47,714 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
Searching the solution space in constructive geometric constraint solving with genetic algorithms
Geometric problems defined by constraints have an exponential number
of solution instances in the number of geometric elements involved.
Generally, the user is only interested in one instance such that
besides fulfilling the geometric constraints, exhibits some additional
properties.
Selecting a solution instance amounts to selecting a given root every
time the geometric constraint solver needs to compute the zeros of a
multi valuated function. The problem of selecting a given root is
known as the Root Identification Problem.
In this paper we present a new technique to solve the root
identification problem. The technique is based on an automatic search
in the space of solutions performed by a genetic algorithm. The user
specifies the solution of interest by defining a set of additional
constraints on the geometric elements which drive the search of the
genetic algorithm. The method is extended with a sequential niche
technique to compute multiple solutions. A number of case studies
illustrate the performance of the method.Postprint (published version
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
Robust Procedures for Obtaining Assembly Contact State Extremal Configurations
Two important components in the selection of an admittance that facilitates force-guided assembly are the identification of: 1) the set of feasible contact states, and 2) the set of configurations that span each contact state, i.e., the extremal configurations. We present a procedure to automatically generate both sets from CAD models of the assembly parts. In the procedure, all possible combinations of principle contacts are considered when generating hypothesized contact states. The feasibility of each is then evaluated in a genetic algorithm based optimization procedure. The maximum and minimum value of each of the 6 configuration variables spanning each contact state are obtained by again using genetic algorithms. Together, the genetic algorithm approach, the hierarchical data structure containing the states, the relationships among the states, and the extremals within each state are used to provide a reliable means of identifying all feasible contact states and their associated extremal configurations
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