Using genetic algorithm and TOPSIS technique for multiobjective transportation problem: a hybrid approach

A hybrid approach to solve the multiobjective transportation problem (TP) is presented. The TP as a special type of the network optimization problems that has the special data structure in solution characterized as transportation graph. In encoding TP, we introduce a new chromosome's structure which is adopted as it is capable of representing all possible feasible solutions. Also, in order to keep the feasibility of the chromosome, the crossover and the mutation were modified. The proposed approach maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ?-dominance. Moreover, to help the decision maker to extract the best compromise solution from a finite set of alternatives, a technique for order performance by similarity to ideal solution (TOPSIS) method is adopted. Numerical simulations show the effectiveness and efficiency of the proposed approach.     

A distance measure for large graphs based on prime graphs

Graphs are universal modeling tools. They are used to represent objects and their relationships in almost all domains: they are used to represent DNA, images, videos, social networks, XML documents, etc. When objects are represented by graphs, the problem of their comparison is a problem of comparing graphs. Comparing objects is a key task in our daily life. It is the core of a search engine, the backbone of a mining tool, etc. Nowadays, comparing objects faces the challenge of the large amount of data that this task must deal with. Moreover, when graphs are used to model these objects, it is known that graph comparison is very complex and computationally hard especially for large graphs. So, research on simplifying graph comparison gainedan interest and several solutions are proposed. In this paper, we explore and evaluate a new solution for the comparison of large graphs. Our approach relies on a compact encoding of graphs called prime graphs. Prime graphs are smaller and simpler than the original ones but they retain the structure and properties of the encoded graphs. We propose to approximate the similarity between two graphs by comparing the corresponding prime graphs. Simulations results show that this approach is effective for large graphs.     

具有大量不规则障碍物的环境下机器人路径规划的一种新型遗传算法

具有大量不规则障碍物的环境下的机器人路径规划问题是一个典型的非线性问题.目前已有多种求解该问题的遗传算法,但这些算法在初始种群的产生和特定遗传算子的构造选取等方面存在着一些不足.为了克服这些缺陷,提出了一种新型的遗传算法.算法采用了折线变长编码方案,使用随机指导式搜索策略来生成初始种群,并设计了特殊的交叉和变异算子.实际的仿真实例验证了算法的正确性和高效性.􀁱     

An Immune-based Genetic Algorithm with Reduced Search Space Coding for Multiprocessor Task Scheduling Problem

Multiprocessor task scheduling is an important problem in parallel applications and distributed systems. In this way, solving the multiprocessor task scheduling problem (MTSP) by heuristic, meta-heuristic, and hybrid algorithms have been proposed in literature. Although the problem has been addressed by many researchers, challenges to improve the convergence speed and the reliability of methods for solving the problem are still continued especially in the case that the communication cost is added to the problem frame work. In this paper, an Immune-based Genetic algorithm (IGA), a meta-heuristic approach, with a new coding scheme is proposed to solve MTSP. It is shown that the proposed coding reduces the search space of MTSP in many practical problems, which effectively influences the convergence speed of the optimization process. In addition to the reduced search space offered by the proposed coding that eventuate in exploring better solutions at a shorter time frame, it guarantees the validity of solutions by using any crossover and mutation operators. Furthermore, to overcome the regeneration phenomena in the proposed GA (generating similar chromosomes) which leads to premature convergence, an affinity based approach inspired from Artificial Immune system is employed which results in better exploration in the searching process. Experimental results showed that the proposed IGA surpasses related works in terms of found makespan (20% improvement in average) while it needs less iterations to find the solutions (90% improvement in average) when it is applied to standard test benches.     

Computing minimal doubly resolving sets of graphs

In this paper we consider the minimal doubly resolving sets problem (MDRSP) of graphs. We prove that the problem is NP-hard and give its integer linear programming formulation. The problem is solved by a genetic algorithm (GA) that uses binary encoding and standard genetic operators adapted to the problem. Experimental results include three sets of ORLIB test instances: crew scheduling, pseudo-boolean and graph coloring. GA is also tested on theoretically challenging large-scale instances of hypercubes and Hamming graphs. Optimality of GA solutions on smaller size instances has been verified by total enumeration. For several larger instances optimality follows from the existing theoretical results. The GA results for MDRSP of hypercubes are used by a dynamic programming approach to obtain upper bounds for the metric dimension of large hypercubes up to 2⁹⁰$2^{90}$ nodes, that cannot be directly handled by the computer.     

