Search results for: search algorithms

Authors: Lamiche Chaabane

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In this study, a new method for solving sequence alignment problem is proposed, which is named ITS (Improved Tabu Search). This algorithm is based on the classical Tabu Search (TS). ITS is implemented in order to obtain results of multiple sequence alignment. Several ideas concerning neighbourhood generation, move selection mechanisms and intensification/diversification strategies for our proposed ITS is investigated. ITS have generated high-quality results in terms of measure of scores in comparison with the classical TS and simple iterative search algorithm.

Keywords: multiple sequence alignment, tabu search, improved tabu search, neighbourhood generation, selection mechanisms

Procedia PDF Downloads 305

Authors: Michael R. Phangtriastu, Herriyandi Herriyandi, Diaz D. Santika

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This paper presents a comparison of the implementation of metaheuristic algorithms to train the antecedent parameters and consequence parameters in the adaptive network-based fuzzy inference system (ANFIS). The algorithms compared are genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC). The objective of this paper is to benchmark well-known metaheuristic algorithms. The algorithms are applied to several data set with different nature. The combinations of the algorithms' parameters are tested. In all algorithms, a different number of populations are tested. In PSO, combinations of velocity are tested. In ABC, a different number of limit abandonment are tested. Experiments find out that ABC is more reliable than other algorithms, ABC manages to get better mean square error (MSE) than other algorithms in all data set.

Keywords: ANFIS, artificial bee colony, genetic algorithm, metaheuristic algorithm, particle swarm optimization

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Authors: Geetanjali Panda, Suvrakanti Chakraborty

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In this paper, Newton-like descent methods are proposed for unconstrained optimization problems, which use q-derivatives of the gradient of an objective function. First, a local scheme is developed with alternative sufficient optimality condition, and then the method is extended to a global scheme. Moreover, a variant of practical Newton scheme is also developed introducing a real sequence. Global convergence of these schemes is proved under some mild conditions. Numerical experiments and graphical illustrations are provided. Finally, the performance profiles on a test set show that the proposed schemes are competitive to the existing first-order schemes for optimization problems.

Keywords: Descent algorithm, line search method, q calculus, Quasi Newton method

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Authors: Jing Zhang, Daniel Nikovski

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We propose an approximation algorithm called LINKUMP to compute the Pan Matrix Profile (PMP) under the unnormalized l∞ distance (useful for value-based similarity search) using double-ended queue and linear interpolation. The algorithm has comparable time/space complexities as the state-of-the-art algorithm for typical PMP computation under the normalized l₂ distance (useful for shape-based similarity search). We validate its efficiency and effectiveness through extensive numerical experiments and a real-world anomaly detection application.

Keywords: pan matrix profile, unnormalized euclidean distance, double-ended queue, discord discovery, anomaly detection

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Authors: Ahmed E. Hodaib, Mohamed A. Hashem

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In engineering applications, a design has to be as fully perfect as possible in some defined case. The designer has to overcome many challenges in order to reach the optimal solution to a specific problem. This process is called optimization. Generally, there is always a function called “objective function” that is required to be maximized or minimized by choosing input parameters called “degrees of freedom” within an allowed domain called “search space” and computing the values of the objective function for these input values. It becomes more complex when we have more than one objective for our design. As an example for Multi-Objective Optimization Problem (MOP): A structural design that aims to minimize weight and maximize strength. In such case, the Pareto Optimal Frontier (POF) is used, which is a curve plotting two objective functions for the best cases. At this point, a designer should make a decision to choose the point on the curve. Engineers use algorithms or iterative methods for optimization. In this paper, we will discuss the Evolutionary Algorithms (EA) which are widely used with Multi-objective Optimization Problems due to their robustness, simplicity, suitability to be coupled and to be parallelized. Evolutionary algorithms are developed to guarantee the convergence to an optimal solution. An EA uses mechanisms inspired by Darwinian evolution principles. Technically, they belong to the family of trial and error problem solvers and can be considered global optimization methods with a stochastic optimization character. The optimization is initialized by picking random solutions from the search space and then the solution progresses towards the optimal point by using operators such as Selection, Combination, Cross-over and/or Mutation. These operators are applied to the old solutions “parents” so that new sets of design variables called “children” appear. The process is repeated until the optimal solution to the problem is reached. Reliable and robust computational fluid dynamics solvers are nowadays commonly utilized in the design and analyses of various engineering systems, such as aircraft, turbo-machinery, and auto-motives. Coupling of Computational Fluid Dynamics “CFD” and Multi-Objective Evolutionary Algorithms “MOEA” has become substantial in aerospace engineering applications, such as in aerodynamic shape optimization and advanced turbo-machinery design.

