A Slime Mold Solver for Linear Programming Problems

The plasmodium stage of the giant single-celled amoeboid organism Physarum polycephalum, or true slime mould, dynamically adapts its body plan in response to environmental stimuli, including nutrient location, temperature gradients, light exposure, and predatory threats. The construction and adaptation of the plasmodial transport network has been shown to be an efficient trade-off between minimising network distance and maximising connectivity. Optimisation of topology is also a desired trait in manufacturing and engineering, whereby the topology of an initially simple component is modified to minimise one or more properties (for example minimising the amount of substrate reduces the weight and material cost of the component) whilst maintaining other desired material properties within the component (for example strength under specific load points and conditions). Biologically inspired approaches to certain specific engineering challenges are well documented and successful. In this paper we explore at a more general level whether a cross-pollination can occur between Physarum computing and Topology Optimisation. Using an interdisciplinary modelling approach we explore whether the evolution of transport networks in a multi-agent model of Physarum has any similarities to networks formed by Topology Optimisation. We find that the Topology Optimisation method generates networks which are similar to the model slime mould networks. The Topology Optimisation networks correspond to higher regions of the Toussaint hierarchy of proximity graphs (i.e. more edges) whereas the model slime mould networks exhibit greater minimisation of network length. Since it is possible to adjust network connectivity in the multi-agent model via nutrient concentration we speculate that similar parametric adjustment may be possible to alter the connectivity of Topology Optimisation networks.

The clade of Myxogastria, commonly described as true or plasmodial slime molds, contains more than 1000 species. During their life cycle many of these slime molds develop extended networks of connected veins, known as unicellular (phanero)plasmodia. Among those, Physarum polycephalum gathered by far the most attention of biologists and physicists. Via oscillating cytoplasmic streams nutrients as well as signaling factors spread through the adaptive plasmodial network. These properties have rendered it not only a model organism for acellular slime molds, but also a model to investigate network dynamics, biological fluid-dynamics and food foraging behavior. Here, we studied parameters of plasmodial growth and network development, including chemotactic responses, in three slime mold species: Physarum polycephalum, Badhamia utricularis, and Fuligo septica. We discovered significant variations in chemotaxis, velocity, and oscillatory behavior of plasmodia among and within these species. Interestingly the patterns of the variations also reflect phylogenetic relationships of the species. In contrast to a common notion, phaneroplasmodia of slime molds develop diverse and specifically organized networks by triggers yet to be explored. This work lays the ground for studying more of these organisms to understand basic features of planar network organization and their variations, which evolved as successful solutions of nature.

A fundamental question regarding biological transport networks is the interplay between the network development or reorganization and the flows it carries. We use Physarum polycephalum, a true slime mould with a transport network which adapts quickly to change of external conditions, as a biological model to make progress in this question. We explore the network formation and reorganization in samples suddenly confined in chambers with ring geometry. Using an image analysis method based on the structure tensor, we quantify the emergence and directionality of the network. We show that confinement induces a reorganization of the network with a typical 104 s timescale, during which veins align circumferentially along the ring. We show that this network evolution relies on local dynamics.

The present work is dedicated to the use of Physarum polycephalum slime mold, an unicellular organism self‐adapting, self‐repairing and self‐repellent, for the realization of elements for unconventional computational systems. Physarum continuously changes its shape under the influence of different stimuli like attractors (food in the most of cases) and repellents (light, temperature, humidity, chemicals), creating optimized networks. Here we introduced a new, softer, element able to influence the motion and the shape of Physarum: the DEFLECTOR. Physarum polycephalum, loaded with magnetic particles and placed under a magnetic field, is conditioned in its active zones routing and shape topology networks. Thus, slime mold can be used as particles carrier and, moreover, it is possible to deflect the mold movement and realize chemical composites in defined places what allows to consider Physarum as a simple version of bio‐robot. On the other hand, we have realized the idea of creating networks with the varied conductivity with the slime mold on polyaniline (PANI) substrates. As the result, it was shown that Physarum growth results in the changing of the conductivity state of PANI layers in different ways, providing negative and positive patterning of the sample.The possibility to control mold's direction with a deflector together with the capability of Physarum to pattern PANI surfaces are the main points of this work. This paper opens new possibilities of the development in many fields and areas from the electrical circuit design and the bio‐actuators (bio‐) robot research, up to the unconventional computing and realization of a novel category of polymer‐mold‐modified. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, we propose a new model for linear fractional programming problem with absolute value functions. The major contribution of this paper is that transformation of linear fractional programming problem into separate linear programming problems with some theorems and then solution of these problems by popular algorithm. This work also used to simplex type algorithms to arrive at an optimal solution for a linear programming problem with absolute value. Moreover, we compare this method with an existing method. Numerical experiments are also given to illustrate the assertions.

