Ahmet Kaya

Metaheuristic optimization algorithms have become one of the most important research areas for solving complex, nonlinear, and high-dimensional optimization problems. These algorithms are widely used in many application domains such as engineering, artificial intelligence, energy systems, healthcare, communication technologies, manufacturing, data science, and industrial applications. Their strong exploration and exploitation capabilities enable them to provide effective solutions for optimization problems where classical optimization methods are insufficient. In addition, many metaheuristic optimization algorithms attempt to establish a balanced and adaptive search behavior between exploration and exploitation processes, reflecting an important form of search symmetry during the optimization process. This systematic review presents a comprehensive analysis of metaheuristic optimization algorithms based on 515 distinct metaheuristic optimization algorithms. In this study, the algorithms are systematically classified into eleven major categories according to their inspiration sources and dominant search behaviors: Evolutionary-Based, Swarm Intelligence-Based, Bio-Inspired, Ecological/Environmental-Based, Physics-Based, Mathematics-Based, Human-Based, Game/Sport-Based, Chemical and Molecular-Based, Music-, Art-, and Culture-Inspired, and Hybrid and Advanced Metaheuristics. The review analyzes the historical evolution, inspiration diversity, search structures, symmetry-oriented search balance, and development trends of modern metaheuristic optimization algorithms. This study also provides a broader understanding of how metaheuristic optimization algorithms have evolved structurally and conceptually over time. In addition, the study highlights the importance of balanced and adaptive search mechanisms for maintaining optimization efficiency under complex problem conditions. The findings show that the number and diversity of metaheuristic optimization algorithms have increased significantly, especially after 2015. Population-based search structures remain the dominant optimization approach in the literature, while hybrid optimization methods, adaptive search mechanisms, and artificial intelligence integration have become major research trends in recent years. The study also discusses important challenges in the field, including algorithm similarity, benchmark standardization, theoretical limitations, and fair performance evaluation.

In this work, we explore compositions of positive integers into parts consisting of 1 and 3 s, highlighting their close connection to the Narayana numbers. We also examine palindromic compositions of this type and introduce arithmetic functions that reflect their structural properties. Furthermore, the Woon and PI tree structures related to the Narayana numbers are constructed and visually illustrated. To provide an intuitive understanding, we present tiling models corresponding to these compositions and use them to derive a variety of combinatorial identities. Moreover, we extend our approach to tiling models associated with Narayana polynomials, establishing additional identities through this framework. We also introduce an n ‐color extension of these compositions, exploring how the additional coloring dimension affects their combinatorial properties. Finally, we consider compositions with 1 and 3 s and derive several related identities that further illustrate their relationship with the Narayana numbers.

Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied in modeling and prediction tasks. In this study, an Adaptive Neuro-Fuzzy Inference System (ANFIS), a well-established AI approach, was employed for the time-series forecasting of Brent oil prices. To ensure effective learning and improve prediction accuracy, ANFIS was trained using nine different metaheuristic algorithms: Artificial Bee Colony (ABC), Selfish Herd Optimizer (SHO), Biogeography-Based Optimization (BBO), Multi-Verse Optimizer (MVO), Teaching–Learning-Based Optimization (TLBO), Cuckoo Search (CS), Moth Flame Optimization (MFO), Marine Predator Algorithm (MPA), and Flower Pollination Algorithm (FPA). Symmetric training procedures were applied across all algorithms to ensure fair and consistent evaluation. The analyses were conducted on the lowest and highest daily, weekly, and monthly Brent oil prices. Mean squared error (MSE) was used as the primary performance metric. The results showed that all algorithms achieved effective prediction performance. Among them, BBO and TLBO demonstrated superior accuracy and stability, particularly in handling the complexities of Brent oil forecasting. This study contributes to the literature by combining ANFIS and metaheuristics within a symmetric framework of experimentation and evaluation.

