Backtracking Approach Research Articles

Sudoku Solver – A Novel Approach Using Recognition of Printed Text Image

Detecting and analyzing text in multimedia is required for recognition of characters which can be used for performing multi-objectives in numerous research areas and applications. Characters or numbers in images can be hand-written, printed document, typewritten or artificially added for the purpose of searching or indexing, editing or image understanding. Various applications such as License Plate Detection, Handwritten documents recognition, Sudoku Solving, multi-oriented recognition focuses on character recognition. Image Sudoku solver works on Sudoku puzzle images. In this paper, the printed text Sudoku image is used as the input. The image is enhanced by filling the horizontal and vertical gaps in the grids that may occur due to shadow or distortion of the scanned image such that all the 81 grids are extracted. Secondly, the numbers and grids in the enhanced image are extracted and a dancing link approach using Algorithm X is adopted to solve the Sudoku. The proposed work is compared with a backtracking approach and dancing link approach without enhancing the image and its computation time for various ranks of difficulty of a puzzle taken. The Sudoku puzzle can be used to secure information stored in an image as the number of solutions to solve a Sudoku puzzle is very large, allowing it to be used as a security tool resistant to brute force attacks.

Disinfection scheduling in water distribution networks considering input time-delay uncertainty

Abstract A significant challenge when attempting to regulate the spatial-temporal concentration of a disinfectant in a water distribution network is the large and uncertain delay between the time that the chemical is injected at the input node and the time that the concentration is measured at the monitoring output nodes. Uncertain time delays are due to varying water flows, which depend mainly on consumer water demands. Existing approaches cannot guarantee that the concentration of the disinfectant will remain within a specified range at the output, even though bounds on time-delay uncertainty may be known. In this work, given bounded water-flow uncertainty, we use the input–output modeling approach to develop a disinfectant scheduling methodology that guarantees a bounded output disinfectant concentration. The proposed methodology creates an input–output model uncertainty characterization by utilizing estimated bounds on water-quality states using the backtracking approach. An optimization problem is formulated and solved to find an input schedule that keeps the disinfectant concentration within predefined bounds for a specified time horizon. Simulation results in two case studies where water demands varied between ±20% of their nominal value show that the proposed scheduler is able to avoid lower bound violations of disinfectant concentration.

Sewer networks monitoring through a topological backtracking

The interest in wastewater monitoring is always growing, with applications mainly aimed at detection of pollutants and at the environmental epidemiological surveillance. However, it often happens that the strategies proposed to manage these problems are inapplicable due to the lack of information on the hydraulics of the systems. To overcome this problem, the present paper develops and proposes a topological backtracking strategy for the optimal monitoring of sewer networks, which acts by subrogating the hydraulic information with the geometric ones, e.g., diameter and slope, thus not requiring any hydraulic simulation. The topological backtracking approach aims at evaluating an impact coefficient for each node of the network used to face with the problems of sensor location and network coverage for purposes related to the spread of contaminants and pathogens. Finally, the positioning of the sensors for each monitoring scheme is addressed by a priority rank, based on the efficiency of each sensor in terms of network coverage with respect to a specific weight (e.g., length, flow). The main goal is to design a monitoring scheme that provide the required coverage of the network by minimizing the number of sensors with respect to specific measurement threshold value.The results show the effectiveness of the strategy in supporting the optimal design with the topological-based backtracking approach without the necessity of performing hydraulic simulations, with great advantage in terms of required data and computational time.

Circinus: Fast Redundancy-Reduced Subgraph Matching

Subgraph matching is one of the most important problems in graph analytics. Many algorithms and systems have been proposed for subgraph matching. Most of these works follow Ullmann's backtracking approach as it is memory-efficient in handling an explosive number of intermediate matching results. However, they have largely overlooked an intrinsic problem of backtracking, namely repeated computation, which contributes to a large portion of the heavy computation in subgraph matching. This paper proposes a subgraph matching system, Circinus, which enables effective computation sharing by a new compression-based backtracking method. Our extensive experiments show that Circinus significantly reduces repeated computation, which transfers to up to several orders of magnitude performance improvement.