Keywords: mathematical optimization, multi-objective evolutionary algorithms "MOEA", computational fluid dynamics "CFD", aerodynamic shape optimization

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Authors: José A. Menezes, Giordano Cabral, Bruno T. Gomes

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Choosing good features is an essential part of machine learning. Recent techniques aim to automate this process. For instance, feature learning intends to learn the transformation of raw data into a useful representation to machine learning tasks. In automatic audio classification tasks, this is interesting since the audio, usually complex information, needs to be transformed into a computationally convenient input to process. Another technique tries to generate features by searching a feature space. Genetic algorithms, for instance, have being used to generate audio features by combining or modifying them. We find this approach particularly interesting and, despite the undeniable advances of feature learning approaches, we wanted to take a step forward in the use of genetic algorithms to find audio features, combining them with more conventional methods, like PCA, and inserting search control mechanisms, such as constraints over a confusion matrix. This work presents the results obtained on particular audio classification problems.

Keywords: feature generation, feature learning, genetic algorithm, music information retrieval

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Authors: Bahare Askarian, Suchithra Rajendran

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Maintaining the freshness and quality of perishable goods during distribution is a critical challenge for logistics companies. This study presents a comprehensive framework aimed at optimizing the distribution of perishable goods through a mathematical model of the Transportation Inventory Location Routing Problem (TILRP). The model incorporates the impact of product age on customer demand, addressing the complexities associated with inventory management and routing. To tackle this problem, we develop both simple and hybrid metaheuristic algorithms designed for small- and medium-scale scenarios. The hybrid algorithm combines Biogeographical Based Optimization (BBO) algorithms with local search techniques to enhance performance in small- and medium-scale scenarios, extending our approach to larger-scale challenges. Through extensive numerical simulations and sensitivity analyses across various scenarios, the performance of the proposed algorithms is evaluated, assessing their effectiveness in achieving optimal solutions. The results demonstrate that our algorithms significantly enhance distribution efficiency, offering valuable insights for logistics companies striving to improve their perishable goods supply chains.

Keywords: perishable goods, meta-heuristic algorithm, vehicle problem, inventory models

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Authors: Halil Ibrahim Demir, Alper Goksu, Onur Canpolat, Caner Erden, Melek Nur

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Traditionally process planning, scheduling and due date assignment are performed sequentially and separately. High interrelation between these functions makes integration very useful. Although there are numerous works on integrated process planning and scheduling and many works on scheduling with due date assignment, there are only a few works on the integration of these three functions. Here we tested the different integration levels of these three functions and found a fully integrated version as the best. We applied genetic search and random search and genetic search was found better compared to the random search. We penalized all earliness, tardiness and due date related costs. Since all these three terms are all undesired, it is better to penalize all of them.

Keywords: process planning, scheduling, due-date assignment, genetic algorithm, random search

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Authors: Dmitriy Kuptsov

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Tree data structures, such as binary or in general k-ary trees, are essential in computer science. The applications of these data structures can range from data search and retrieval to sorting and ranking algorithms. Naive implementations of these data structures can consume prohibitively large volumes of random access memory limiting their applicability in certain solutions. Thus, in these cases, more advanced representation of these data structures is essential. In this paper we present the design of the compact version of ternary tree data structure and demonstrate the results for the experimental evaluation using static dictionary problem. We compare these results with the results for binary and regular ternary trees. The conducted evaluation study shows that our design, in the best case, consumes up to 12 times less memory (for the dictionary used in our experimental evaluation) than a regular ternary tree and in certain configuration shows performance comparable to regular ternary trees. We have evaluated the performance of the algorithms using both 32 and 64 bit operating systems.

Keywords: algorithms, data structures, succinct ternary tree, per- formance evaluation

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Authors: Fuzhang Zhao

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Particle swarm optimization (PSO) is becoming one of the most important swarm intelligent paradigms for solving global optimization problems. Although some progress has been made to improve PSO algorithms over the last two decades, additional work is still needed to balance parameters to achieve better numerical properties of accuracy, efficiency, and stability. In the optimal PSO algorithm, the optimal weightings of (√ 5 − 1)/2 and (3 − √5)/2 are used for the cognitive factor and the social factor, respectively. By the same token, the same optimal weightings have been applied for intensification searches and diversification searches, respectively. Perturbation and constriction effects are optimally balanced. Simulations of the de Jong, the Rosenbrock, and the Griewank functions show that the optimal PSO algorithm indeed achieves better numerical properties and outperforms the canonical PSO algorithm.

