Vertex rankings of chordal graphs and weighted trees

In this paper we consider the vertex ranking problem of weighted trees. We show that this problem is strongly NP-hard. We also give a polynomial-time reduction from the problem of vertex ranking of weighted trees to the vertex ranking of (simple) chordal graphs, which proves that the latter problem is NP-hard. In this way we solve an open problem of Aspvall and Heggernes. We use this reduction and the algorithm of Bodlaender et al.'s for vertex ranking of partial k-trees to give an exact polynomial-time algorithm for vertex ranking of a tree with bounded and integer valued weight functions. This algorithm serves as a procedure in designing a PTAS for weighted vertex ranking problem of trees with bounded weight functions.     

Weighted sum of maximum regrets in an interval MOLP problem

This paper presents a multiobjective linear programming problem with interval objective function coefficients. Considering the concept of maximum regret, the weighted sum problem of maximum regrets is introduced and its properties are investigated. It is proved that an optimal solution of the weighted sum problem of maximum regrets is at least possibly weakly efficient. Further, the circumstances under which the optimal solution is necessarily efficient (necessarily weakly efficient or possibly efficient) are discussed. Moreover, using a relaxation procedure, an algorithm is proposed, which for a given set of weights finds one feasible solution that minimizes the weighted sum of maximum regrets. A numerical example is provided to illustrate the proposed algorithm.     

Median line location problem with positive and negative weights and Euclidean norm

Let n existing facilities be given in the plane. The classical version of the median line location problem asks to find a line L in the plane, so that the sum of the weighted distances from L to all existing facilities is minimized. We consider the semi-obnoxious case, where every point has either a positive or a negative weight. In this paper, we discuss some properties of semi-obnoxious median line location problem with Euclidean norm and propose a particle swarm optimization algorithm for this problem.     

The pos/neg-weighted 1-median problem on tree graphs with subtree-shaped customers

In this paper we consider the pos/neg-weighted median problem on a tree graph where the customers are modeled as continua subtrees. We address the discrete and continuous models, i.e., the subtrees’ boundary points are all vertices, or possibly inner points of an edge, respectively. We consider two different objective functions. If we minimize the overall sum of the minimum weighted distances of the subtrees from the facilities, there exists an optimal solution satisfying a generalized vertex optimality property, e.g., there is an optimal solution such that all facilities are located at vertices or the boundary points of the subtrees. Based on this property we devise a polynomial time algorithm for the pos/neg-weighted 1-median problem on a tree with subtree-shaped customers.     

A two-phase algorithm for the biobjective integer minimum cost flow problem

We present an algorithm to compute a complete set of efficient solutions for the biobjective integer minimum cost flow problem. We use the two phase method, with a parametric network simplex algorithm in phase 1 to compute all non-dominated extreme points. In phase 2, the remaining non-dominated points (non-extreme supported and non-supported) are computed using a k best flow algorithm on single-objective weighted sum problems.     

A clustering method combining differential evolution with the K-means algorithm

The present paper considers the problem of partitioning a dataset into a known number of clusters using the sum of squared errors criterion (SSE). A new clustering method, called DE-KM, which combines differential evolution algorithm (DE) with the well known K-means procedure is described. In the method, the K-means algorithm is used to fine-tune each candidate solution obtained by mutation and crossover operators of DE. Additionally, a reordering procedure which allows the evolutionary algorithm to tackle the redundant representation problem is proposed. The performance of the DE-KM clustering method is compared to the performance of differential evolution, global K-means method, genetic K-means algorithm and two variants of the K-means algorithm. The experimental results show that if the number of clusters K is sufficiently large, DE-KM obtains solutions with lower SSE values than the other five algorithms.     

Spanning trees with minimum weighted degrees

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this problem within a 2−ε factor.     

一种基于目标空间转换权重求和的超多目标进化算法

权重求和是基于分解的超多目标进化算法中常用的方法,相比其他方法具有计算简单、搜索效率高等优点,但难以有效处理帕累托前沿面(Pareto optimal front,PF)为非凸型的问题.为充分发挥权重求和方法的优势,同时又能处理好PF为非凸型的问题,本文提出了一种基于目标空间转换权重求和的超多目标进化算法,简称NSGA...     