A novel approach for prediction of transverse thermal conductivity of unidirectional random fiber composites

In fiber-reinforced composites, fibers are randomly positioned during the manufacturing process. Most of the theoretical studies assume regular arrangement of fibers in matrix that permits the use of representative volume element (RVE) for prediction of mechanical properties. Theoretical methods established in the literature for random fiber composites are complex and approximate. A simple approach is established in this work to accurately predict the transverse thermal conductivity of unidirectional random fiber-reinforced composites using the principle of electrical analogy (EA). In this study, circular fiber is transformed into an equivalent square fiber that facilitates the application of EA, and predicted the transverse thermal conductivity of random fiber composites. The conductivity of equivalent square fiber is evaluated by back-track approach using an equivalent thermal system. Python code is developed to generate the random location of fibers in the composite. The results obtained in this way are verified and found to be in good agreement with benchmark results over a wide range of fiber composites with varying conductivity ratios, fiber volume fraction, and randomness.

An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms

This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially.

The vehicle routing problem with time windows and flexible delivery locations

We introduce a new variant of the well-known vehicle routing problem (VRP): the VRP with time windows and flexible delivery locations (VRPTW-FL). Generally, in the VRP each customer is served in one fixed service location. However, in the VRPTW-FL each customer is served in one of a set of potential service locations, each of which has a certain capacity. From a practical point of view, the VRPTW-FL is highly relevant due to its numerous applications, e.g. parcel delivery, routing with limited parking space, and hospital-wide scheduling of physical therapists. Theoretically, the VRPTW-FL is challenging to solve due to the limited location capacities. When serving a customer, location availability must be ensured at every time. To solve this problem, we present a mathematical model and a tailored hybrid adaptive large neighborhood search. Our heuristic makes use of an innovative backtracking approach during the construction phase to alter unsatisfactory decisions at an early stage. In the meta-heuristic phase, we employ novel neighborhoods and dynamic updates of the objective violation weights. For our computational analysis, we use hospital data to evaluate the utility of flexible delivery locations and various cost functions. Our algorithmic features improve the solution quality considerably.

Fatigue behavior of stainless steel 316L microstruts fabricated by laser powder bed fusion

A better understanding of mechanical behavior under cyclic loading is needed for thin struts fabricated by laser powder bed fusion, whose mechanical responses are significantly influenced by their as-built surface morphologies. The current work presents an attempt to characterize tensile-tensile cyclic stresses behavior of 250μm nomoinal diameter LPBF SS316L microstruts at R∼0.04−0.06. The resultant lower fatigue performance of the microstruts was investigated via fracture surface imaging and X-ray microtomography. In particular, microtomography combined with a back-tracking approach was used to characterize the location, shape, and size of the defect responsible for fatigue crack initiation. The identified defect, located at the root of a notch-like surface feature, was analyzed using a modified Murakami Area parameter model. The modified Area parameter of the crack initiating defect estimated the fatigue strength as 130±19MPa, explaining the role of microstrut surface morphological towards the depreciation of fatigue performance compared to as-built macro-scale specimens. The propagation of the initiated crack was characterized using the modified model via interrupted cyclic testing and corresponding tomography at various stress cycle intervals. The obtained crack growth rate vs. the crack's stress intensity range was obtained and compared with crack propagation in macroscale specimens that follow the Paris-law curve.

Insights into the spatio‐temporal variability of spawning in a territorial coastal fish by combining observations, modelling and literature review

AbstractIn bipartite life cycle fishes, spawning represents the onset of propagules dispersal, with eggs and larvae experiencing anisotropic transport and high mortality rates, before eventually metamorphosing and settling. Hence, early‐life stages operate as bottlenecks for population demography by strongly constraining recruitment. Despite its significance, spawning is rarely explicitly considered in ecosystem management due to a lack of knowledge, for many species, about where and when spawning occurs. Previous evidences suggest that temperature is among the main drivers of spawning in Teleosts. Using the ecologically and economically relevant white seabream Diplodus sargus in the central Mediterranean Sea as a case study, we assess the abiotic factors that regulate the onset and duration of spawning and subsequent dispersal. Lagrangian backtracking simulations fed with early‐life observations allow locating 11 spawning events, which are then associated to simulated temperatures ranging from 14.8° C to 20.6° C, in close agreement with previous estimates. Based on this range of suitable temperatures, we model the spatio‐temporal variability of spawning success at broad‐scale over 10 years (2005–2014) following the backtracking approach with hypothetical constant settlement areas. It highlights a prominent inter‐annual variability in the Adriatic and Siculo‐Tunisian strait driven by oceanographic processes. Moreover, a powerful clustering method uncovers relatively stable spawning areas in the Ligurian and Tyrrhenian seas with both early (January to Mid‐February) and late (April to June) spawning peaks. Our methodology can be applied to other species and oceanic systems to investigate how oceanic processes impact spawning success, enabling the design of sound management strategies.