Keywords: diversification search, intensification search, optimal weighting, particle swarm optimization

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Authors: Ahmed Tarek, Ahmed Alveed

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Vehicle routing problem is a well-known re-search avenue in computing. Modern vehicle routing is more focused with the GPS-based coordinate system, as the state-of-the-art vehicle, and trucking systems are equipped with digital navigation. In this paper, a new two dimensional coordinate-based algorithm for addressing the vehicle routing problem for a supply chain network is proposed and explored, and the algorithm is compared with other available, and recently devised heuristics. For the algorithms discussed, which includes the pro-posed coordinate-based search heuristic as well, the advantages and the disadvantages associated with the heuristics are explored. The proposed algorithm is studied from the stand point of a small supermarket chain delivery network that supplies to its stores in four different states around the East Coast area, and is trying to optimize its trucking delivery cost. Minimizing the delivery cost for the supply network of a supermarket chain is important to ensure its business success.

Keywords: coordinate-based optimal routing, Hamiltonian Circuit, heuristic algorithm, traveling salesman problem, vehicle routing problem

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Authors: Gemma García López

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The goal of this study is to analyze if search queries carried out in search engines such as Google, can offer emotional information about the user that performs them. Knowing the emotional state in which the Internet user is located can be a key to achieve the maximum personalization of content and the detection of worrying behaviors. For this, two studies were carried out using tools with advanced natural language processing techniques. The first study determines if a query can be classified as positive, negative or neutral, while the second study extracts emotional content from words and applies the categorical and dimensional models for the representation of emotions. In addition, we use search queries in Spanish and English to establish similarities and differences between two languages. The results revealed that text search queries performed by users on the Internet can be classified emotionally. This allows us to better understand the emotional state of the user at the time of the search, which could involve adapting the technology and personalizing the responses to different emotional states.

Keywords: emotion classification, text search queries, emotional analysis, sentiment analysis in text, natural language processing

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Authors: Daljinder Singh, J.S.Dhillon, Balraj Singh

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According to no free lunch theorem, a single search technique cannot perform best in all conditions. Optimization method can be attractive choice to solve optimization problem that may have exclusive advantages like robust and reliable performance, global search capability, little information requirement, ease of implementation, parallelism, no requirement of differentiable and continuous objective function. In order to synergize between exploration and exploitation and to further enhance the performance of Bat algorithm, the paper proposed a modified bat algorithm that adds additional search procedure based on bat’s previous experience. The proposed algorithm is used for solving the economic load dispatch (ELD) problem. The practical constraint such valve-point loading along with power balance constraints and generator limit are undertaken. To take care of power demand constraint variable elimination method is exploited. The proposed algorithm is tested on various ELD problems. The results obtained show that the proposed algorithm is capable of performing better in majority of ELD problems considered and is at par with existing algorithms for some of problems.

Keywords: bat algorithm, economic load dispatch, penalty method, variable elimination method

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Authors: Netanel Stern

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Artificial intelligence (AI) algorithms have emerged as powerful tools in the field of psychiatry, offering new possibilities for enhancing diagnosis and treatment outcomes. This article explores the utilization of AI algorithms in psychiatry, highlighting their potential to revolutionize patient care. Various AI algorithms, including machine learning, natural language processing (NLP), reinforcement learning, clustering, and Bayesian networks, are discussed in detail. Moreover, ethical considerations and future directions for research and implementation are addressed.

Keywords: AI, software engineering, psychiatry, neuroimaging

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Authors: Mohammed Belloufi, Rachid Benzine, Badreddine Sellami

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Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given.

Keywords: unconstrained optimization, conjugate gradient method, strong Wolfe line search, global convergence

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Authors: Laicheng Cao, Xiangqian Su, Youxiao Wu

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Feature selection is one of the important problems in network security, pattern recognition, data mining and other fields. In order to remove redundant features, effectively improve the detection speed of intrusion detection system, proposes a new feature selection method, which is based on the invasive weed optimization (IWO) algorithm and tabu search algorithm(TS). Use IWO as a global search, tabu search algorithm for local search, to improve the results of IWO algorithm. The experimental results show that the feature selection method can effectively remove the redundant features of network data information in feature selection, reduction time, and to guarantee accurate detection rate, effectively improve the speed of detection system.

