Browsing by Subject "Global optimization"

Now showing 1 - 11 of 11

Open Access
“Backward differential flow” may not converge to a global minimizer of polynomials
(Springer New York LLC, 2015) Arıkan, Orhan; Burachik, R. S.; Kaya, C. Y.
We provide a simple counter-example to prove and illustrate that the backward differential flow approach, proposed by Zhu, Zhao and Liu for finding a global minimizer of coercive even-degree polynomials, can converge to a local minimizer rather than a global minimizer. We provide additional counter-examples to stress that convergence to a local minimum via the backward differential flow method is not a rare occurence.
Open Access
A finite concave minimization algorithm using branch and bound and neighbor generation
(Springer, 1994) Benson, H. P.; Sayin, S.
In this article we present a new finite algorithm for globally minimizing a concave function over a compact polyhedron. The algorithm combines a branch and bound search with a new process called neighbor generation. It is guaranteed to find an exact, extreme point optimal solution, does not require the objective function to be separable or even analytically defined, requires no nonlinear computations, and requires no determinations of convex envelopes or underestimating functions. Linear programs are solved in the branch and bound search which do not grow in size and differ from one another in only one column of data. Some preliminary computational experience is also presented.
Open Access
Levy walk evolution for global optimization
(ACM, 2008-07) Urfalıoğlu, Onay; Çetin, A. Enis; Kuruoğlu, E. E.
A novel evolutionary global optimization approach based on adaptive covariance estimation is proposed. The proposed method samples from a multivariate Levy Skew Alpha-Stable distribution with the estimated covariance matrix to realize a random walk and so to generate new solution candidates in the mutation step. The proposed method is compared to the popular Differential Evolution method, which is one of the best general evolutionary global optimizers available. Experimental results indicate that the proposed approach yields a general improvement in the required number of function evaluations to solve global optimization problems. Especially, as shown in experiments, the underlying heavy tailed alpha-stable distribution enables a considerably more effective global search in more complex problems. Track: Evolution Strategies.
Open Access
On the optimality of stochastic signaling under an average power constraint
(IEEE, 2010-09-10) Göken, Çağrı; Gezici, Sinan; Arıkan, Orhan
In this paper, stochastic signaling is studied for scalar valued binary communications systems over additive noise channels in the presence of an average power constraint. For a given decision rule at the receiver, the effects of using stochastic signals for each symbol instead of conventional deterministic signals are investigated. First, sufficient conditions are derived to determine the cases in which stochastic signaling can or cannot outperform the conventional signaling. Then, statistical characterization of the optimal signals is provided and it is obtained that an optimal stochastic signal can be represented by a randomization of at most two different signal levels for each symbol. In addition, via global optimization techniques, the solution of the generic optimal stochastic signaling problem is obtained, and theoretical results are investigated via numerical examples. ©2010 IEEE.
Open Access
Optimal signaling and detector design for power constrained on-off keying systems in Neyman-Pearson framework
(IEEE, 2011) Dulek, Berkan; Gezici, Sinan
Optimal stochastic signaling and detector design are studied for power constrained on-off keying systems in the presence of additive multimodal channel noise under the Neyman-Pearson (NP) framework. The problem of jointly designing the signaling scheme and the decision rule is addressed in order to maximize the probability of detection without violating the constraints on the probability of false alarm and the average transmit power. Based on a theoretical analysis, it is shown that the optimal solution can be obtained by employing randomization between at most two signal values for the on-signal (symbol 1) and using the corresponding NP-type likelihood ratio test at the receiver. As a result, the optimal parameters can be computed over a significantly reduced optimization space instead of an infinite set of functions using global optimization techniques. Finally, a detection example is provided to illustrate how stochastic signaling can help improve detection performance over various optimal and sub-optimal signaling schemes. © 2011 IEEE.
Open Access
Optimization over the efficient set: four special cases
(Springer, 1994) Sayin, S.; Benson, H. P.