Crude oil is one of the most important assets that are used in the production of many industrial products in a wide variety of areas. The importance of crude oil has made it important to predict its future price. Therefore, it is possible to come across many studies in the literature in which the price of crude oil is estimated in the short or long term. In this study, innovative adaptive neuro-fuzzy inference systems (ANFIS) based approaches are proposed to estimate the daily minimum and maximum prices of crude oil. The used data was taken from the period between January 3, 2022, and December 29, 2023. A total of 516 different days of data were collected to create the dataset for analysis. For daily forecasting, time series data were transformed into a data set consisting of two inputs and one output. Moth-flame optimization algorithm (MFO), flower pollination algorithm (FPA), biogeography-based optimization (BBO) and artificial bee colony (ABC) were used in training ANFIS. The results obtained in the training and testing processes were compared. When the results obtained were compared, it was shown that the relevant algorithms were effective in the daily estimation of crude oil. It has been observed that effective results are also achieved at low evaluation numbers, especially thanks to the fast convergence feature of the MFO and BBO algorithms.

Bu çalışmada, 01 Kasım 2021 ile 31 Ekim 2022 tarihleri arasında volumetrik yöntem uyarınca “Lanzoni VPPS 2010” marka polen yakalama aracı kullanılarak Tire ilçesinin atmosferik polen konsantrasyonlarındaki aylık değişimler ortaya konulmuştur. Atmosferde 27 odunsu ve 15 otsu olmak üzere toplam 42 taksona ait polene rastlanmıştır. En yüksek polen konsantrasyonları Pinaceae %29.6 (6.969 polen/m3), Cupressaceae/Taxaceae %25.8 (6.079 polen/m3), Quercus %11.2 (2.636 polen/m3), Olea europaea %10.7 (2.520 polen/m3), Morus %5.69 (1.332 polen/m3), Poaceae %4.43 (1.043 polen/m3), Urticaceae %1.45 (350 polen/m3) ve Plantago %1.31 (304 polen/m3) taksonlarına aittir. Havada toplam polen miktarları en fazla olan ayların sırasıyla Nisan %28.8 (6.775 polen/m3), Mayıs %26.55 (6.254 polen/m3) ve Mart %26.22 (6.176 polen/m3) olduğu tespit edilmiştir. Havadaki polen konsantrasyonları ile yağış miktarı, sıcaklık, rüzgar hızı ve nisbi nem gibi atmosferik parametreler arasındaki ilişkiler istatistiksel olarak ortaya konulmuştur. Tüm bitki gruplarına ait toplam polen miktarlarının sıcaklık ve yağış parametrelerinden istatistiksel olarak önemli düzeyde etkilendiği belirlenmiştir (p

In this paper, we introduce the Pell-Lucas and the symmetric Pell-Lucas matrices. The study delves into the linear algebra aspects of these matrices, analyzing their mathematical properties and relationships. We construct decompositions for both the Pell-Lucas matrix and its inverse matrix. We present the Cholesky factorization of the symmetric Pell-Lucas matrices. Furthermore, we derive some valuable identities and bounds for the eigenvalues of these symmetric matrices through the application of majorization notation.

In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.

Risk theory has always played a significant role in mathematical finance and actuarial sciences. A novel approach to the risk theory of non-life insurance is quantum mechanics. To compute finite-time non-ruin probability, I introduce the quantum mechanics formalism in discrete space and continuous space with the appropriately chosen Hamiltonian. By using the quantum mechanics approach and the stochastic method, the non-ruin operator is defined, and tensor products of operator concepts are presented for several examples. In this paper, Dirac notations are operated to find the Hamiltonian matrix with the eigenvector basis for two and three-state cases, and its tensor product version with a change of basis.

Bu çalışmada, Drinfeld–Sokolov–Satsuma–Hirota (DSSH) denkleminin yaklaşık çözümü rezidual kuvvet seri metodu (RKSM) kullanılarak elde edildi. Kesirli türevleri karakterize etmek için uyumlu türev yaklaşımı kullanıldı ve farklı operatör değerleri için RKSM yaklaşık çözümleri kesin çözümlerle çeşitli tablo ve grafikler kullanılarak karşılaştırıldı. Sonuçlar; uygulanan tekniğin kullanımının kolay, çok başarılı ve tutarlı olduğunu göstermekle birlikte daha önceki yapılmış çalışmalara kıyasla da önemli bir ilerleme getirdiğini göstermektedir.