Adaptive Ranking Based Constraint Handling for Explicitly Constrained Black-Box Optimization

A novel explicit constraint handling technique for the covariance matrix adaptation evolution strategy (CMA-ES) is proposed. The proposed constraint handling exhibits two invariance properties. One is the invariance to arbitrary element-wise increasing transformation of the objective and constraint functions. The other is the invariance to arbitrary affine transformation of the search space. The proposed technique virtually transforms a constrained optimization problem into an unconstrained optimization problem by considering an adaptive weighted sum of the ranking of the objective function values and the ranking of the constraint violations that are measured by the Mahalanobis distance between each candidate solution to its projection onto the boundary of the constraints. Simulation results are presented and show that the CMA-ES with the proposed constraint handling exhibits the affine invariance and performs similarly to the CMA-ES on unconstrained counterparts.Comment: 9 page

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

Tracking moving optima using Kalman-based predictions

The dynamic optimization problem concerns finding an optimum in a changing environment. In the field of evolutionary algorithms, this implies dealing with a timechanging fitness landscape. In this paper we compare different techniques for integrating motion information into an evolutionary algorithm, in the case it has to follow a time-changing optimum, under the assumption that the changes follow a nonrandom law. Such a law can be estimated in order to improve the optimum tracking capabilities of the algorithm. In particular, we will focus on first order dynamical laws to track moving objects. A vision-based tracking robotic application is used as testbed for experimental comparison

A new evolutionary search strategy for global optimization of high-dimensional problems

Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population's capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones. © 2011 Elsevier Inc. All rights reserved