Graphillion: software library for very large sets of labeled graphs

Several graph libraries have been developed in the past few decades, and they were basically designed to work with a few graphs. However, there are many problems in which we have to consider all subgraphs satisfying certain constraints on a given graph. Since the number of subgraphs can increase exponentially with the graph size, explicitly representing these sets is infeasible. Hence, libraries concerned with efficiently representing a single graph instance are not suitable for such problems. In this paper, we develop Graphillion, a software library for very large sets of (vertex-)labeled graphs, based on zero-suppressed binary decision diagrams. Graphillion is not based on a traditional representation of graphs. Instead, a graph set is simply regarded as a “set of edge sets” ignoring vertices, which allows us to employ powerful tools of a “family of sets” (a set of sets) and permits large graph sets to be handled efficiently. We also utilize advanced graph enumeration algorithms, which enable the simple family tools to understand the graph structure. Graphillion is implemented as a Python library to encourage easy development of its applications, without introducing significant performance overheads. In experiments, we consider two case studies, a puzzle solver and a power network optimizer, in which several operations and heavy optimization have to be performed over very large sets of constrained graphs (i.e., cycles or forests with complicated conditions). The results show that Graphillion allows us to manage a huge number of graphs with very low development effort.     

一般图中的最小概要表示集问题

在一般图中,通常基于图的拓扑结构来刻画任意2个节点之间的相似度。基于节点相似度提出概要表示集SRS的概念,从图中寻找最少节点数的概要表示集称为最小概要表示集问题。证明了在一般图中求解最小概要表示集问题是NP (非确定性多项式)难的,不太可能存在多项式时间复杂度的精确算法。基于次模函数提出了多项式时间复杂度的贪心近似算法,用于求解最小概要表示集问题,得出近似比结果。     

A hybrid algorithmic model for the minimum weight dominating set problem

Iterated greedy algorithms belong to the class of stochastic local search methods. They are based on the simple and effective principle of generating a sequence of solutions by iterating over a constructive greedy heuristic using destruction and construction phases. This paper, first, presents an efficient randomized iterated greedy approach for the minimum weight dominating set problem, where—given a vertex-weighted graph—the goal is to identify a subset of the graphs’ vertices with minimum total weight such that each vertex of the graph is either in the subset or has a neighbor in the subset. Our proposed approach works on a population of solutions rather than on a single one. Moreover, it is based on a fast randomized construction procedure making use of two different greedy heuristics. Secondly, we present a hybrid algorithmic model in which the proposed iterated greedy algorithm is combined with the mathematical programming solver CPLEX. In particular, we improve the best solution provided by the iterated greedy algorithm with the solution polishing feature of CPLEX. The simulation results obtained on a widely used set of benchmark instances shows that our proposed algorithms outperform current state-of-the-art approaches.     

An optimal algorithm for solving the searchlight guarding problem on weighted two-terminal series-parallel graphs

In this paper, we consider a graph problem on a connected weighted undirected graph, called the searchlight guarding problem. Our problem is an extension of so-called graph searching/guarding problem by considering the time slot parameter in addition to the traditional building cost. Suppose that there is a fugitive who moves along the edges of the graph at any speed. We want to place a set of searchlights at the vertices to search the edges of the graph and capture the fugitive. It costs some building cost to place a searchlight at some vertex. The searchlight guarding problem is to allocate a set S of searchlights at the vertices such that the total costs of the vertices in S is minimized. If there is more than one set of searchlights with the minimum building cost, then find the one with the minimum searching time, that is, the time slots needed to capture the fugitive is the minimum. The problem is known to be NP-hard on weighted bipartite graphs, split graphs, and chordal graphs; and it is linear time solvable on weighted trees and interval graphs. In this paper, an algorithm is designed to solve the problem on weighted two-terminal series-parallel graphs. It works on the parsing tree structure of the given two-terminal series-parallel graph. The algorithm is divided into two phases. In the phase one, we first extract some useful properties of optimal solutions. Employing these properties, an algorithm is designed to find the set of searchlights with the minimum guarding cost and to assign the searching directions of all edges by the dynamic programming strategy. In the phase two, the searched time slots of all edges are determined by the breadth-first-search from the root of the parsing tree. The time complexities of both phases are linear. Thus, our algorithm is time optimal. Received: 12 March 1996 / 27 May 1997     

Querying massive graph data: A compress and search approach

Querying graph data is a fundamental problem that witnesses an increasing interest especially for massive graph databases which come as a promising alternative to relational databases for big data modeling. In this paper, we study the problem of subgraph isomorphism search which consists to enumerate the embedding of a query graph in a data graph. The most known solutions of this NP-complete problem are backtracking-based and result in a high computational cost when we deal with massive graph databases. We address this problem and its challenges via graph compression with modular decomposition. In our approach, subgraph isomorphism search is performed on compressed graphs without decompressing them yielding substantial reduction of the search space and consequently a significant saving in processing time as well as in storage space for the graphs. We evaluated our algorithms on nine real-word datasets. The experimental results show that our approach is efficient and scalable.     

Neural network for optimal steiner tree computation

Hopfield neural network model for finding the shortest path between two nodes in a graph was proposed recently in some literatures. In this paper, we present a modified version of Hopfield model to a more general problem of searching an optimal tree (least total cost tree) from a source node to a number of destination nodes in a graph. This problem is called Steiner tree in graph theory, where it is proved to be a NP-complete. Through computer simulations, it is shown that the proposed model could always find an optimal or near-optimal valid solution in various graphs.     

