Browsing by Author "Kargar, Kamyar"

Now showing 1 - 5 of 5

Open Access
Bilateral trade with risk-averse intermediary using linear network optimization
(Wiley Periodicals, Inc., 2019) Bayrak, Halil İ.; Kargar, Kamyar; Pınar, Mustafa Ç.
We consider bilateral trade of an object between a seller and a buyer through an intermediary who aims to maximize his/her expected gains as in the previous study, in a Bayes‐Nash equilibrium framework where the seller and buyer have private, discrete valuations for the object. Using duality of linear network optimization, the intermediary's initial problem is transformed into an equivalent linear programming problem with explicit formulae of expected revenues of the seller and the expected payments of the buyer, from which the optimal mechanism is immediately obtained. Then, an extension of the same problem is considered for a risk‐averse intermediary. Through a computational analysis, we observe that the structure of the optimal mechanism is fundamentally changed by switching from risk‐neutral to risk‐averse environment.
Open Access
Codon optimization: A mathematical programing approach
(Oxford University Press, 2020-04) Şen, Alper; Kargar, Kamyar; Akgün, E.; Pınar, Mustafa Ç.
Motivation: Synthesizing proteins in heterologous hosts is an important tool in biotechnology. However, the genetic code is degenerate and the codon usage is biased in many organisms. Synonymous codon changes that are customized for each host organism may have a significant effect on the level of protein expression. This effect can be measured by using metrics, such as codon adaptation index, codon pair bias, relative codon bias and relative codon pair bias. Codon optimization is designing codons that improve one or more of these objectives. Currently available algorithms and software solutions either rely on heuristics without providing optimality guarantees or are very rigid in modeling different objective functions and restrictions. Results: We develop an effective mixed integer linear programing (MILP) formulation, which considers multiple objectives. Our numerical study shows that this formulation can be effectively used to generate (Pareto) optimal codon designs even for very long amino acid sequences using a standard commercial solver. We also show that one can obtain designs in the efficient frontier in reasonable solution times and incorporate other complex objectives, such as mRNA secondary structures in codon design using MILP formulations. Availability and implementation: http://alpersen.bilkent.edu.tr/codonoptimization/CodonOptimization.zip
Open Access
Comparison of the formulations for a hub-and-spoke network design problem under congestion
(Elsevier, 2016) Kian, Ramer; Kargar, Kamyar
In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set. © 2016 Elsevier Ltd
Open Access
Feature selection using stochastic approximation with Barzilai and Borwein non-monotone gains
(Elsevier Ltd, 2021-08) Aksakallı, V.; Yenice, Z. D.; Malekipirbazari, Milad; Kargar, Kamyar
With recent emergence of machine learning problems with massive number of features, feature selection (FS) has become an ever-increasingly important tool to mitigate the effects of the so-called curse of dimensionality. FS aims to eliminate redundant and irrelevant features for models that are faster to train, easier to understand, and less prone to overfitting. This study presents a wrapper FS method based on Simultaneous Perturbation Stochastic Approximation (SPSA) with Barzilai and Borwein (BB) non-monotone gains within a pseudo-gradient descent framework wherein performance is measured via cross-validation. We illustrate that SPSA with BB gains (SPSA-BB) provides dramatic improvements in terms of the number of iterations for convergence with minimal degradation in cross-validated error performance over the current state-of-the art approach with monotone gains (SPSA-MON). In addition, SPSA-BB requires only one internal parameter and therefore it eliminates the need for careful fine-tuning of numerous other internal parameters as in SPSA-MON or comparable meta-heuristic FS methods such as genetic algorithms (GA). Our particular implementation includes gradient averaging as well as gain smoothing for better convergence properties. We present computational experiments on various public datasets with Nearest Neighbors and Naive Bayes classifiers as wrappers. We present comparisons of SPSA-BB against full set of features, SPSA-MON, as well as seven popular meta-heuristics based FS algorithms including GA and particle swarm optimization. Our results indicate that SPSA-BB converges to a good feature set in about 50 iterations on the average regardless of the number of features (whether a dozen or more than 1000 features) and its performance is quite competitive. SPSA-BB can be considered extremely fast for a wrapper method and therefore it stands as a high-performing new feature selection method that is also computationally feasible in practice.
Open Access
Robust bilateral trade with discrete types
(Springer, 2018) Kargar, Kamyar; Bayrak, Halil İbrahim; Pınar, Mustafa Çelebi
Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ-divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.