NP Problem Research Articles

A Hybrid Firefly Algorithm Approach for Job Shop Scheduling Problem

Abstract: Job shop scheduling has always been one of the most sought out research problems in Combinatorial optimization. Job Shop Scheduling problems (JSSP) are categorized under NP hard problems. In recent years the meta heuristic algorithms have been proved effective to solve hardcore NP problem. Firefly Algorithm is one of such meta heuristic techniques which is nature inspired from firefly characteristic. Its potential can be enhanced further by hybridizing it with other known evolutionary algorithms and thereby getting improved results in less computational time. In this paper we have proposed a new hybrid technique christened as HyFA, by hybridizing Firefly algorithm(FA) with simulated annealing (SA) and Greedy heuristics approach (GHA). The hybrid technique has the advantages of all three algorithms and are combined in such a way that a quicker and better optimal solution is obtained. Our proposed HyFA is coded in Matlab with an objective to minimize the makespan (Cm). The novel hybrid technique is then used to evaluate 1-25 Lawrence problems taken from literature. The results show the proposed technique is more effective not only in getting optimal results but has significantly reduced computational time. Keywords: Scheduling, Optimisation, Job shop scheduling, Meta-heuristics, Firefly, Simulated Annealing, Greedy heuristics Approach.

On some FPT problems without polynomial Turing compressions

An impressive hardness theory which can prove compression lower bounds for a large number of FPT problems has been established under the assumption that NP ⊈ coNP/poly. However, there are no problems in FPT for which the existence of polynomial Turing compressions under any widely believed complexity assumptions has been excluded. In this paper, we provide a technique which can be used to prove that some FPT problems have no small Turing compressions under the assumption that there exists a problem in NP which does not have small-sized circuits. These FPT problems, which include edge clique cover parameterized by the number of cliques, integer linear programming and a-choosability parameterized by some structural parameters, etc. have the property that they remain NP-hard under Cook reductions even if their parameter values are small. Moreover, a trade-off between the size of the Turing compression lower bound and the robustness of the complexity assumption is obtained. In particular, we demonstrate that these FPT problems have no polynomial Turing compressions unless every set in NP has quasi-polynomial-sized circuits, and have no 2o(k) Turing compressions unless every set in NP has sub-exponential-sized circuits. Additionally, Turing kernelization lower bounds for these FPT problems are provided under some weaker complexity assumptions. Lastly, compression lower bounds for the above-mentioned FPT problems are proved under some complexity assumptions which are weaker than NP ⊈ coNP/poly, moreover, these results are proved under a method which is different from the previous hardness theory for compression lower bounds.

Active P-Colonies

P-Systems are abstract machines inspired to the behaviour of cells which we can see like simple biological processing units. Many types of P-Systems have been developed considering different aspects of the cells working principles, obtaining different computational models. In this paper we introduce Active P-Colonies (APC), a variant of the model P-Colony systems. P-Colony systems are a model of computation based on the collaboration among different agents placed in a shared passive environment (i.e. a space where no computing operations take place). First of all, we show that using the P-Colony system basic model it is not possible to solve problems in the computational class NP (unless P=NP). Inspired by what has been done for the basic variant of P-Systems, we extend the original model by including new types of rules and new biological behaviours like duplication and membrane dissolution. In fact, in APC the agents are able to duplicate themselves obtaining new processing units having the same computational power as the original unit. The cells can also dissolve their membrane, releasing the contents into the environment. The obtained systems are able to solve in polynomial time (and exponential space) computationally hard problems. In particular, we focus on the development of systems able to solve problems in the classes NP (SAT), coNP (UNSAT) and #P (#SAT).

