Feasibility and dominance rules in the electromagnetism-like algorithm for constrained global optimization

This paper presents the use of a constraint-handling technique, known as feasibility and dominance rules, in a electromagnetismlike (ELM) mechanism for solving constrained global optimization problems. Since the original ELM algorithm is specifically designed for solving bound constrained problems, only the inequality and equality constraints violation together with the objective function value are used to select points and to progress towards feasibility and optimality. Numerical experiments are presented, including a comparison with other methods recently reported in the literature

An artificial fish swarm filter-based Method for constrained global optimization

Ana Maria A.C. Rocha, M. Fernanda P. Costa and Edite M.G.P. Fernandes, An Artificial Fish Swarm Filter-Based Method for Constrained Global Optimization, B. Murgante, O. Gervasi, S. Mirsa, N. Nedjah, A.M. Rocha, D. Taniar, B. Apduhan (Eds.), Lecture Notes in Computer Science, Part III, LNCS 7335, pp. 57–71, Springer, Heidelberg, 2012.An artificial fish swarm algorithm based on a filter methodology for trial solutions acceptance is analyzed for general constrained global optimization problems. The new method uses the filter set concept to accept, at each iteration, a population of trial solutions whenever they improve constraint violation or objective function, relative to the current solutions. The preliminary numerical experiments with a wellknown benchmark set of engineering design problems show the effectiveness of the proposed method.Fundação para a Ciência e a Tecnologia (FCT

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity

Multi-level ranking for constrained multi-objective evolutionary optimisation

In real-world optimisation problems, feasibility of solutions is invariably an essential requirement. A natural way to deal with feasibility is to cast it as an additional objective in a multi-objective optimisation setting. In this paper, we consider two possible ways to do this, using a multi-level scheme for ranking solutions. One strategy considers feasibility first, before considering objective values, while the other reverses this ordering. The first strategy has been explored before, while the second has not. Experiments show that the second strategy can be much more successful on some difficult problems

Comparison-Based Optimizers Need Comparison-Based Surrogates

International audienceTaking inspiration from approximate ranking, this paper nvestigates the use of rank-based Support Vector Machine as surrogate model within CMA-ES, enforcing the invariance of the approach with respect to monotonous transformations of the fitness function. Whereas the choice of the SVM kernel is known to be a critical issue, the proposed approach uses the Covariance Matrix adapted by CMA-ES within a Gaussian kernel, ensuring the adaptation of the kernel to the currently explored region of the fitness landscape at almost no computational overhead. The empirical validation of the approach on standard benchmarks, comparatively to CMA-ES and recent surrogate-based CMA-ES, demonstrates the efficiency and scalability of the proposed approach