allocation problem where the social planner has to locate some new facilities minimizing the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity acquisition costs plus the distribution costs in the service regions. In order to find the optimal location of the new facilities and the optimal partition of the consumers, we consider a two-stage optimization model. Theoretical and computational aspects of the location-allocation problem are discussed for a planar region and illustrated with examples.

A Game Theoretical Model for Experiment Design Optimization

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. The resulting game has nice properties, so that a computational procedure is performed by using genetic algorithm approach. We consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. The problem arises from a concrete situation: find the optimal location of n receivers able to pick up particles of cosmic ray in a given platform (some experiment to measure the quantities of gamma rays are ongoing in Nepal thanks to the altitude of the region). Theoretical and computational results are presented for this location problem.

Horizontal Axis Hydroturbine Shroud Airfoil Optimization

The present work concerns the optimization of the shroud of an horizontal axis hydro turbine (HAHT). The main aim is to improve the hydro-turbine efficiency by designing a new shroud airfoil through an optimization process that maximize, as objective function, the power coefficient. The optimization process is carried out by MATLAB on the supercomputing infrastructure SCoPE of the University of Naples, “Federico II”. Results are obtained with CFD calculations, namely by STARCCM+ for an axisymmetric model, taking advantage of the symmetry of the problem, to minimize the computational time; in addition the HAHT is simulated with an actuator disk that gave reliable results in good agreement with previous works, developed with different software, and with experimental results. The original airfoil was designed for high-lift regimes, so it already gave excellent performance in these kind of applications. For that reason, is not expected a very high increase of the power coefficient. Nevertheless the optimization process results into a power coefficient increase of 4.5 %, with respect to the original airfoil.

A Genetic Algorithm for a Sensor Device Location Problem

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. We consider the case where the design variables are the coordinates of \(n\) points in a region of the plane and we look for the optimal configuration of the points under some constraints. Arising from a concrete situation, concerning the ARGO-YBJ experiments, the goal is to find the optimal configuration of the detector, consisting of a single layer of resistive plate counters. Theoretical and computational results are presented for this location problem.

Location Methods in Experimental Design

The design variables of an experiment is modeled as a facility location problem: we consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. In this paper we present a non-cooperative game theoretical model for the problem of experimental design: each of n virtual players decides the location of a point in the admissible region optimizing a pay-off function. The Nash equilibrium solutions will be the optimal solutions of the design variables problem. The resulting game has nice properties, so that a computational procedure is performed by using genetic algorithm approach and some existence results are obtained.

Experimental Design Problems and Nash Equilibrium Solutions

In this paper we present a non-cooperative game theoretical model for the well-known problem of experimental design. Nash equilibrium solutions of a suitable game will be the optimal values of the design variables, given by the coordinates of points in a region in the spirit of the facility location model. Because of the dependency of the objective functions on the distance from the domain’s boundary, this problem has a strong analogy with the classical sphere packing problem. Theoretical and computational results are presented for this location problem by virtue of a genetic algorithm procedure for both two- and three-dimensional test cases.