Pose estimation for the case of prolonged under-ice based AUV

The technological operation of AUV docking is considered. An approach to its solution and modeling is proposed. A system for determining the relative position based on cameras and active-light markers is described. Active markers are offered to improve detection in dark deep water. A system of equations for modeling the dynamics of an underwater vehicle is described and a complete mathematical modeling of the whole pipeline of the positioning system is performed: image synthesis based on scene geometry, position determination based on the solution of the PnP problem, generating control based on synthesized measurements and modelling of the corresponding movement of the AUV. The presented model can be used to test various scenarios for the execution of a docking operation.

From strong to exact Petri net computers

Petri net paradigm of computing is concerned discussing basic types of Petri net computers and their relations. We developed a technique of parametric specification of Petri nets, built of a few connected components which are repeated depending on a parameter or a set of parameters, and composition of software to generate automatically the corresponding models in a vivid graphical form. We construct explicitly a Petri net that is a strong computer of double exponent after R.J. Lipton. Its nondeterministic computation is represented by a Petri net reachability graph to which a successful branch belongs. Then we minimise and transform the net to obtain twice smaller construct than the original one. Moreover, the obtained net possesses such a marvellous property that addingto it four priority arcs makes it an exact (deterministic) computer having a single firable sequence only. Same as the Lipton’s net, the minimized net allows the proof that the Petri net reachability problem is exponential in space. Besides, it represents an example when simple transformations allow guessing the successful branch of a nondeterministic computation. The practical significance of the approach in applications consists in a state-of-art heuristic technique of solving some NP problems in polynomial time.

SLA-DQTS: SLA Constrained Adaptive Online Task Scheduling Based on DDQN in Cloud Computing

Task scheduling is key to performance optimization and resource management in cloud computing systems. Because of its complexity, it has been defined as an NP problem. We introduce an online scheme to solve the problem of task scheduling under a dynamic load in the cloud environment. After analyzing the process, we propose a server level agreement constraint adaptive online task scheduling algorithm based on double deep Q-learning (SLA-DQTS) to reduce the makespan, cost, and average overdue time under the constraints of virtual machine (VM) resources and deadlines. In the algorithm, we prevent the change of the model input dimension with the number of VMs by taking the Gaussian distribution of related parameters as a part of the state space. Through the design of the reward function, the model can be optimized for different goals and task loads. We evaluate the performance of the algorithm by comparing it with three heuristic algorithms (Min-Min, random, and round robin) under different loads. The results show that the algorithm in this paper can achieve similar or better results than the comparison algorithms at a lower cost.

Redefining Cartesian Reductionism in Biological Issues with Big Data, such as COVID-19 Worldwide Pandemic, Using Formalism based on the Intermediate Attitude of Rationalism and Empiricism

Reduction is a concept first introduced by Descartes in explaining his view of the rationalization of philosophy through mathematics. He seeks to consider length, breadth, and depth for phenomena so that reducing the phenomenon to his own analytical geometric apparatus; thus shrinking the whole world into a small machine. In the present study, the authors took into account the deficiency in defining the reduction of phenomena to a mathematically sound system as the reason for a large group of problems and therefore they came to redefine the Cartesian reductionism of phenomena by removing the search space through a learning system. In due definition, it is possible to reduce the NP problems to P space without using a quantum algorithm that requires a quantum computer to exist. The present study points out that the problems arising from the mathematical modeling of the Covid-19 pandemic are due to a deficiency in the definition of Cartesian reduction, which leads to an increase in the computational complexity of its diagnosis and treatment using computational tools.

Non-iterative pose estimation method based on the polarization information via a parallelogram