Recently, researchers and practitioners have been increasingly interested in the problem (P) of maximizing a linear function over the efficient set of a multiple objective linear program. Problem (P) is generally a difficult global optimization problem which requires numerically intensive procedures for its solution. In this paper, simple linear programming procedures are described for detecting and solving four special cases of problem (P). When solving instances of problem (P), these procedures can be used as screening devices to detect and solve these four special cases.
Open Access
Positioning algorithms for cooperative networks in the presence of an unknown turn-around time
(IEEE, 2011) Gholami, M.R.; Gezici, Sinan; Ström, E.G.; Rydström, M.
This paper addresses the problem of single node positioning in cooperative network using hybrid two-way time-of-arrival and time-difference-of-arrival where, the turn-around time at the target node is unknown. Considering the turn-around time as a nuisance parameter, the derived maximum likelihood estimator (MLE) brings a difficult global optimization problem due to local minima in the cost function of the MLE. To avoid drawbacks in solving the MLE, we obtain a linear two-step estimator using non-linear pre-processing which is algebraic and closed-form in each step. To compare different methods, Cramér-Rao lower bound (CRLB) is derived. Simulation results confirm that the proposed linear estimator attains the CRLB for sufficiently high signal-to-noise ratios. © 2011 IEEE.
Open Access
A problem space algorithm for single machine weighted tardiness problems
(Taylor & Francis Inc., 2003) Avcı, S.; Aktürk, M. S.; Storer, R. H.
We propose a problem space genetic algorithm to solve single machine total weighted tardiness scheduling problems. The proposed algorithm utilizes global and time-dependent local dominance rules to improve the neighborhood structure of the search space. They are also a powerful exploitation (intensifying) tool since the global optimum is one of the local optimum solutions. Furthermore, the problem space search method significantly enhances the exploration (diversification) capability of the genetic algorithm. In summary, we can improve both solution quality and robustness over the other local search algorithms reported in the literature.
Open Access
Randomized and rank based differential evolution
(IEEE, 2009-12) Urfalıoğlu, Onay; Arıkan, Orhan
Many real world problems which can be assigned to the machine learning domain are inverse problems. The available data is often noisy and may contain outliers, which requires the application of global optimization. Evolutionary Algorithms (EA's) are one class of possible global optimization methods for solving such problems. Within population based EA's, Differential Evolution (DE) is a widely used and successful algorithm. However, due to its differential update nature, given a current population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitnesses of the population. This paper presents a novel extension of DE called Randomized and Rank based Differential Evolution (R2DE) to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the fitnesses. In experiments including non-linear dimension reduction by autoencoders, it is shown that R2DE improves robustness and speed of global convergence. © 2009 IEEE.
Open Access
Steklov regularization and trajectory methods for univariate global optimization
(Springer, 2020) Arıkan, Orhan; Burachik, R. S.; Kaya, C. Y.
We introduce a new regularization technique, using what we refer to as the Steklov regularization function, and apply this technique to devise an algorithm that computes a global minimizer of univariate coercive functions. First, we show that the Steklov regularization convexifies a given univariate coercive function. Then, by using the regularization parameter as the independent variable, a trajectory is constructed on the surface generated by the Steklov function. For monic quartic polynomials, we prove that this trajectory does generate a global minimizer. In the process, we derive some properties of quartic polynomials. Comparisons are made with a previous approach which uses a quadratic regularization function. We carry out numerical experiments to illustrate the working of the new method on polynomials of various degree as well as a non-polynomial function.
Open Access
Time-delay estimation in multiple-input single-output systems
(IEEE, 2010) Koçak, Fatih; Gezici, Sinan
In this paper, the time-delay estimation problem is studied for multiple-input single-output (MISO) systems. First, a theoretical analysis is carried out by deriving the Cramer-Rao lower bound (CRLB) for time-delay estimation in a MISO system. Then, the maximum likelihood (ML) estimator for the time-delay parameter is obtained, which results in a complex optimization problem in general. In order to provide a solution of the ML estimator with low computational complexity, ML estimation based on a genetic global optimization algorithm, namely, differential evolution (DE), is proposed. Simulation studies for various fading scenarios are performed to investigate the performance of the proposed algorithm. ©2010 IEEE.