7,708 research outputs found
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
Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control
Constrained optimization of high-dimensional numerical problems plays an
important role in many scientific and industrial applications. Function
evaluations in many industrial applications are severely limited and no
analytical information about objective function and constraint functions is
available. For such expensive black-box optimization tasks, the constraint
optimization algorithm COBRA was proposed, making use of RBF surrogate modeling
for both the objective and the constraint functions. COBRA has shown remarkable
success in solving reliably complex benchmark problems in less than 500
function evaluations. Unfortunately, COBRA requires careful adjustment of
parameters in order to do so.
In this work we present a new self-adjusting algorithm SACOBRA, which is
based on COBRA and capable to achieve high-quality results with very few
function evaluations and no parameter tuning. It is shown with the help of
performance profiles on a set of benchmark problems (G-problems, MOPTA08) that
SACOBRA consistently outperforms any COBRA algorithm with fixed parameter
setting. We analyze the importance of the several new elements in SACOBRA and
find that each element of SACOBRA plays a role to boost up the overall
optimization performance. We discuss the reasons behind and get in this way a
better understanding of high-quality RBF surrogate modeling
Comparison of constraint-handling techniques for metaheuristic optimization
Many design problems in engineering have highly nonlinear constraints and the proper handling of such constraints can be important to ensure solution quality. There are many different ways of handling constraints and different algorithms for optimization problems, which makes it difficult to choose for users. This paper compares six different constraint-handling techniques such as penalty methods, barrier functions, epsilon-constrained method, feasibility criteria and stochastic ranking. The pressure vessel design problem is solved by the flower pollination algorithm, and results show that stochastic ranking and epsilon-constrained method are most effective for this type of design optimization
Extensions of firefly algorithm for nonsmooth nonconvex constrained optimization problems
Publicado em: "Computational science and its applications – ICCSA 2016: 16th International Conference, Beijing, China, July 4-7, 2016, Proceedings, Part I". ISBN 978-3-319-42084-4Firefly Algorithm (FA) is a stochastic population-based algorithm
based on the flashing patterns and behavior of fireflies. Original FA was created
and successfully applied to solve bound constrained optimization problems. In
this paper we present extensions of FA for solving nonsmooth nonconvex
constrained global optimization problems. To handle the constraints of the
problem, feasibility and dominance rules and a fitness function based on the
global competitive ranking, are proposed. To enhance the speed of convergence,
the proposed extensions of FA invoke a stochastic local search procedure.
Numerical experiments to validate the proposed approaches using a set of well
know test problems are presented. The results show that the proposed extensions
of FA compares favorably with other stochastic population-based methods.COMPETE: POCI-01-0145- FEDER-007043FCT – Fundação para a Ciência e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/201
Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles
"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission
Self-adaptive fitness formulation for constrained optimization
A self-adaptive fitness formulation is presented for
solving constrained optimization problems. In this method, the dimensionality
of the problem is reduced by representing the constraint
violations by a single infeasibility measure. The infeasibility
measure is used to form a two-stage penalty that is applied to the
infeasible solutions. The performance of the method has been examined
by its application to a set of eleven test cases from the specialized
literature. The results have been compared with previously
published results from the literature. It is shown that the method
is able to find the optimum solutions. The proposed method requires
no parameter tuning and can be used as a fitness evaluator
with any evolutionary algorithm. The approach is also robust in
its handling of both linear and nonlinear equality and inequality
constraint functions. Furthermore, the method does not require an
initial feasible solution
Global competitive ranking for constraints handling with modified differential evolution
Constrained nonlinear programming problems involving a nonlinear objective function with inequality and/or equality constraints introduce the possibility of multiple local optima. The task of global optimization is to find a solution where the objective function obtains its most extreme value while satisfying the constraints. Depending on the nature of the involved functions many solution methods have been proposed. Most of the existing population-based stochastic methods try to make the solution feasible by using a penalty function method. However, to find the appropriate penalty parameter is not an easy task. Population-based differential evolution is shown to be very efficient to solve global optimization problems with simple bounds. To handle the constraints effectively, in this paper, we propose a modified constrained differential evolution that uses self-adaptive control parameters, a mixed modified mutation, the inversion operation, a modified selection and the elitism in order to progress efficiently towards a global solution. In the modified selection, we propose a fitness function based on the global competitive ranking technique for handling the constraints. We test 13 benchmark problems. We also compare the results with the results found in literature. It is shown that our method is rather effective when solving constrained problemsFundação para a Ciência e a Tecnologia (FCT
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