Spanning tree-based genetic algorithm for bicriteria transportation problem

In this paper, we present a new approach which is spanning tree-based genetic algorithm for bicriteria transportation problem. The transportation problem have the special data structure in solution characterized as a spanning tree. In encoding transportation problem, we introduce one of node encoding which is adopted as it is capable of equally and uniquely representing all possible basic solutions. The crossover and mutation was designed based on this encoding. And we designed the criterion that chromosome always feasibility converted to a transportation tree. In the evolutionary process, the mixed strategy and roulette wheel selection is used. Numerical experiments will be shown the effectiveness and efficiency of the proposed algorithm.     

Approximation of graph edit distance based on Hausdorff matching

Graph edit distance is a powerful and flexible method for error-tolerant graph matching. Yet it can only be calculated for small graphs in practice due to its exponential time complexity when considering unconstrained graphs. In this paper we propose a quadratic time approximation of graph edit distance based on Hausdorff matching. In a series of experiments we analyze the performance of the proposed Hausdorff edit distance in the context of graph classification and compare it with a cubic time algorithm based on the assignment problem. Investigated applications include nearest neighbor classification of graphs representing letter drawings, fingerprints, and molecular compounds as well as hidden Markov model classification of vector space embedded graphs representing handwriting. In many cases, a substantial speedup is achieved with only a minor loss in accuracy or, in one case, even with a gain in accuracy. Overall, the proposed Hausdorff edit distance shows a promising potential in terms of flexibility, efficiency, and accuracy.     

Multihierarchical graph search

The use of hierarchical graph searching for finding paths in graphs is well known in the literature, providing better results than plain graph searching, with respect to computational costs, in many cases. This paper offers a step forward by including multiple hierarchies in a graph-based model. Such a multi-hierarchical model has the following advantages: First, a multiple hierarchy permits us to choose the best hierarchy to solve each search problem; second, when several search problems have to be solved, a multiple hierarchy provides the possibility of solving some of them simultaneously; and third, solutions to the search problems can be expressed in any of the hierarchies of the multiple hierarchy, which allows us to represent the information in the most suitable way for each specific purpose. In general, multiple hierarchies have proven to be a more adaptable model than single-hierarchy or non-hierarchical models. This paper formalizes the multi-hierarchical model, describes the techniques that have been designed for taking advantage of multiple hierarchies in a hierarchical path search, and presents some experiments and results on the performance of these techniques     

A linear programming approach for the weighted graph matchingproblem

A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L₁ norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian method on the real solutions of the linear program. The complexity of the proposed algorithm is polynomial time, and it is O(n ⁶L) for matching graphs of size n. The developed algorithm is compared to two other algorithms. One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods     

Evolutionary truss topology optimization using a graph-based parameterization concept

A novel parameterization concept for the optimization of truss structures by means of evolutionary algorithms is presented. The main idea is to represent truss structures as mathematical graphs and directly apply genetic operators, i.e., mutation and crossover, on them. For this purpose, new genetic graph operators are introduced, which are combined with graph algorithms, e.g., Cuthill–McKee reordering, to raise their efficiency. This parameterization concept allows for the concurrent optimization of topology, geometry, and sizing of the truss structures. Furthermore, it is absolutely independent from any kind of ground structure normally reducing the number of possible topologies and sometimes preventing innovative design solutions. A further advantage of this parameterization concept compared to traditional encoding of evolutionary algorithms is the possibility of handling individuals of variable size. Finally, the effectiveness of the concept is demonstrated by examining three numerical examples.     

Graph-based evolutionary design of arithmetic circuits

We present an efficient graph-based evolutionary optimization technique, called evolutionary graph generation (EGG), and the proposed approach is applied to the design of combinational and sequential arithmetic circuits based on parallel counter-tree architecture. The fundamental idea of EGG is to employ general circuit graphs as individuals and manipulate the circuit graphs directly using new evolutionary graph operations without encoding the graphs into other indirect representations, such as the bit strings used in genetic algorithm (GA) proposed by Holland (1992) and trees used in genetic programming (GP) proposed by Koza et al. (1997). In this paper, the EGG system is applied to the design of constant-coefficient multipliers and the design of bit-serial data-parallel adders. The results demonstrate the potential capability of EGG to solve the practical design problems for arithmetic circuits with limited knowledge of computer arithmetic algorithms. The proposed EGG system can help to simplify and speed up the process of designing arithmetic circuits and can produce better solutions to the given problem     

A constant approximation algorithm for the densest k-subgraph problem on chordal graphs

The densest k-subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The DkS problem is NP-hard even for special graph classes including bipartite, planar, comparability and chordal graphs, while no constant approximation algorithm is known for any of these classes. In this paper we present a 3-approximation algorithm for the class of chordal graphs. The analysis of our algorithm is based on a graph theoretic lemma of independent interest.     

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of graph. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory.