8,899 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
A Geometric Approach to Sound Source Localization from Time-Delay Estimates
This paper addresses the problem of sound-source localization from time-delay
estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel
geometric formulation is proposed, together with a thorough algebraic analysis
and a global optimization solver. The proposed model is thoroughly described
and evaluated. The geometric analysis, stemming from the direct acoustic
propagation model, leads to necessary and sufficient conditions for a set of
time delays to correspond to a unique position in the source space. Such sets
of time delays are referred to as feasible sets. We formally prove that every
feasible set corresponds to exactly one position in the source space, whose
value can be recovered using a closed-form localization mapping. Therefore we
seek for the optimal feasible set of time delays given, as input, the received
microphone signals. This time delay estimation problem is naturally cast into a
programming task, constrained by the feasibility conditions derived from the
geometric analysis. A global branch-and-bound optimization technique is
proposed to solve the problem at hand, hence estimating the best set of
feasible time delays and, subsequently, localizing the sound source. Extensive
experiments with both simulated and real data are reported; we compare our
methodology to four state-of-the-art techniques. This comparison clearly shows
that the proposed method combined with the branch-and-bound algorithm
outperforms existing methods. These in-depth geometric understanding, practical
algorithms, and encouraging results, open several opportunities for future
work.Comment: 13 pages, 2 figures, 3 table, journa
Modified constrained differential evolution for solving nonlinear global optimization problems
Nonlinear optimization problems introduce the possibility of
multiple local optima. The task of global optimization is to find a point
where the objective function obtains its most extreme value while satisfying
the constraints. Some methods try to make the solution feasible
by using penalty function methods, but the performance is not always
satisfactory since the selection of the penalty parameters for the problem
at hand is not a straightforward issue. Differential evolution has
shown to be very efficient when solving global optimization problems
with simple bounds. In this paper, we propose a modified constrained
differential evolution based on different constraints handling techniques,
namely, feasibility and dominance rules, stochastic ranking and global
competitive ranking and compare their performances on a benchmark
set of problems. A comparison with other solution methods available in
literature is also provided. The convergence behavior of the algorithm to
handle discrete and integer variables is analyzed using four well-known
mixed-integer engineering design problems. It is shown that our method
is rather effective when solving nonlinear optimization problems.Fundação para a Ciência e a Tecnologia (FCT
Digital Filter Design Using Improved Artificial Bee Colony Algorithms
Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods
Automating Vehicles by Deep Reinforcement Learning using Task Separation with Hill Climbing
Within the context of autonomous driving a model-based reinforcement learning
algorithm is proposed for the design of neural network-parameterized
controllers. Classical model-based control methods, which include sampling- and
lattice-based algorithms and model predictive control, suffer from the
trade-off between model complexity and computational burden required for the
online solution of expensive optimization or search problems at every short
sampling time. To circumvent this trade-off, a 2-step procedure is motivated:
first learning of a controller during offline training based on an arbitrarily
complicated mathematical system model, before online fast feedforward
evaluation of the trained controller. The contribution of this paper is the
proposition of a simple gradient-free and model-based algorithm for deep
reinforcement learning using task separation with hill climbing (TSHC). In
particular, (i) simultaneous training on separate deterministic tasks with the
purpose of encoding many motion primitives in a neural network, and (ii) the
employment of maximally sparse rewards in combination with virtual velocity
constraints (VVCs) in setpoint proximity are advocated.Comment: 10 pages, 6 figures, 1 tabl
A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems
The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a non-elitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the (μ+λ) μ λ Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison with MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69 % performance increase according to the Inverse Generational Distance (IGD) metric
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