Cédric Leboucher

Convergence proof of an enhanced Particle Swarm Optimisation method integrated with Evolutionary Game Theory

This paper proposes an enhanced Particle Swarm Optimisation (PSO) algorithm and examines its performance. In the proposed PSO approach, PSO is combined with Evolutionary Game Theory to improve convergence. One of the main challenges of such stochastic optimisation algorithms is the difficulty in the theoretical analysis of the convergence and performance. Therefore, this paper analytically investigates the convergence and performance of the proposed PSO algorithm. The analysis results show that convergence speed of the proposed PSO is superior to that of the Standard PSO approach. This paper also develops another algorithm combining the proposed PSO with the Standard PSO algorithm to mitigate the potential premature convergence issue in the proposed PSO algorithm. The combined approach consists of two types of particles, one follows Standard PSO and the other follows the proposed PSO. This enables exploitation of both diversification of the particles exploration and adaptation of the search direction.

A Swarm Intelligence Method Combined to Evolutionary Game Theory Applied to the Resources Allocation Problem

This paper addresses an allocation problem and proposes a solution using a swarm intelligence method. The application of swarm intelligence has to be discrete. This allocation problem can be modelled as a multi-objective optimization problem where the authors minimize the time and the distance of the total travel in a logistic context. This study uses a hybrid Discrete Particle Swarm Optimization DPSO method combined to Evolutionary Game Theory EGT. One of the main implementation issues of DPSO is the choice of inertial, individual, and social coefficients. In order to resolve this problem, those coefficients are optimised by using a dynamical approach based on EGT. The strategies are either to keep going with only inertia, only with individual, or only with social coefficients. Since the optimal strategy is usually a mixture of the three, the fitness of the swarm can be maximized when an optimal rate for each coefficient is obtained. Evolutionary game theory studies the behaviour of large populations of agents who repeatedly engage in strategic interactions. Changes in behaviour in these populations are driven by natural selection via differences in birth and death rates. To test this algorithm, the authors create a problem whose solution is already known. This study checks whether this adapted DPSO method succeeds in providing an optimal solution for general allocation problems.

A Two-Step Optimisation Method for Dynamic Weapon Target Assignment Problem

The weapon target assignment (WTA) problem has been designed to match the Command & Control (C2) requirement in military context, of which the goal is to find an allocation plan enabling to treat a specific scenario in assigning available weapons to oncoming targets. The WTA always get into situation weapons defending an area or assets from an enemy aiming to destroy it. Because of the uniqueness of each situation, this problem must be solved in real-time and evolve accordingly to the aerial/ground situation. By the past, the WTA was solved by an operator taking all the decisions, but because of the complexity of the modern warfare, the resolution of the WTA in using the power of computation is inevitable to make possible the resolution in real time of very complex scenarii involving different type of targets. Nowadays, in most of the C2 this process is designed in order to be as a support for a human operator and in helping him in the decision making process. The operator will give its final green light to proceed the intervention.

Novel Evolutionary Game Based Multi-Objective Optimisation for Dynamic Weapon Target Assignment

Abstract This paper develops a novel multi-objective optimisation method based on the Evolutionary Game Theory to solve Weapon Target Assignment problems in real-time. The main research question of this study was how to consider multi-objective functions all together and choose a best solution among many possible non-dominant optimal solutions. The key idea is the best solution can be considered as a solution which best survives in other solution spaces. Therefore, the proposed method first obtains individual solutions for each objective function. Then, Evolutionary Game Theory considers each solution as a player and evaluates them in the solution spaces of other players to check how they can survive in those spaces. The main innovation is that, unlike other multi-objective optimisation approaches, the proposed approach not only considers a set of optimal solutions regarding multi-objective functions, but also finds the best optimal solution in terms of the survivability. The stability and the real-time computation of the proposed algorithm is tested on an adapted and constrained Dynamic Weapon Target Assignment problem matching a real military requirement. The performance of the proposed approach is evaluated via numerical simulations.

Optimal Weapon Target Assignment Based on an Geometric Approach

Abstract In this paper, dynamic weapon target assignment is proposed for area air defence. The focus of this study is to optimally protect a convoy of friendly assets from oncoming targets whose manoeuvres are hard to be predicted. The earliest geometry provides a boundary of the intercept region without prediction of target manoeuvre. If any of friendly asset is located in this region, this asset might be destroyed by the targets. Therefore, the safety margin can be defined as the minimum distance between the earliest geometry and friendly asset. This safety margin naturally copes with the unpredictability of the target manoeuvre. In many-on-many engagement scenarios, the safety margin changes in accordance with allocation policies and it is closely related to the performance of the area air defence system. Thus, we formulate an optimal assignment problem using the safety margin and introduce an optimisation approach. The proposed optimisation method integrates the evolutionary game and particle swarm optimisation in order to improve the optimality as well as to reduce computational load. The performance of the proposed scheme for weapon target assignment is evaluated by non-linear simulations.

An Enhanced Particle Swarm Optimisation Algorithm Combined with Neural Networks to Decrease Computational Time

This paper proposes to reduce the computational time of an algorithm based on the combination of the Evolutionary Game Theory (EGT) and the Particle Swarm Optimisation (PSO), named C-EGPSO, by using Neural Networks (NN) in order to lighten the computation of the identified heavy part of the C-EGPSO. This computationally burdensome task is the resolution of the EGT part that consists in solving iteratively a differential equation in order to optimally adapt the direction search and the size step of the PSO at each iteration. Therefore, it is proposed to use NN to learn the solution of this differential equation according to the initial conditions in order to gain a precious time.