Conquer Algorithm Research Articles

Optimization of transition from open-pit to underground mining considering environmental costs

The problem of optimizing the transition from open-pit to underground mining remains a challenge within the field of mining engineering, with far-reaching implications for sustainable development. Several researchers have tackled this transition problem, primarily focusing on maximizing project profitability while grappling with the complexities associated with solving it for real large-scale ore deposits. This study presents a mixed integer programming model that accounts for costs associated with preventing, mitigating, or compensating for adverse environmental impacts on net present value (NPV). Then, a Python-based code was developed using the Divide and Conquer algorithm, with the goal of reducing various operational modes and boosting solver speed to overcome the limitations encountered in the existing literature, particularly when dealing with large-scale deposits. The developed solution aims to transform a block model with varying dimensions into a selective mining unit with uniform dimensions, align the pushback's size and location with the mine's depth, length, and width, convert the matrix into a functional format, and clear previous calculations and results upon achieving the maximum NPV in the new phase. The study also evaluated the environmental impact on the transition problem using this methodology, applying it to the Sungun large-scale copper deposit. The results favor a sequential combined mining approach, yielding an NPV of 7.51 billion USD at a transition depth of 887.5 m with environmental costs included, and 7.61 billion USD at a depth of 950 m without environmental cost considerations.

Turkish Cashier Problem with time windows and its solution by matheuristic algorithms

Turkish Cashier Problem (TCP) is a new application area of the traveling salesman problem that was introduced to the literature recently. In this problem, the cashier can use public transportation or take a taxi where the cashier must visit multiple customer locations while minimizing the total transportation cost. In this study, we introduce a more realistic version of this problem where time has been integrated. This aspect is achieved by imposing time intervals within which the cashier must visit the customers. We name this problem as the TCP with time windows (TCPwTW). We develop several matheuristic algorithms to solve the TCPwTW: a modified version of the Simplify and Conquer (SAC) algorithm that was suggested for the TCP, simulated annealing (SA), original and modified versions of the migrating birds optimization (MBO) algorithm coupled with mathematical programming. We also tried to find the exact optimum using a Solver where for complex problems, only lower bounds were found. Numerical experimentation reveals that while for problems with loose time intervals, an exact solver can be considered. Once the time intervals tighten up, the best solutions can be obtained using matheuristics involving SA and MBO.

Finding Packet Dropper and Collecting Missing Packet due to Packet Dropping Attackers in Mobile Adhoc Network Using Divide and Conquer Algorithm

Objective: Finding the Packet dropping attacker and collecting the missing packet in the MANET is one of the challenging task since the characteristics of the MANET node mobility. Packet Transmission from the source node to the Destination node is done after sending the Route Request and Route Reply, reliable path chosen based on the protocol selection in Mobile Adhoc Network which is self-organized running without any basic infrastructure. Data which is going to send by the sender is divided in to the packet and put sequence numbering on the packet finally transmitted on the medium. Each and every packet get travelled on the assigned path to reach to the destination. If any packet missed on the transmission the source node has to retransmit to the destination. while forwarding the packet from one hop to another the packet dropper attacks are play dropping the packets. Methods: There are several methods were proposed for elaborating the packet dropping attacks and solution for finding the attackers in the MANET, but none of the methods proposed for collecting the missed packet instead of getting retransmission. Divide and conquer method between the route to destination path applied to finding the packet dropper attacker and collecting the missing packet from the previous node. Findings: The proposed method could be implement using network simulator and performance result could be better than existing packet dropper attacker work. Novelty: This proposed article shows packet dropper attackers in the MANET and collecting the missing packet by using the divide and conquer algorithm in the source to destination path route.

Packet Dropper and Collecting Missing Packet due to Packet Dropping Attackers in Mobile Adhoc Network using Divide and Conquer Algorithm

In a mobile ad hoc network, packet transmission is essential to prevent packet drops along the transmission path. Attackers who drop forwarded packets are present in the MANET and are attempting to lower the MANET's performance. There are several ways to identify packet dropper attackers and warn the MANET about them. The divide and conquer tactic is used in this research study to identify the attacker who dropped the packets and to obtain the missing packet from the intermediary source. This task will be accomplished by adding an extra buffer to hold the forwarded packet during its whole round trip from source to destination. The findings of the suggested work's implementation using the network simulator and comparisons with those of the current methodology ultimately demonstrate that the divide and conquer approach has demonstrated the MANET's performance.

