73,976 research outputs found
Proposed shunt rounding technique for large-scale security constrained loss minimization
The official published version can be obtained from the link below - Copyright @ 2010 IEEE.Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.This work was supported in part by the National Grid and in part by the EPSRC. Paper no. TPWRS-00653-2009
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
A Feature-Based Analysis on the Impact of Set of Constraints for e-Constrained Differential Evolution
Different types of evolutionary algorithms have been developed for
constrained continuous optimization. We carry out a feature-based analysis of
evolved constrained continuous optimization instances to understand the
characteristics of constraints that make problems hard for evolutionary
algorithm. In our study, we examine how various sets of constraints can
influence the behaviour of e-Constrained Differential Evolution. Investigating
the evolved instances, we obtain knowledge of what type of constraints and
their features make a problem difficult for the examined algorithm.Comment: 17 Page
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
Optimization of force-limiting seismic devices connecting structural subsystems
This paper is focused on the optimum design of an original force-limiting floor anchorage system for the seismic protection of reinforced concrete (RC) dual wall-frame buildings. This protection strategy is based on the interposition of elasto-plastic links between two structural subsystems, namely the lateral force resisting system (LFRS) and the gravity load resisting system (GLRS). The most efficient configuration accounting for the optimal position and mechanical characteristics of the nonlinear devices is obtained numerically by means of a modified constrained differential evolution algorithm. A 12-storey prototype RC dual wall-frame building is considered to demonstrate the effectiveness of the seismic protection strategy
Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements
We consider the problem of maximizing aggregate user utilities over a
multi-hop network, subject to link capacity constraints, maximum end-to-end
delay constraints, and user throughput requirements. A user's utility is a
concave function of the achieved throughput or the experienced maximum delay.
The problem is important for supporting real-time multimedia traffic, and is
uniquely challenging due to the need of simultaneously considering maximum
delay constraints and throughput requirements. We first show that it is
NP-complete either (i) to construct a feasible solution strictly meeting all
constraints, or (ii) to obtain an optimal solution after we relax maximum delay
constraints or throughput requirements up to constant ratios. We then develop a
polynomial-time approximation algorithm named PASS. The design of PASS
leverages a novel understanding between non-convex maximum-delay-aware problems
and their convex average-delay-aware counterparts, which can be of independent
interest and suggest a new avenue for solving maximum-delay-aware network
optimization problems. Under realistic conditions, PASS achieves constant or
problem-dependent approximation ratios, at the cost of violating maximum delay
constraints or throughput requirements by up to constant or problem-dependent
ratios. PASS is practically useful since the conditions for PASS are satisfied
in many popular application scenarios. We empirically evaluate PASS using
extensive simulations of supporting video-conferencing traffic across Amazon
EC2 datacenters. Compared to existing algorithms and a conceivable baseline,
PASS obtains up to improvement of utilities, by meeting the throughput
requirements but relaxing the maximum delay constraints that are acceptable for
practical video conferencing applications
Semidefinite approximation for mixed binary quadratically constrained quadratic programs
Motivated by applications in wireless communications, this paper develops
semidefinite programming (SDP) relaxation techniques for some mixed binary
quadratically constrained quadratic programs (MBQCQP) and analyzes their
approximation performance. We consider both a minimization and a maximization
model of this problem. For the minimization model, the objective is to find a
minimum norm vector in -dimensional real or complex Euclidean space, such
that concave quadratic constraints and a cardinality constraint are
satisfied with both binary and continuous variables. {\color{blue}By employing
a special randomized rounding procedure, we show that the ratio between the
norm of the optimal solution of the minimization model and its SDP relaxation
is upper bounded by \cO(Q^2(M-Q+1)+M^2) in the real case and by
\cO(M(M-Q+1)) in the complex case.} For the maximization model, the goal is
to find a maximum norm vector subject to a set of quadratic constraints and a
cardinality constraint with both binary and continuous variables. We show that
in this case the approximation ratio is bounded from below by
\cO(\epsilon/\ln(M)) for both the real and the complex cases. Moreover, this
ratio is tight up to a constant factor
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