Too much information: Why CDCL solvers need to forget learned clauses.

Conflict-driven clause learning (CDCL) is a remarkably successful paradigm for solving the satisfiability problem of propositional logic. Instead of a simple depth-first backtracking approach, this kind of solver learns the reason behind occurring conflicts in the form of additional clauses. However, despite the enormous success of CDCL solvers, there is still only a limited understanding of what influences the performance of these solvers in what way. Considering different measures, this paper demonstrates, quite surprisingly, that clause learning (without being able to get rid of some clauses) can not only help the solver but can oftentimes deteriorate the solution process dramatically. By conducting extensive empirical analysis, we furthermore find that the runtime distributions of CDCL solvers are multimodal. This multimodality can be seen as a reason for the deterioration phenomenon described above. Simultaneously, it also gives an indication of why clause learning in combination with clause deletion is virtually the de facto standard of SAT solving, in spite of this phenomenon. As a final contribution, we show that Weibull mixture distributions can accurately describe the multimodal distributions. Thus, adding new clauses to a base instance has an inherent effect of making runtimes long-tailed. This insight provides an explanation as to why the technique of forgetting clauses is useful in CDCL solvers apart from the optimization of unit propagation speed.

Common hippopotamus in the upper Dhidhessa River and its conflicts with Arjo‐Dhidhessa Sugar Factory, Ethiopia

AbstractDue to the loss of wetlands, land‐use change, and confrontations with humans, the common hippopotamus (Hippopotamus amphibius) is one of the largest land mammals currently threatened and classified as vulnerable by the International Union for Conservation of Nature (IUCN). The common hippo is found in protected and unprotected habitats, marshes, and inland major rivers of Ethiopia. However, little is known about the population status of hippos in the country. Hence, this study aimed to reveal the current population size of hippos and its conflicts with sugarcane plantation in Arjo‐Dhidhessa Sugar Factory. Data on population size, diet composition, and potential hippo conflicts was also collected from August 2020 to February 2021. The complete on‐foot count method was used to estimate the hippo population during the wet and dry seasons. The backtracking approach was used to determine the hippo's diet, which involved identifying and quantifying foraged species using quadrats. The total sugarcane stalk damage was counted in the sampled fields to determine sugarcane damage. Direct observation and interviews with sugarcane guards were used to identify mitigation methods employed to prevent hippo attacks. During the wet and dry seasons, a total of 96 and 182 hippos were documented in the upper Dhidhessa River, respectively. Hippos ate 23 plant species from 11 different families. The Poaceae family made up 51.32% of the hippo's diet. During the wet and dry seasons, a total of 662 (36.5%) and 1156 (63.5%) sugarcane stalks/ha were damaged, respectively. The best mitigation techniques against hippo assaults in the area were guarding, fencing, trenching, and burning fire. A sound conservation action plan for hippos along the Dhidhessa River and associated banks must be developed. Furthermore, while hippos are encircled by the Arjo‐Dhidhessa sugarcane irrigation scheme, modern mitigation measures and corridors for hippos should be implemented.

Relational e-matching

We present a new approach to e-matching based on relational join; in particular, we apply recent database query execution techniques to guarantee worst-case optimal run time. Compared to the conventional backtracking approach that always searches the e-graph "top down", our new relational e-matching approach can better exploit pattern structure by searching the e-graph according to an optimized query plan. We also establish the first data complexity result for e-matching, bounding run time as a function of the e-graph size and output size. We prototyped and evaluated our technique in the state-of-the-art egg e-graph framework. Compared to a conventional baseline, relational e-matching is simpler to implement and orders of magnitude faster in practice.