Analyzing Time and Space Complexity: Kadane vs. Divide and Conquer Algorithms for Maximum Sub-Array Problem

Analyzing Time and Space Complexity: Kadane vs. Divide and Conquer Algorithms for Maximum Sub-Array Problem

Barracuda, an Open Source Framework for Parallelizing Divide and Conquer Algorithm

This paper presents a newly-created Barracuda open-source framework which aims to parallelize Java divide and conquer applications. This framework exploits implicit for-loop parallelism in dividing and merging operations. So, this makes it a mixture of parallel for-loop and task parallelism. It targets shared-memory multiprocessors and hybrid distributed shared-memory architectures. We highlight the effectiveness of the framework and focus on the performance gain and programming effort by using this framework. Barracuda aims at large public actors as well as various application domains. In terms of performance achievement, it is very close to Fork/Join framework while allowing end-users to only focus on refactoring code and experts to have the opportunity to improve it.

A Divide and Conquer Algorithm for Predict+Optimize with Non-convex Problems

The predict+optimize problem combines machine learning and combinatorial optimization by predicting the problem coefficients first and then using these coefficients to solve the optimization problem. While this problem can be solved in two separate stages, recent research shows end to end models can achieve better results. This requires differentiating through a discrete combinatorial function. Models that use differentiable surrogates are prone to approximation errors, while existing exact models are limited to dynamic programming, or they do not generalize well with scarce data. In this work we propose a novel divide and conquer algorithm based on transition points to reason over exact optimization problems and predict the coefficients using the optimization loss. Moreover, our model is not limited to dynamic programming problems. We also introduce a greedy version, which achieves similar results with less computation. In comparison with other predict+optimize frameworks, we show our method outperforms existing exact frameworks and can reason over hard combinatorial problems better than surrogate methods.

SCARI: Separate and conquer algorithm for action rules and recommendations induction

This article describes an action rule induction Algorithmbased on a sequential covering. Two variants of the Algorithmare presented. The Algorithmallows the action rule induction from a source and a target decision class point of view. The application of rule quality measures enables the induction of action rules that meet various quality criteria. The article also presents a method for recommendation induction. A recommendation indicates the actions required to move an example representing a given source class to the appropriate target class. The recommendation method is based on a set of induced action rules. The experimental part of the article presents the results of the Algorithmoperation on sixteen data sets. As a result of the conducted research, the Ac-Rules package was made available.

IMPLEMENTATION OF DIVIDE AND CONQUER IN THE HANOI TOWER GAME

Artificial Intelligence (AI) is a technology in the field of computer science that simulates human intelligence into computers to solve various problems and jobs as well as humans do. Games / games are an implementation of the field of computer science which also embraces the concept of AI. In the midst of the rampant types of games available, the author chose the Hanoi Tower which is a mathematical game / puzzle that requires logic. Players are challenged to complete in a short time with a certain number of discs. The benefit of this game is that it can train how to think with certain patterns so as to improve the memory of players. To make it easier to solve it, the Divide and Conquer Algorithm can be used which can solve problems in the Tower of Hanoi game by breaking them down into sub-problems which will later be able to help speed up finding solutions. From the results of testing the application of the Divide and Conquer Algorithm in the hanoi tower game application by solving the disk arrangement problem. Players can finish the game in a large number of plates in a short time. Keywords – Artificial Intelligence, Divide and Conquer Algorithm, Games, Tower of Hanoi.

