Differential evolution based bi-level programming algorithm for computing normalized nash equilibrium

The Generalised Nash Equilibrium Problem (GNEP) is a Nash game with the distinct feature that the feasible strategy set of a player depends on the strategies chosen by all her opponents in the game. This characteristic distinguishes the GNEP from a conventional Nash Game. These shared constraints on each player’s decision space, being dependent on decisions of others in the game, increases its computational difficulty. A special solution of the GNEP is the Nash Normalized Equilibrium which can be obtained by transforming the GNEP into a bi-level program with an optimal value of zero in the upper level. In this paper, we propose a Differential Evolution based Bi-Level Programming algorithm embodying Stochastic Ranking to handle constraints (DEBLP-SR) to solve the resulting bi-level programming formulation. Numerical examples of GNEPs drawn from the literature are used to illustrate the performance of the proposed algorithm

Hybrid behavioural-based multi-objective space trajectory optimization

In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behaviorism, combinedwith the decomposition of the solutions pace was tested on a set of standard multi-objective optimization problems and on a simple but representative case of space trajectory design

SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

In the context of industrial engineering, it is important to integrate efficient computational optimization methods in the product development process. Some of the most challenging simulation-based engineering design optimization problems are characterized by: a large number of design variables, the absence of analytical gradients, highly non-linear objectives and a limited function evaluation budget. Although a huge variety of different optimization algorithms is available, the development and selection of efficient algorithms for problems with these industrial relevant characteristics, remains a challenge. In this communication, a hybrid variant of Differential Evolution (DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG) methods within the framework of DE, in order to improve optimization efficiency on problems with the previously mentioned characteristics. The performance of the resulting derivative-free algorithm is compared with other state-of-the-art DE variants on 25 commonly used benchmark functions, under tight function evaluation budget constraints of 1000 evaluations. The experimental results indicate that the new algorithm performs excellent on the 'difficult' (high dimensional, multi-modal, inseparable) test functions. The operations used in the proposed mutation scheme, are computationally inexpensive, and can be easily implemented in existing differential evolution variants or other population-based optimization algorithms by a few lines of program code as an non-invasive optional setting. Besides the applicability of the presented algorithm by itself, the described concepts can serve as a useful and interesting addition to the algorithmic operators in the frameworks of heuristics and evolutionary optimization and computing

A hybrid multiagent approach for global trajectory optimization

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers(corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods

A multi-cycled sequential memetic computing approach for constrained optimisation

In this paper, we propose a multi-cycled sequential memetic computing structure for constrained optimisation. The structure is composed of multiple evolutionary cycles. At each cycle, an evolutionary algorithm is considered as an operator, and connects with a local optimiser. This structure enables the learning of useful knowledge from previous cycles and the transfer of the knowledge to facilitate search in latter cycles. Specifically, we propose to apply an estimation of distribution algorithm (EDA) to explore the search space until convergence at each cycle. A local optimiser, called DONLP2, is then applied to improve the best solution found by the EDA. New cycle starts after the local improvement if the computation budget has not been exceeded. In the developed EDA, an adaptive fully-factorized multivariate probability model is proposed. A learning mechanism, implemented as the guided mutation operator, is adopted to learn useful knowledge from previous cycles. The developed algorithm was experimentally studied on the benchmark problems in the CEC 2006 and 2010 competition. Experimental studies have shown that the developed probability model exhibits excellent exploration capability and the learning mechanism can significantly improve the search efficiency under certain conditions. The comparison against some well-known algorithms showed the superiority of the developed algorithm in terms of the consumed fitness evaluations and the solution quality

Differential Evolution for Multiobjective Portfolio Optimization

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution

Constrained Optimization with Evolutionary Algorithms: A Comprehensive Review

Global optimization is an essential part of any kind of system. Various algorithms have been proposed that try to imitate the learning and problem solving abilities of the nature up to certain level. The main idea of all nature-inspired algorithms is to generate an interconnected network of individuals, a population. Although most of unconstrained optimization problems can be easily handled with Evolutionary Algorithms (EA), constrained optimization problems (COPs) are very complex. In this paper, a comprehensive literature review will be presented which summarizes the constraint handling techniques for COP