Mitochondrial DNA (mtDNA) is highly organized into a compact structure, the mitochondrial nucleoid (mt-nucleoid). To facilitate our understanding of the regulation of mtDNA genetic activity within the mt-nucleoid structure, we have identified a novel mt-nucleoid protein Pmn34 (Physarum polycephalum mitochondrial nucleoid protein 34), having a molecular weight of 34 kDa, from pure mt-nucleoids isolated from the true slime mold, Physarum polycephalum. The Pmn34 protein is composed of 326 amino acids with mitochondrial transit peptides and its primary sequence contains a conserved 3′ to 5′ exonuclease motif of the “DEDD” superfamily. DNA mobility shift assays demonstrated that recombinant Pmn34 binds weakly to both mtDNA and λDNA with no apparent sequence specificity. Furthermore, immunoblotting and immunostaining analyses revealed that Pmn34 localizes specifically in the peripheral region of mt-nucleoids. These results indicate that Pmn34 functions in the peripheral region of mt-nucleoids, suggesting that the mt-nucleoid is compartmentalized into functional domains.

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the Edmonds-Karp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n(m + n log n)) time. Using a standard transformation, this approach yields an O(m log n(m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n2/m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say m′, is much less than m. In this case, the running time of the algorithm is O((m′ + n) log n(m + n log n)).

Individual or cooperation as the producer who produces more than one product always has a problem to determine the amount of each product, as well as the smallest packaging used to generate the maximum revenue but still meet the inventory of existing facilities. If the inventory of facilities and functions form a linear function of income then the problem is called the program a maximu m linear case, where all supplies are limited means of the standard linear program is called maximal. Although the system has available a linear program to solve the problem, the system is only owned by a limited circle, this system also does not provide the smallest packaging option. In general linear programming problem is solved by the simplex method with any number of real output in decimal or fractional format mix. Settlement is not operational because the manufacturers do not always able to make the smallest product packaging in accordance with the unit on completion, to become operational, the results of this settlement may be rounded according to the smallest package selected. The problem of limited manufactures which have a system of linear program application can be overcome by providing a system similar to a web-based applications. This study compiled a web-based application system to solve a standard linear program that generates the maximum revenue that maximum use PHP software, data entered through the form and then taken by the POST method, then set up a matrix, carried out by iterating between the rows in the matrix operations that met the criteria optimal. By ch oosing the smallest packaging which is used 0.25 units or 0.50 units, the system check the number of products that have the smallest rounding according to the package selected, then the system prepare and present the inventory and revenue report. Keywords: Simplex metho; The smallest packaging; Web-based

Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function

In this paper, we propose a method of solving the fully fuzzy linear fractional programming problems, Express all the parameters and variables are triangular fuzzy numbers. Convert all the triangular fuzzy numbers in their parametric form, we convert the fractional programming problem in to a single objective linear programming problem in parametric form. We put new fuzzy arithmetic and fuzzy ranking, we obtain the optimal solution the given fully fuzzy linear fractional programming problem without converting to its equivalent crisp linear programming problem. A numerical example is provided to illustrate the efficiency of the proposed method.

There are two important approaches based on linear ranking functions for solving linear programming problems with cost coefficients as an auxiliary problem to obtain a fuzzy solution of fuzzy variable linear programming problem. The first approach uses the primal simplex method that assumes an initial primal feasible basic solution is at hand. The second approach is based on dual simplex method that begins with a basic dual feasible basic solution and proceeds by pivoting through a series of dual basic solutions until the associated complementary primal basic fuzzy solution is feasible. In this paper, we propose a new method called the primal-dual algorithm, which is similar to the dual simplex method and begins with dual feasibility and proceeds to obtain primal feasibility while maintaining complementary slackness. An important difference between the dual simplex method and the primal-dual method is that the primal-dual algorithm does not require a dual feasible solution to be basic. This algorithm is useful specially for solving minimum fuzzy cost flow problem in which finding an initial dual feasible solution turns out to be a trivial task.

In this paper, an efficient approach is presented to solve fully fuzzy linear fractional programming problems. In this approach, first by Alpha-cuts on the objective function and the constraints, the problem is transforming into a bi-objective linear programming problem, and then the resulting problem is converted into two crisp linear programming problems. A numerical example is presented to illustrate the proposed approach. The obtained results demonstrate the acceptable performance of the proposed solution approach.

The fuzzy set theory is being applied massively in many fields these days. One of these is linear programming problems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzy linear programming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheirfam and Hasani. In this paper, those cases are considered and numerical examples are solved.

A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with α-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, α-level at α = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.