Parametric Design Techniques Apply to Creative Hollow out Product Design with 3d Voronoi Patterns

The creation of hollow out art includes a variety of materials, techniques and categories, its content mostly emphasizes the ancient philosophy performance of the alternation of virtual and real, and Yin-Yang depends on the essence of Chinese culture deduction. If this feature is applied to product design, in addition to emphasizing functional orientation, this traditional arts integration with the new media, will give users a different visual inspire. This thesis is mainly in view of the importance of hollow out art in Chinese cultural heritage, and the 3D hollow out production craft has gradually lost. Therefore, the Delaunay triangle is constructed based on the Convex Hull interpolation algorithm, and the Voronoi Diagram feature is constructed based on the Divide and Conquer algorithm. And with Rhino modeling software as the main body, combined with the application of the parametric plug-in design program (GH), the 3D models of the parametric creative hollow pen holder and the parametric creative hollow lampshade were respectively completed. The traditional craftsmanship is integrated into the modern manufacturing process with innovative techniques, and the Chinese cultural spirit and beauty of nature are successfully connected.

An Effective Design and Implementation of Hybrid MPP Tracking Scheme Based on Linear Tangents & Neville Interpolation (LT-NI) Technique for Photovoltaic (PV) System

Solar power is free from environmental pollution and also offers economic benefits to the investors. In order to optimize at most solar power, tracking schemes are employed and traditional schemes from the family of perturbation suffer from slow response, due to specific step size disruption and oscillations around operating point. Therefore, this paper proposes an effective design and implementation of a hybrid Maximum Power Point Tracking (MPPT) scheme based on Linear Tangents - Neville Interpolation (LT-NI) techniques. Two tangents are drawn on the P-V characteristics at 75% and 90% of open circuit voltage (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> ).The chosen two tangents intersect and gives rise to a third voltage (N) point. In continuation, the three voltage points (0.75V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> , N & 0.9V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OC</sub> ) are computed using Neville Interpolation. The performance of the proposed LT-NI scheme is compared with Perturb & Observe (P&O) and advanced Divide and Conquer (DC) algorithms.

Sound matching on the translation of Al-Quran ayat as a learning media for children using mobile-based fast fourier transform and divide conquer algorithm

In this paper, a sound matching application was built on the pronunciation of Ayat Al-Quran as a learning medium for children using the Fast Fourier Transform (FFT) Algorithm and Divide Conquer (DC) that support learning independently. The system built in the final project is to utilize the Google API feature on android as voice matching. Furthermore, the incoming sound will convert into text form using the Google API. The conversion method used is a Fast Fourier Transform (FFT). The valuation method, Divide Conquer is used by calculating the sound proximity value of the Google API conversion results by matching Arabic text in the database. Based on the testing that has been done on the system testing. The results of the test found 61.1% accuracy for the appropriate reading and 38.9% for inappropriate reading.

Multi-objective optimization of a plug flow reactor using a divide and conquer approach

Lower profit margins and tighter environmental constraints push chemical companies to search for sustainable development and operation. To ensure sustainable development and operation in practice, multiple and conflicting objectives (e.g., maximize production vs. minimize energy consumption) typically have to be optimized simultaneously. The frame of multi-objective optimization allows to systematically propose improvements and evaluate trade-offs between different objectives. Solving a multi-objective optimization problem yields a set of solutions called the Pareto front, in which no improvement can be made in one objective without worsening another objective. The posteriori analysis of this set by a smart filter aims to keep only the significant solutions for the decision maker who is interested in a specific level of trade-offs. However, this strategy suffers from the large overhead of insignificant solutions produced in the original set. This situation makes applying this strategy to the complex multi-objective optimal control problems time consuming. In this paper, the smart filter by Mattson et al. (2004) is compared to a novel Divide and Conquer (D&C) algorithm to obtain a Pareto front with adaptive resolution for a case study of a plug flow reactor. The new algorithm depends on obtaining the Pareto front recursively while terminating the exploration of a Pareto front segment as soon as an insignificant point is found. It is shown that the D&C algorithm produces representations with similar quality to the smart filter with higher speed and a more intuitive trade-off oriented solution procedure.