Keywords: intrusion detection, feature selection, iwo, tabu search

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Authors: Marwa Hussien Mohamed, Mohamed Helmy Khafagy

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Map-Reduce is a programming model which is widely used to extract valuable information from enormous volumes of data. Map-reduce designed to support heterogeneous datasets. Apache Hadoop map-reduce used extensively to uncover hidden pattern like data mining, SQL, etc. The most important operation for data analysis is joining operation. But, map-reduce framework does not directly support join algorithm. This paper explains and compares two-way and multi-way map-reduce join algorithms for map reduce also we implement MR join Algorithms and show the performance of each phase in MR join algorithms. Our experimental results show that map side join and map merge join in two-way join algorithms has the longest time according to preprocessing step sorting data and reduce side cascade join has the longest time at Multi-Way join algorithms.

Keywords: Hadoop, MapReduce, multi-way join, two-way join, Ubuntu

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Authors: Meng-Hui Chen, Chiao-Wei Yu, Pei-Chann Chang

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Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist. The main idea in this paper is using the peculiarity of ICA to explore the search space to solve the kinds of combinational problems. Otherwise, we also study to use the greed search to increase the local search ability. To verify the proposed algorithm in this paper, the experimental results of traveling salesman problem (TSP) is according to the traveling salesman problem library (TSPLIB). The results show that the proposed algorithm has higher performance than the other known methods.

Keywords: traveling salesman problem, artificial chromosomes, greedy search, imperial competitive algorithm

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Authors: Feng Tao, Ma Jing, Guo Xian, Wang Jing

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Named Data Networking (NDN) replaces IP address of traditional network with data name, and adopts dynamic cache mechanism. In the existing mechanism, however, only one-to-one search can be achieved because every data has a unique name corresponding to it. There is a certain mapping relationship between data content and data name, so if the data name is intercepted by an adversary, the privacy of the data content and user’s interest can hardly be guaranteed. In order to solve this problem, this paper proposes a one-to-many fuzzy search scheme based on order-preserving encryption to reduce the query overhead by optimizing the caching strategy. In this scheme, we use hash value to ensure the user’s query safe from each node in the process of search, so does the privacy of the requiring data content.

Keywords: NDN, order-preserving encryption, fuzzy search, privacy

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Authors: Khaled Moh. Alhamad

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This paper describes a tabu search heuristic for a ship routing and scheduling problem (SRSP). The method was developed to address the problem of loading cargos for many customers using heterogeneous vessels. Constraints relate to delivery time windows imposed by customers, the time horizon by which all deliveries must be made and vessel capacities. The results of a computational investigation are presented. Solution quality and execution time are explored with respect to problem size and parameters controlling the tabu search such as tenure and neighbourhood size.

Keywords: heuristic, scheduling, tabu search, transportation

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Authors: F. Debbat, F. T. Bendimerad

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The efficient frequency assignment for radio communications becomes more and more crucial when developing new information technologies and their applications. It is consists in defining an assignment of frequencies to radio links, to be established between base stations and mobile transmitters. Separation of the frequencies assigned is necessary to avoid interference. However, unnecessary separation causes an excess requirement for spectrum, the cost of which may be very high. This problem is NP-hard problem which cannot be solved by conventional optimization algorithms. It is therefore necessary to use metaheuristic methods to solve it. This paper proposes Hybrid approach based on simulated annealing (SA) and Tabu Search (TS) methods to solve this problem. Computational results, obtained on a number of standard problem instances, testify the effectiveness of the proposed approach.

Keywords: cellular mobile communication, frequency assignment problem, optimization, tabu search, simulated annealing

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Authors: Rutuja Desai

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Search engine is fundamentally a framework used to search the data which is pertinent to the client via WWW. Looking close-by spot identified with the keywords is an imperative concept in developing web advances. For such kind of searching, extent pursuit or closest neighbor is utilized. In range search the forecast is made whether the objects meet to query object. Nearest neighbor is the forecast of the focuses close to the query set by the client. Here, the nearest neighbor methodology is utilized where Data recovery R+ tree is utilized rather than IR2 tree. The disadvantages of IR2 tree is: The false hit number can surpass the limit and the mark in Information Retrieval R-tree must have Voice over IP bit for each one of a kind word in W set is recouped by Data recovery R+ tree. The inquiry is fundamentally subordinate upon the key words and the geometric directions.