Mutation Screening at Diagnosis Reveals a High Frequency of ASXL1 Mutations in CML Patients Who Fail to Achieve Molecular Remission Criteria after One Year of TKI Treatment

Background: Tyrosine kinase inhibitors (TKI) revolutionized treatment of chronic myeloid leukemia (CML). While response rates are high, a subset of patients does not show the expected decrease or eradication of BCR-ABL1 . According to ELN guidelines (Baccarani et al. 2013) BCR-ABL1/ABL1 ratio>1% after one year of TKI is considered failure. Mechanisms of failure include the acquisition of additional genetic changes, e.g. cytogenetic aberrations and mutations in the ABL1 kinase domain but also in other genes. Here, we ask the question, if specific mutations are not only acquired but may already be present at initial diagnosis of patients with slow or no TKI response (primary failure according to ELN). Aim: To screen CML patients at diagnosis, who failed ELN remission criteria after one year, for mutations in genes, which are frequently mutated in myeloid malignancies. Patients and Methods: In a backtracking approach, we selected diagnostic samples of 48 CML patients (25 males, 23 females) with a median age of 64 (range: 23-84) years, who failed first year molecular remission criteria. Median BCR-ABL1/ABL1 ratio was 3.603 [1.158-58.318] after 12 (11-16) months of imatinib (n=42), second generation TKI (n=5) treatment or both (n=1). Patients had a p210 BCR-ABL1 fusion (e13a2 [n=24], e14a2 [n=18], both [n=6]) and no additional cytogenetic aberrations at diagnosis. We sequenced DNA of bone marrow (n=28) or peripheral blood (n=20) samples drawn at diagnosis on NextSeq or MiSeq sequencers after TruSeq library preparation (Illumina, San Diego, CA). We used SeqNext 4.3 for data analysis (JSI, Kippenheim, Germany). The panel covered 48 genes including the epigenetic regulators: ASXL1, ASXL2, BCOR, DNMT3A, EZH2, IDH1, IDH2 and TET2 . Results: We identified mutations in 13/48 samples at initial diagnosis (27%). Only one patient had two mutations (total, n=14 mutations). There was no correlation of mutations with types of transcript, age, gender, hemoglobin level, WBC count, percentage of Ph+ cells by FISH, BCR-ABL1/ABL1 ratio at diagnosis or with BCR-ABL1/ABL1 ratio after one year of TKI. Twelve of the 14 (86%) mutations were found in genes involved in chromatin modification or DNA methylation. We screened four splicing machinery genes (SF3B1, SRSF2, U2AF1, ZRSR2), which are frequently mutated in other myeloid malignancies, but no mutation was found. In 8/48 (17%) patients, we found an ASXL1 mutation (57% of all mutations). Other mutated genes were ASXL2, BCOR, CALR, NRAS (n=1 each) and DNMT3A (n=2). The comparison of ASXL1 mutation types in this CML cohort to other myeloid malignancies revealed a significant shift in mutation types: e.g. in myelodysplastic syndrome (Haferlach et al. 2014) and chronic myelomonocytic leukemia (Meggendorfer et al . 2012), c.1934dup and c.1900_1922del (ENS0375687) constitute the majority of mutations (64 [42%] and 23 [15%] of 152, respectively), whereas there was only one c.1900_1922del and no c.1934dup in our CML cohort (p=0.023). Further, we used follow-up samples after one year of TKI to evaluate if mutations are derived from the CML clones. In all patients with available data for ASXL1 (n=6), mutation burdens showed a quantitative course which paralleled BCR-ABL1 ratio indicating that ASXL1 mutations are part of the CML clone present at diagnosis. In the patient with a CALR mutation, the CALR burden remained unchanged despite BCR-ABL1 reduction, indicating a BCR-ABL1 gain in a preexisting CALR mutated myeloproliferative neoplasm. In comparison to ASXL1 mutation rates (4/74 [5%]) in a published cohort with optimal responders (Kim et. al. 2017), we found a significantly higher number of ASXL1 mutations (8/48 [17%]) at diagnosis of our CML patients, who failed first year molecular remission criteria (p=0.041). Conclusions: (1) At diagnosis of CML, mutations were detected (esp. in ASXL1) in 27% of patients with TKI failure according to ELN criteria after one year. Compared to other myeloid malignancies, patients showed a different pattern of ASXL1 mutations. (2) No mutations in spliceosome genes were found. (3) Stringent BCR-ABL1 monitoring allows early adjustment of therapy in case of suboptimal response, but analysis of additional mutation patterns could help understanding the biology of failure and would allow up-front adjusted therapy decisions or different monitoring strategies. (4) Mutations such as ASXL1 at diagnosis may contribute to suboptimal TKI response. Disclosures Baer: MLL Munich Leukemia Laboratory: Employment. Kern: MLL Munich Leukemia Laboratory: Employment, Equity Ownership. Haferlach: MLL Munich Leukemia Laboratory: Employment, Equity Ownership. Haferlach: MLL Munich Leukemia Laboratory: Employment, Equity Ownership.