As for vision-based pose estimation, which is also known as the PnP problem, non-iterative algorithms are more efficient. Precise extraction of 2D projections of feature points is important. If the projections of the feature points are not accurately extracted, the pose estimation accuracy is reduced. Under the condition of natural light, a camera captures the images of feature points, and the existence of high-light regions in the image affects the extraction accuracy of 2D projections of feature points, which reduces the number of effective feature points and leads to poor pose estimation accuracy. In the redundant cases (n > 4), redundant feature points are introduced as additional information, increasing the number of effective feature points to reduce the impact of high-light regions and improve the pose estimation accuracy. For the non-redundant cases (n = 4), it was difficult to ensure pose estimation accuracy. To solve this problem, a non-iterative pose estimation method based on the optimum polarization angle via four corner points of a parallelogram was proposed in this study. First, a model for solving optimum polarization angle was established. Thereafter, on the premise of the optimum polarization angle, the images were captured. Finally, the projections of the four corner points of a parallelogram were extracted, and the object pose was solved non-iteratively according to the four corner points. The corner point extraction experimental results show that the slope difference between the two parallel sides of each parallelogram under the condition of optimum polarization angle is less than that under the condition of natural light, thereby proving the improvement of the imaging quality. Measurement accuracy verification experiments prove that our pose estimation algorithm and the optimum polarization angle is the best combination to improve the non-iterative pose estimation accuracy in non-redundant cases. In the measurement range of −60-+60°, the angle measurement error was less than ±0.0491°. In the measurement range of 0–20 mm, the displacement measurement error was less than ±0.0435 mm.

Meaningful Translation and Transliteration for Marathi Language

Meaningful translation and transliteration is NP problem in case of languages like Marathi language as there are so many word disambiguation and multiple use and meaning of single word in different context is available. That is why identifying correct informational need and translating text into meaningful information is a tedious and error prone task. Google translate works on machine neuron network and WorldNet is an online reference system works on psycholinguistic theory of human memory. Both approaches are promising tools for language translation. Complete translation of Marathi text to English or English to Marathi also having problem of more complicated meaningless or tedious translation. Proposed algorithm is taking into consideration meaningful translation or transliteration as per user’s informational need. This novel approach consider machine neuron network for meaningful formation of translated sentence and morphological structure for correct translation of word based on ontological analysis of word.

Population Diversity in Ant-inspired Optimization Algorithms

Finding a balance between exploration and exploitation is very important in the case of metaheuristics optimization, especially in the systems leveraging population of individuals expressing (as in Evolutionary Algorithms, etc.) or constructing (as in Ant Colony Optimization) solutions. Premature convergence is a real problem and finding means of its automatic detection and counteracting are of great importance. Measuring diversity in Evolutionary Algorithms working in real-value search space is often computationally complex, but feasible while measuring diversity in combinatorial domain is practically impossible (cf. Closest String Problem). Nevertheless, we propose several practical and feasible diversity measurement techniques dedicated to Ant Colony Optimization algorithms, leveraging the fact that even though analysis of the search space is at least an NP problem, we can focus on the pheromone table, where the direct outcomes of the search are expressed and can be analyzed. Besides proposing the measurement techniques, we apply them to assess the diversity of several variants of ACO, and closely analyze their features for the classic ACO. The discussion of the results is the first step towards applying the proposed measurement techniques in auto-adaptation of the parameters affecting directly the exploitation and exploration features in ACO in the future.

NGPSO algorithm is improved based on difficult NP problem

NGPSO algorithm is improved based on difficult NP problem

P vs NP: P is Equal to NP: Desired Proof

Computations and computational complexity are fundamental for mathematics and all computer science, including web load time, cryptography (cryptocurrency mining), cybersecurity, artificial intelligence, game theory, multimedia processing, computational physics, biology (for instance, in protein structure prediction), chemistry, and the P vs. NP problem that has been singled out as one of the most challenging open problems in computer science and has great importance as this would essentially solve all the algorithmic problems that we have today if the problem is solved, but the existing complexity is deprecated and does not solve complex computations of tasks that appear in the new digital age as efficiently as it needs. Therefore, we need to realize a new complexity to solve these tasks more rapidly and easily. This paper presents proof of the equality of P and NP complexity classes when the NP problem is not harder to compute than to verify in polynomial time if we forget recursion that takes exponential running time and goes to regress only (every problem in NP can be solved in exponential time, and so it is recursive, this is a key concept that exists, but recursion does not solve the NP problems efficiently). The paper’s goal is to prove the existence of an algorithm solving the NP task in polynomial running time. We get the desired reduction of the exponential problem to the polynomial problem that takes O(log n) complexity.

