Solve NP Complete Problems Research Articles

МЕТАЭВРИСТИЧЕСКИЙ МЕТОД ОПТИМИЗАЦИИ НА ОСНОВЕ МОДЕЛИ ПОВЕДЕНИЯ СТВОЛОВЫХ КЛЕТОК

The paper discusses optimization methods that are based on processes occurring in nature. Suchmethods have become increasingly used to solve complex problems. However, such methods have somedrawbacks, which stimulates the development of new and more advanced optimization methods. SolvingNP complete problems requires optimal methods that will meet all design requirements, so there is aneed to develop new and more advanced methods for solving this class of problems. As such a method,the authors propose an optimization method based on a model of the behavior of stem cells in the naturalenvironment. The conducted studies of the proposed method provide solutions that can overcomemany of the shortcomings of standard optimization approaches, such as getting into the local optimumor low convergence rate of the algorithm based on the method under consideration. The purpose of thiswork is to develop an optimization method and an algorithm based on it for solving a complex objectivefunction. The scientific novelty lies in the development of an optimization method based on the stem cellbehavior model for solving NP complete problems. The aim of the work is to create conditions for theoptimal search for a solution to complex functions by applying the search method and, based on it, analgorithm for the behavior of stem cells. The practical value of the work lies in the development of a newmetaheuristic optimization method for the efficient solution of NP complete problems. Also in the work,a comparative analysis with well-known competitors was carried out. The main difference of the proposedmethod from other known methods is the use of a new approach of bioinspired search based onthe behavior of stem cells, which, as shown by practical comparison, has an advantage over knownanalogues. The results of a practical comparison of methods and algorithms based on them showed theadvantages of the approach proposed in the work on known test functions. After analyzing the problemof creating methods, algorithms and software for solving NP complete problems, we can conclude thatthe development of such approaches is currently an urgent task.

МЕТАЭВРИСТИКА НА ОСНОВЕ ПОВЕДЕНИЯ КОЛОНИИ БЕЛЫХ КРОТОВ

Optimization algorithms inspired by the natural world have turned into powerful tools for solvingcomplex problems. However, they still have some disadvantages that require the study of new andmore advanced optimization algorithms. In this regard, when solving NP complete problems, there isa need to develop new methods for solving this class of problems. One of these methods can bemetaheuristics based on the behavior of a colony of white moles. This paper proposes a newmetaheuristic algorithm called the blind white moles algorithm. This algorithm was developed basedon the social behavior of blind moles in search of food and protecting the colony from intruders. Theproposed solution will be able to overcome many disadvantages of conventional optimization algorithms,including falling into the trap of local minima or a low convergence rate. The purpose of thiswork is to develop an algorithm for optimizing a complex objective function. The scientific noveltylies in the development of a genetic algorithm based on the behavior of a colony of white moles forsolving NP complete problems. The problem statement in this paper is as follows: to optimize thesearch for solutions to complex functions by applying an algorithm based on the behavior of a colonyof white moles. The practical value of the work lies in the creation of a new search architecture thatallows using the developed algorithm for the effective solution of NP complete problems, as well asconducting a comparative analysis with existing analogues. The fundamental difference from theknown approaches is in the application of a new bioinspired search structure based on the behaviorof a colony of white moles, which will allow to exclude falling into a local minimum or a low convergencerate. The presented results of the computational experiment showed the advantages of the proposedmultidimensional approach to solving the problems of placing VLSI elements in comparisonwith existing analogues. Thus, the problem of creating methods, algorithms and software for solvingNP complete problems is currently of particular relevance.

АВТОМАТИЗИРОВАННЫЙ СТРУКТУРНО-ПАРАМЕТРИЧЕСКИЙ СИНТЕЗ СТУПЕНЧАТОГО НАПРАВЛЕННОГО ОТВЕТВИТЕЛЯ НА СВЯЗАННЫХ ЛИНИЯХ НА ОСНОВЕ ГЕНЕТИЧЕСКОГО АЛГОРИТМА

An automated approach to the structural-parametric synthesis of a stepped directional coupleron connected lines based on a genetic algorithm (GA) is described, which makes it possible tocreate an algorithmic environment in the field of genetic search for solving NP complete problems,in particular, the structural-parametric synthesis of a stepped directional coupler on connectedlines. The purpose of this work is to find ways of structural-parametric synthesis of a stepped directionalcoupler on coupled lines based on the bionspiration theory. The scientific novelty lies inthe development of a modified genetic algorithm for automated structural-parametric synthesis ofa stepped directional coupler on connected lines. The problem statement in this work is as follows:to optimize the synthesis of passive and active microwave circuits by using a modified GA. A fundamentaldifference from the known approaches in the use of new modified genetic structures inautomated structural-parametric synthesis, in addition, a new method for calculating a steppeddirectional coupler on connected lines based on a modified GA is righteous in the work. Thus, theproblem of creating methods, algorithms and software for automated structural synthesis of microwavemodules is currently of particular relevance. Its solution will improve the quality characteristicsof the designed devices, reduce design time and costs, and reduce the requirements fordeveloper qualifications.