Applications Based on a Novel Sudoku Solver Algorithm and Grid Based Models

Numerous algorithms for solving sudoku puzzles have been explored, most of which use a backtracking approach. Thus computational efficiency of such algorithms can sometimes yield poor results. We propose a probabilistic solver algorithm which, iteratively fills the sudoku grid and solves the same. In this approach we make use of a dynamic random number set, we identify unassigned sudoku grids for a given puzzle where only one possible value can be filled in and iteratively identify and assign cells with least number of possible values. We not only elaborate on our solver algorithm logic, but also explore application areas based on algorithm devised, after reviewing relevant similar approaches illustrated in the referenced articles. We believe by extension of this algorithm, many combinatorial problems in the field of material characterization, cryptography, cybersecurity can be solved and advanced. We also envision that with application of neural networks, Machine Learning techniques the algorithm will take a very adaptive and robust form, useful for solving complex problems in accurate estimation of missing data, discrete event analysis and prediction. Uniqueness is the ability to use high probability for faster computation and low execution time. With cyberattacks of varied vectors and types, its important to devise a mechanism to create a deliberate mismatch every time a possible attack is detected.

Reconstructing Point Sets From Distance Distributions

We address the problem of reconstructing a set of points on a line or a loop from their unassigned noisy pairwise distances. When the points lie on a line, the problem is known as the turnpike; when they are on a loop, it is known as the beltway. We approximate the problem by discretizing the domain and representing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> points via an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -hot encoding, which is a density supported on the discretized domain. We show how the distance distribution is then simply a collection of quadratic functionals of this density and propose to recover the point locations so that the estimated distance distribution matches the measured distance distribution. This can be cast as a constrained nonconvex optimization problem which we solve using projected gradient descent with a suitable spectral initializer. We derive conditions under which the proposed distance distribution matching approach locally converges to a global optimizer at a linear rate. Compared to the conventional backtracking approach, our method jointly reconstructs all the point locations and is robust to noise in the measurements. We substantiate these claims with state-of-the-art performance across a number of numerical experiments. Our method is the first practical approach to solve the large-scale noisy beltway problem where the points lie on a loop.

An experimental evaluation of refinement techniques for the subgraph isomorphism backtracking algorithms

AbstractIn this paper, we study a well-known computationally hard problem, called the subgraph isomorphism problem where the goal is for a given pattern and target graphs to determine whether the pattern is a subgraph of the target graph. Numerous algorithms for solving the problem exist in the literature and most of them are based on the backtracking approach. Since straightforward backtracking is usually slow, many algorithmic refinement techniques are used in practical algorithms. The main goal of this paper is to study such refinement techniques and to determine their ability to speed up backtracking algorithms. To do this we use a methodology of experimental algorithmics. We perform an experimental evaluation of the techniques and their combinations and, hence, demonstrate their usefulness in practice.