A solution of dialectical systems theory to P/NP problem

The key to solve the NP problem is how to judge the existence of an algorithm for a conversion from NP to P? For this purpose, dialectical systems theory is introduced for a transformations which processes “self-denial” from its structure and function conversely and interactively of some kind of NP, a dualistic contradiction indeed. Mathematics is subject to the “identity” rule and difficult to tackle self-denial transformations. Furthermore, mathematics, being of incompleteness, isn’t helpful to solve the NP problem. Dialectics is an evolutionary theory, a dynamic process, demanding connection all aspects of things, so a systematic approach is adopted. Regarding the transformation from NP to P as an emergence of self-organization evolution, four requirements for dissipative structure can be proposed for the judging possibility of emergence of evolution: opening, non-equilibrium, non-linearity, fluctuation. Taken the “Travelling Salesman Problem” as a typical example of NPC, it be concluded that none of the four requirements could be met. The reason is that the condition given by TSP is one-dimensional data only, which is the essence of Monism that couldn’t boost evolution and emergence quickly and efficiently.

Algorithm and Convergence Analysis of Absolute Value Equation Based on Hybrid Network

In view of the shortcomings of structured networks that it is difficult to manage complex shapes and unstructured networks cannot calculate the boundary layer viscous flow, an implicit algorithm based on mixed network points is proposed to solve the problem of successful calculation and high viscosity. Comparing absolute values is a difficult NP problem. It is caused by the interval problem and has a wide range of applications in many practical problems, such as: situation problems, semi-monitored and unprotected classification problems, and bag feasibility problems. When solving linear programming, double matrix strategy, quadratic programming and other problems, they must be converted into linear complementarity problems for processing, and linear complementarity problems can be summarized as absolute value equations. This article mainly introduces the smoothing Newton method of absolute value equation and the conjugate gradient algorithm of absolute value equation. This paper uses a hybrid network to analyze the algorithm and convergence of the absolute value equation, and establishes a potential mathematical model. The model is solved by the smoothing Newton method of the absolute value equation and the conjugate gradient algorithm of the absolute value equation, and the algorithm and convergence analysis results of the absolute value equation based on the hybrid network are evaluated, and the model is revised using historical data to improve The algorithm of the absolute value equation and the accuracy of the assessment of convergence analysis results. The experimental results in this paper show that the smoothing Newton method of the absolute value equation and the conjugate gradient algorithm of the absolute value equation increase the efficiency of the algorithm and convergence analysis of the absolute value equation by 23%, and reduce the false alarm rate and the false alarm rate. Finally, by comparing the experimental data analysis of the management strategy of sports services and the analysis of the reconstruction of sports services, the system illustrates the influence of artificial intelligence on the analysis of sports services’ management strategies.

Graph compression based on transitivity for neighborhood query

In recent years, many graph compression methods have been introduced. One successful category of them is based on local decompression designed to answer neighborhood queries. These techniques mainly rely on local similarities of vertices. Besides, their performance is usually a function of graph sparsity. The proposed approach, in this paper, is a lossy compression technique used to answer neighborhood queries with a more general precondition, called transitivity. The output of this method is a sparse graph optimized to keep original adjacent vertices, in at most 2-distance from each other and vice versa. In other words, by traversing a compressed graph by depth of 2, from any desired vertex, its original adjacency list is reconstructed, with an acceptable error. This paper models an optimization problem to solve the inverse problem of finding the best compressed graph in order to minimize the reconstruction error. Then, this NP problem is approximated by a heuristic with a low degree polynomial time-complexity near to the complexity of the forward problem. The results of applying the proposed method on toy and real datasets are compared with the state of the art that improves compression ratio and performance with an acceptable query response time.