Comparison of application of various crossovers in solving inhomogeneous minimax problem modified by Goldberg model

This paper considers one of the classical NP complete problems - an inhomogeneous minimax problem. When solving such large-scale problem, there appear difficulties in obtaining an exact solution. Therefore, let us propose getting an optimum solution in an acceptable time. Among a wide range of genetic algorithm models, let us choose the modified Goldberg model, which earlier was successfully used by authors in solving NP complete problems. The classical Goldberg model uses a single-point crossover and a singlepoint mutation, which somewhat decreases the accuracy of the obtained results. In the article, let us propose using a full two-point crossover with various mutations previously researched. In addition, the work studied the necessary probability to apply it to the crossover in order to obtain results that are more accurate. Results of the computation experiment showed that the higher the probability of a crossover, the higher the quality of both the average results and the best solutions. In addition, it was found out that the higher the values of the number of individuals and the number of repetitions, the closer both the average results and the best solutions to the optimum. The paper shows how the use of a full two-point crossover increases the accuracy of solving an inhomogeneous minimax problem, while the time for getting the solution increases, but remains polynomial.

On the Verification Complexity of Group Decision-Making Tasks

A popular use of crowdsourcing is to collect and aggregate individual worker responses to problems to reach a correct answer. This paper studies the relationship between the computation complexity class of problems, and the ability of a group to agree on a correct solution. We hypothesized that for NP-Complete (NPC) problems, groups would be able to reach a majority-based correct solution once it was suggested by a group member and presented to the other members, due to the "easy to verify" (i.e., verification in polynomial time) characteristic of this complexity class. In contrast, when posed with PSPACE-Complete (PSC) "hard to verify" problems (i.e., verification in exponential time), groups will not necessarily be able to choose a correct solution even if such a solution has been presented. Consequently, increasing the size of the group is expected to facilitate the ability of the group to converge on a correct solution when solving NPC problems, but not when solving PSC problems. To test this hypothesis we conducted preliminary experiments in which we evaluated people's ability to solve an analytical problem and their ability to recognize a correct solution. In our experiments, participants were significantly more likely to recognize correct and incorrect solutions for NPC problems than for PSC problems, even for problems of similar difficulties (as measured by the percentage of participants who solved the problem). This is a first step towards formalizing a relationship between the computationally complexity of a problem and the crowd's ability to converge to a correct solution to the problem.

A polynomial alternative to unbounded environment for tissue P systems with cell division

The standard definition of tissue P systems includes a special alphabet whose elements are assumed to appear in the initial configuration of the system in an arbitrarily large number of copies. These objects reside in a distinguished place of the system, called the environment. Such potentially infinite supply of objects seems an unfair tool when designing efficient solutions to computationally hard problems in the framework of membrane computing, by performing a space–time trade-off. This paper deals with computational aspects of tissue P systems with cell division where there is no environment having the property mentioned above. Specifically, we prove that the polynomial complexity classes associated with tissue P systems with cell division and with or without environment are actually identical. As a consequence, we conclude that it is not necessary to have infinitely many copies of some objects in the initial configuration in order to solve NP–complete problems in an efficient way.

Solving a Hamiltonian Path Problem with a bacterial computer

BackgroundThe Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time.ResultsWe programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected.ConclusionWe successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof-of-concept experiment demonstrates that bacterial computing is a new way to address NP-complete problems using the inherent advantages of genetic systems. The results of our experiments also validate synthetic biology as a valuable approach to biological engineering. We designed and constructed basic parts, devices, and systems using synthetic biology principles of standardization and abstraction.

DNA Computing Adopting DNA Coding Method for NP-complete Problems

DNA computing suggests the potential of DNA with immense parallelism and huge storage capacity by solving NPcomplete problems such as the Traveling Salesman Problem (TSP). If DNA computing is used to solve TSP, however, weights between vertexes in sequence design cannot be encoded effectively. This study proposes an algorithm for code optimization (ACO) that applies DNA coding method to DNA computing in order to encode weights in TSP effectively. By applying ACO to TSP, we designed sequence more effectively than Adleman's DNA computing algorithm. Furthermore, we could find the shortest path quickly and reduce biological error rate.

P SYSTEMS WITH INPUT IN BINARY FORM

Current P systems which solve NP–complete numerical problems represent the instances of the problems in unary notation. However, in classical complexity theory, based upon Turing machines, switching from binary to unary encoded instances generally corresponds to simplify the problem. In this paper we show that, when working with P systems, we can assume without loss of generality that instances are expressed in binary notation. More precisely, we propose a simple method to encode binary numbers using multisets, and a family of P systems which transforms such multisets into the usual unary notation. Such a family could thus be composed with the unary P systems currently proposed in the literature to obtain (uniform) families of P systems which solve NP–complete numerical problems with instances encoded in binary notation.We introduce also a framework which can be used to design uniform families of P systems which solve NP–complete problems (both numerical and non-numerical) working directly on binary encoded instances, i.e., without first transforming them to unary notation. We illustrate our framework by designing a family of P systems which solves the 3-SAT problem. Next, we discuss the modifications needed to obtain a family of P systems which solves the PARTITION numerical problem.

Speedup in Quantum Adiabatic Evolution Algorithm

The quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving NPcomplete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one in the evolution. In this paper we show a way of speedup in the quantum adiabatic evolution algorithm, using an extended Hamiltonian. We present the exact relation between the energy gap and the elements of the extended Hamiltonian, which provides a new point of view to reduce the running time.

On The Scheduling Of Identical Processors With Entrapment

Abstract In an attempt to reduce computational requirements, parallel processor tardiness related scheduling algorithms incorporate a fathoming condition, “entrapment,” which at times helps, whereas, at other times, increases CPU time requirements. This paper establishes certain guidelines that can be used as a priori rule deciding the inclusion or exclusion of the entrapment subroutine part of the scheduling algorithm to solve a given problem. Since entrapment is a dominance condition, the implications of this work can be used to examine the applicability of other such conditions in algorithms designed to solve NP complete problems.