固有値分解を目的としたツイスト分解法による分割統治法の改善(行列・固有値問題の解法とその応用, 平成20年研究部会連合発表)

固有値分解を目的としたツイスト分解法による分割統治法の改善(行列・固有値問題の解法とその応用, 平成20年研究部会連合発表)

A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

Proving Divide and Conquer Complexities in Isabelle/HOL

The Akra---Bazzi method (Akra and Bazzi in Comput Optim Appl 10(2):195---210, 1998. doi:10.1023/A:1018373005182), a generalisation of the well-known Master Theorem, is a useful tool for analysing the complexity of Divide and Conquer algorithms. This work describes a formalisation of the Akra---Bazzi method (as generalised by Leighton in Notes on better Master theorems for divide-and-conquer recurrences, 1996. http://courses.csail.mit.edu/6.046/spring04/handouts/akrabazzi.pdf) in the interactive theorem prover Isabelle/HOL and the derivation of a generalised version of the Master Theorem from it. We also provide some automated proof methods that facilitate the application of this Master Theorem and allow mostly automatic verification of $$\varTheta $$ź-bounds for these Divide and Conquer recurrences. To our knowledge, this is the first formalisation of theorems for the analysis of such recurrences.

A Robust Divide and Conquer Algorithm for Progressive Medial Axes of Planar Shapes.

The medial axis is an important shape representation that finds a wide range of applications in shape analysis. For large-scale shapes of high resolution, a progressive medial axis representation that starts with the lowest resolution and gradually adds more details is desired. In this paper, we propose a fast and robust geometric algorithm that computes progressive medial axes of a large-scale planar shape. The key ingredient of our method is a novel structural analysis of merging medial axes of two planar shapes along a shared boundary. Our method is robust by separating the analysis of topological structure from numerical computation. Our method is also fast and we show that the time complexity of merging two medial axes is O(n lognv) , where n is the number of total boundary generators, nv is strictly smaller than n and behaves as a small constant in all our experiments. Experiments on large-scale polygonal data and comparison with state-of-the-art methods show the efficiency and effectiveness of the proposed method.

ATrunk—An ALS-Based Trunk Detection Algorithm

This paper presents a rapid multi-return ALS-based (Airborne Laser Scanning) tree trunk detection approach. The multi-core Divide &amp; Conquer algorithm uses a CBH (Crown Base Height) estimation and 3D-clustering approach to isolate points associated with single trunks. For each trunk, a principal-component-based linear model is fitted, while a deterministic modification of LO-RANSAC is used to identify an optimal model. The algorithm returns a vector-based model for each identified trunk while parameters like the ground position, zenith orientation, azimuth orientation and length of the trunk are provided. The algorithm performed well for a study area of 109 trees (about 2/3 Norway Spruce and 1/3 European Beech), with a point density of 7.6 points per m2, while a detection rate of about 75% and an overall accuracy of 84% were reached. Compared to crown-based tree detection methods, the aTrunk approach has the advantages of a high reliability (5% commission error) and its high tree positioning accuracy (0.59m average difference and 0.78m RMSE). The usage of overlapping segments with parametrizable size allows a seamless detection of the tree trunks.

A Divide and Conquer Algorithm for Exploiting Policy Function Monotonicity

A divide and conquer algorithm for exploiting policy function monotonicity is proposed and analyzed. To solve a discrete problem with n states and n choices, the algorithm requires at most n log2(n) + 5n objective function evaluations. In contrast, existing methods for non-concave problems require n^2 evaluations in the worst case. For concave problems, the solution technique can be combined with a method exploiting concavity to reduce evaluations to 14n + 2 log2(n). A version of the algorithm exploiting monotonicity in two state variables allows for even more efficient solutions. The algorithm can also be efficiently employed in a common class of problems that do not have monotone policies, including problems with many state and choice variables. In the sovereign default model of Arellano (2008) and the real business cycle model, the algorithm reduces run times by an order of magnitude for moderate grid sizes and orders of magnitude for larger ones. Sufficient conditions for monotonicity are provided.

A fixed point theorem for preordered complete fuzzy quasi-metric spaces and an application

Abstract We obtain a fixed point theorem for a type of generalized contractions on preordered complete fuzzy quasi-metric spaces which is applied to deduce, among other results, a procedure to show in a direct and easy fashion the existence of solution for the recurrence equations that are typically associated to Quicksort and Divide and Conquer algorithms, respectively. MSC:47H10, 54H25, 06A06, 68Q25.