Camera and inertial sensor fusion for the PnP problem: algorithms and experimental results

In this work, we face the problem of estimating the relative position and orientation of a camera and an object, when they are both equipped with inertial measurement units (IMUs), and the object exhibits a set of n landmark points with known coordinates (the so-called Pose estimation or PnP Problem). We present two algorithms that, fusing the information provided by the camera and the IMUs, solve the PnP problem with good accuracy. These algorithms only use the measurements given by IMUs’ inclinometers, as the magnetometers usually give inaccurate estimates of the Earth magnetic vector. The effectiveness of the proposed methods is assessed by numerical simulations and experimental tests. The results of the tests are compared with the most recent methods proposed in the literature.

Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

New enhanced colliding body optimization algorithm based on a novel strategy for exploration

Researchers use the improvement strategies to enhance the current version of optimization algorithms to establish the right balance between local and global search phases to escape from a local minimum in some NP-hard problems. Colliding Bodies Optimization (CBO) and its enhanced version (ECBO) use the concept of mass and energy conservation law based on Newtonian Classic Physics. The quality of mentioned algorithm performance can be improved by changing how the bodies collide with each other. New enhanced colliding bodies Optimization (NECBO) moves all bodies towards the best solution in consecutive iterations to increase the chance of accessing a better solution and exploring all promised solution space. In this paper, the recently developed meta-heuristic algorithm, so-called Enhanced Colliding Bodies Optimization (ECBO), and one new proposed version of ECBO (called NECBO), including a new mechanism for finding new solutions, and two hybrid versions of both methods mentioned above (ECBO, NECBO) are utilized for the optimal design of sloped-roof rigid frames with non-prismatic members. The steel sloped portal frames, or steel gable frames, are frequently used in industrial buildings, gyms, schools, colleges, fire stations, storages, hangars , and many other low-rise structures. The gable frames' weight and shape are considerably affected by the member cross-sections' properties. The optimization of steel portal frames with tapered web members is a hard NP problem because of discrete variables, multiple local optimum, and corresponding constraints. The obtained results show the capability of NECBO and its hybridized version with ECBO in find a better solution than the conventional ECBO and CBO. • New enhanced colliding bodies’ optimization (NECBO) is developed by altering how bodies colide each other. • Enhanced Colliding Bodies Optimization (ECBO) and the new proposed NECBO include a new mechanism for finding new solutions. • The hybrid version of both ECBO and NECBO are utilized for optimal design of gable frames with tapered members. • Optimization of gable rigid frames with tapered web members is performed. • Results obtained from this study show the capability of NECBO and its hybridized version with ECBO.

Mathematical Programming Computational for Solving NP-Hardness Problem

In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the two methods which is Penalty and Augmented Lagrangian methods base on the numerical result. Moreover, we tested the K-cluster problem and found the Augmented Lagrangian Method faster than Penalty method. Finally, our research is not just focus on the numerical computational but also improving the theoretical converges properties.

Cryptanalysis Using DNA-Sticker Algorithm

Sticker model is one of the basic computer models of filtering model which is part of Non-Autonomous DNA computing models. This model inputs are represented by encoded one of a double (single - double) strand of DNA molecules, which is annealed with a short fraction of strings at some positions, and therefore these strands called memory complexes. Since its inception, DNA computing has provided a highly efficient and energy efficient technology for solving complete NP problems because of its really high data density and inherent parallels. In this paper, we explain how to use the sticker model, which is one of the types of molecular computations in DNA computing, to design an algorithm for coding analysis of the coded text in an unsystematic cipher method. The cipher text is broken by employing the idea of brute force attack, which works to represent all possible keys and then try it to break the encrypted text until reaching the correct key from among the total keys group representing by solution space. Theoretically, both the cipher text and all possible keys are represented using memory complexes of the DNA strands. Then, using sticker operations, as separation, combination, and proposed operation named length, we can remove the incorrect keys from the solution space of memory complexes, by taking advantage of the parallel processing of DNA computing, therefore this model is classified as filtering model.