Keywords: information retrieval, nearest neighbor search, keyword search, R+ tree

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Authors: Samia Dardouri, Ridha Bouallegue

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Scheduling is the process of dynamically allocating physical resources to User Equipment (UE) based on scheduling algorithms implemented at the LTE base station. Various algorithms have been proposed by network researchers as the implementation of scheduling algorithm which represents an open issue in Long Term Evolution (LTE) standard. This paper makes an attempt to study and compare the performance of PF, MLWDF and EXP/PF scheduling algorithms. The evaluation is considered for a single cell with interference scenario for different flows such as Best effort, Video and VoIP in a pedestrian and vehicular environment using the LTE-Sim network simulator. The comparative study is conducted in terms of system throughput, fairness index, delay, packet loss ratio (PLR) and total cell spectral efficiency.

Keywords: LTE, multimedia flows, scheduling algorithms, mobile computing

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Authors: Dmitrii Starikov, Evgeny Rybakov, Denis Zhuravlev

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Plastic for 3D printing is very necessary material part for printers. But plastic production is technological process, which implies application of different control algorithms. Possible algorithms of providing set diameter of plastic fiber are proposed and described in the article. Results of research were proved by existing unit of filament production.

Keywords: ABS-plastic, automation, control system, extruder, filament, PID-algorithm

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Authors: Mikiyas Adugna

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Effort estimation is among the activities carried out in software development processes. An accurate model of estimation leads to project success. The method of agile effort estimation is a complex task because of the dynamic nature of software development. Researchers are still conducting studies on agile effort estimation to enhance prediction accuracy. Due to these reasons, we investigated and proposed a model on LASSO and Elastic Net regression to enhance estimation accuracy. The proposed model has major components: preprocessing, train-test split, training with default parameters, and cross-validation. During the preprocessing phase, the entire dataset is normalized. After normalization, a train-test split is performed on the dataset, setting training at 80% and testing set to 20%. We chose two different phases for training the two algorithms (Elastic Net and LASSO) regression following the train-test-split. In the first phase, the two algorithms are trained using their default parameters and evaluated on the testing data. In the second phase, the grid search technique (the grid is used to search for tuning and select optimum parameters) and 5-fold cross-validation to get the final trained model. Finally, the final trained model is evaluated using the testing set. The experimental work is applied to the agile story point dataset of 21 software projects collected from six firms. The results show that both Elastic Net and LASSO regression outperformed the compared ones. Compared to the proposed algorithms, LASSO regression achieved better predictive performance and has acquired PRED (8%) and PRED (25%) results of 100.0, MMRE of 0.0491, MMER of 0.0551, MdMRE of 0.0593, MdMER of 0.063, and MSE of 0.0007. The result implies LASSO regression algorithm trained model is the most acceptable, and higher estimation performance exists in the literature.

Keywords: agile software development, effort estimation, elastic net regression, LASSO

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Authors: Halil Ibrahim Demir, Caner Erden, Abdullah Hulusi Kokcam, Mumtaz Ipek

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Process planning, scheduling, and due date assignment are three important manufacturing functions which are studied independently in literature. There are hundreds of works on IPPS and SWDDA problems but a few works on IPPSDDA problem. Integrating these three functions is very crucial due to the high relationship between them. Since the scheduling problem is in the NP-Hard problem class without any integration, an integrated problem is even harder to solve. This study focuses on the integration of these functions. Sum of weighted tardiness, earliness, and due date related costs are used as a penalty function. Random search and hybrid metaheuristics are used to solve the integrated problem. Marginal improvement in random search is very high in the early iterations and reduces enormously in later iterations. At that point directed search contribute to marginal improvement more than random search. In this study, random and genetic search methods are combined to find better solutions. Results show that overall performance becomes better as the integration level increases.

Keywords: process planning, genetic algorithm, hybrid search, random search, weighted due-date assignment, weighted scheduling

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Authors: Farshad Ghassemi Toosi, Nikola S. Nikolov

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We present a visualization technique for radial drawing of trees consisting of two slightly different algorithms. Both of them make use of node-link diagrams for visual encoding. This visualization creates clear drawings without edge crossing. One of the algorithms is suitable for real-time visualization of large trees, as it requires minimal recalculation of the layout if leaves are inserted or removed from the tree; while the other algorithm makes better utilization of the drawing space. The algorithms are very similar and follow almost the same procedure but with different parameters. Both algorithms assign angular coordinates for all nodes which are then converted into 2D Cartesian coordinates for visualization. We present both algorithms and discuss how they compare to each other.