Algorithmic Counting of Zero-Dimensional Finite Topological Spaces With Respect to the Covering Dimension

Taking the covering dimension dim as notion for the dimension of a topological space, we first specify the number zdimT0(n) of zero-dimensional T0-spaces on {1,…,n} and the number zdim(n) of zero-dimensional arbitrary topological spaces on {1,…,n} by means of two mappings po and P that yield the number po(n) of partial orders on {1,…,n} and the set P(n) of partitions of {1,…,n}, respectively. Algorithms for both mappings exist. Assuming one for po to be at hand, we use our specification of zdimT0(n) and modify one for P in such a way that it computes zdimT0(n) instead of P(n). The specification of zdim(n) then allows to compute this number from zdimT0(1) to zdimT0(n) and the Stirling numbers of the second kind S(n, 1) to S(n, n). The resulting algorithms have been implemented in C and we also present results of practical experiments with them. To considerably reduce the running times for computing zdimT0(n), we also describe a backtracking approach and its parallel implementation in C using the OpenMP library.

Balanced scheduling of distributed workflow tasks based on clustering

Distributed computing, such as Cloud, provides traditional workflow applications with completely new deployment architecture offering high performance and scalability. However, when executing the workflow tasks in a distributed computing environment, significant scheduling overheads are generated. Task clustering is a key technology to optimize process execution. Unreasonable task clustering can lead to the problems of runtime and dependency imbalance, which reduces the degree of parallelism during task execution. In order to solve the problem of runtime imbalance, we propose Runtime Balance Clustering Algorithm (RBCA), which employs the Backtracking approach to make the runtime of each cluster more balanced. In addition, to address the problem of dependency imbalance, we also propose Dependency Balance Clustering Algorithm (DBCA), which defines the dependency correlation to measure the similarity between tasks in terms of data dependencies. The tasks with high dependency correlation are clustered together so as to avoid the dependency imbalance to most extent. We conducted extensive experiments on the WorkflowSim platform and compared our algorithms with the existing task clustering algorithms. The results show that RBCA and DBCA significantly reduce the execution time of the whole workflow.

Hybrid on-demand greedy routing protocol with backtracking for mobile ad-hoc networks

PurposeThe purpose of this paper is to design an efficient on-demand routing protocol for mobile ad hoc networks (MANETs) which combines greedy forwarding and backtracking.Design/methodology/approachIt uses a hybrid approach. It uses greedy approach to determine a route from source to the destination. If the greedy approach fails, then it uses a backtracking approach. Combining greedy and backtracking approaches results in a more efficient protocol.FindingsA new routing algorithm for MANETs which performs better than some of the existing algorithms.Research limitations/implicationsA major limitation of this work is that the authors did not implement the protocol on a test bed and evaluated the performance. They neither had the infrastructure nor the resources to actually implement the protocol. Instead, like most of the researchers, they evaluated the performance of their protocol based on extensive simulation. The mobility model, the area of deployment and the density of nodes chosen to simulate the protocol are consistent with what many of the other researchers have done. Intuitively, the authors’ protocol, as the performance evaluation indicates, is likely to perform well in small networks.Practical implicationsThe authors did not implement the protocol on a test bed to evaluate the performance of the protocol. The authors used simulation to study the performance of their protocol. Their simulation model is similar to many of the research works published in the literature.Originality/valueTo the authors’ knowledge, no other paper has combined the greedy and backtracking approach to design a routing protocols for MANETs.

RRT-A*-BT approach for optimal collision-free path planning for mobile robots

This paper deals with the problem of optimal collision-free path planning for mobile robots evolving inside indoor cluttered environments. Addressing this challenge, a hybrid approach is proposed combining Rapidly-exploring Random Trees (RRT), A-Star (A*) and Back-Tracking (BT) algorithms (RRT-A*-BT). Thus, a vision system is used for a nearly-exact modeling of the environment through image processing. Moreover, each iteration of the basic RRT approach is guided by A* algorithm while trying to take the shortest path linking the robot current position to target . In case of a blockage, BT algorithm is used to get out the robot from this situation. Finally, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is used to smooth the generated optimal path. RRT-A*-BT approach is validated through different scenarios; obtained results are compared with previous works on same environments with same conditions. The results prove that RRT-A*-BT is better and faster than other algorithms of the literature, such as Genetic Algorithms and Conventional RRT, in terms of (i) computation time,(ii) path length and (iii) transfer time..