Keywords: Radial drawing, Visualization, Algorithm, Use of node-link diagrams

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Authors: Richard Tanaka, Ying Zhu

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This paper studies a few randomized algorithms in application-layer peer-to-peer networks. The significant gain in scalability and resilience that peer-to-peer networks provide has made them widely used and adopted in many real-world distributed systems and applications. The unique properties of peer-to-peer networks make them particularly suitable for randomized algorithms such as random walks and gossip algorithms. Instead of simulations of peer-to-peer networks, we leverage the Docker virtual container technology to develop implementations of the peer-to-peer networks and these distributed randomized algorithms running on top of them. We can thus analyze their behaviour and performance in realistic settings. We further consider the problem of identifying high-risk bottleneck links in the network with the objective of improving the resilience and reliability of peer-to-peer networks. We propose a randomized algorithm to solve this problem and evaluate its performance by simulations.

Keywords: distributed randomized algorithms, peer-to-peer networks, virtual container technology, resilient networks

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Authors: Farhat Imtiaz, Umar Farooq

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In this work, we developed a computational model to predict ply level failure in impacted composite laminates. Data obtained from physical testing from flat and round nose impacts of 8-, 16-, 24-ply laminates were considered. Routine inspections of the tested laminates were carried out to approximate ply by ply inflicted damage incurred. Plots consisting of load–time, load–deflection, and energy–time history were drawn to approximate the inflicted damages. Impact test generated unwanted data logged due to restrictions on testing and logging systems were also filtered. Conventional filters (built-in, statistical, and numerical) reliably predicted load thresholds for relatively thin laminates such as eight and sixteen ply panels. However, for relatively thick laminates such as twenty-four ply laminates impacted by flat nose impact generated clipped data which can just be de-noised using oscillatory algorithms. The literature search reveals that modern oscillatory data filtering and extrapolation algorithms have scarcely been utilized. This investigation reports applications of filtering and extrapolation of the clipped data utilising fast Fourier Convolution algorithm to predict load thresholds. Some of the results were related to the impact-induced damage areas identified with Ultrasonic C-scans and found to be in acceptable agreement. Based on consistent findings, utilizing of modern data filtering and extrapolation algorithms to data logged by the existing machines has efficiently enhanced data interpretations without resorting to extra resources. The algorithms could be useful for impact-induced damage approximations of similar cases.

Keywords: fibre reinforced laminates, fast Fourier algorithms, mechanical testing, data filtering and extrapolation

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Authors: Ebert Brea

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We propose a novel direct search algorithm for identifying at least a local minimum of mixed integer nonlinear unconstrained optimization problems. The Mixed Integer Randomized Pattern Search Algorithm (MIRPSA), so-called by the author, is based on a randomized pattern search, which is modified by the MIRPSA for finding at least a local minimum of our problem. The MIRPSA has two main operations over the randomized pattern search: moving operation and shrinking operation. Each operation is carried out by the algorithm when a set of conditions is held. The convergence properties of the MIRPSA is analyzed using a Markov chain approach, which is represented by an infinite countable set of state space λ, where each state d(q) is defined by a measure of the qth randomized pattern search Hq, for all q in N. According to the algorithm, when a moving operation is carried out on the qth randomized pattern search Hq, the MIRPSA holds its state. Meanwhile, if the MIRPSA carries out a shrinking operation over the qth randomized pattern search Hq, the algorithm will visit the next state, this is, a shrinking operation at the qth state causes a changing of the qth state into (q+1)th state. It is worthwhile pointing out that the MIRPSA never goes back to any visited states because the MIRPSA only visits any qth by shrinking operations. In this article, we describe the MIRPSA for mixed integer nonlinear unconstrained optimization problems for doing a deep study of its convergence properties using Markov chain viewpoint. We herein include a low dimension case for showing more details of the MIRPSA, when the algorithm is used for identifying the minimum of a mixed integer quadratic function. Besides, numerical examples are also shown in order to measure the performance of the MIRPSA.

Keywords: direct search, mixed integer optimization, random search, convergence, Markov chain

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