Multi-Objective Genetic Algorithms for Vehicle Routing Problem with Time Windows

The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NP-Complete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multi-objective problem and present a genetic algorithm solution using the Pareto ranking technique. We use a direct interpretation of the VRPTW as a multi-objective problem, in which the two objective dimensions are number of vehicles and total cost (distance). An advantage of this approach is that it is unnecessary to derive weights for a weighted sum scoring formula. This prevents the introduction of solution bias towards either of the problem dimensions. We argue that the VRPTW is most naturally viewed as a multi-objective problem, in which both vehicles and cost are of equal value, depending on the needs of the user. A result of our research is that the multi-objective optimization genetic algorithm returns a set of solutions that fairly consider both of these dimensions. Our approach is quite effective, as it provides solutions competitive with the best known in the literature, as well as new solutions that are not biased toward the number of vehicles. A set of well-known benchmark data are used to compare the effectiveness of the proposed method for solving the VRPTW.     

GACRM: A dynamic multi-Attribute decision making approach to large-Scale Web service composition

The problem of QoS-aware Web service composition (QWSC), i.e., how to select from a pool of candidate services to construct a composite service with the best overall QoS performance, is an NP-hard problem. To address a large-scale QWSC problem, a novel method is proposed based on information theory, multi-attribute decision making (MADM) and genetic algorithm. To capture complex judgments, the QWSC problem is formulated into a MADM representation which aims to find acceptable solutions assessed by multiple QoS attributes with varying distributions. To solve the MADM problem for QWSC, each QoS attribute is weighted in both a priori, subjective perspective and a posteriori, information-based perspective based on the discriminative capability of QoS attributes for a dynamic pool of candidate services. Furthermore, to solve the large-scale QWSC problem that conventional MADM methods cannot navigate, we develop a GACRM algorithm by integrating genetic algorithm (GA) with Compromise Ratio Method (CRM). Experiments demonstrate that GACRM obtains nearly the same solution ranking by the CRM but scales much better in terms of computation time for large-scale QWSC problems.     

Exact and Approximation Algorithms for Geometric and Capacitated Set Cover Problems

First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general (non-necessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets. We show that any polynomial-time algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r+1.357. In particular, the composition of these two results yields a polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio?2.357. This substantially improves on the best known approximation ratio for the latter antenna problem equal to?3. Furthermore, we provide a PTAS for the dual problem where the number of sets (e.g., antennas) to use is fixed and the task is to minimize the maximum set load, in case the sets correspond to line intervals or arcs. Finally, we discuss the approximability of the generalization of the antenna problem to include several base stations for antennas, and in particular show its APX-hardness already in the uncapacitated case.     

An efficient search direction for linear programming problems

In this paper, we present an auxiliary algorithm, in terms of the speed of obtaining the optimal solution, that is effective in helping the simplex method for commencing a better initial basic feasible solution. The idea of choosing a direction towards an optimal point presented in this paper is new and easily implemented. From our experiments, the algorithm will release a corner point of the feasible region within few iterative steps, independent of the starting point. The computational results show that after the auxiliary algorithm is adopted as phase I process, the simplex method consistently reduce the number of required iterations by about 40%.Scope and purposeRecent progress in the implementations of simplex and interior point methods as well as advances in computer hardware has extended the capability of linear programming with today's computing technology. It is well known that the solution times for the interior point method improve with problem size. But, experimental evidence suggests that interior point methods dominate simplex-based methods only in the solution of very large scale linear programs. If the problem size is medium, how to combine the best features of these two methods to produce an effective algorithm for solving linear programming problems is still an interesting problem. In this research we present a new effective ε-optimality search direction based on the interior point method to start an initial basic feasible solution near the optimal point for the simplex method.     

On best response dynamics in weighted congestion games with polynomial delays

We investigate the speed of convergence of best response dynamics to approximately optimal solutions in weighted congestion games with polynomial delay functions. Awerbuch et?al. (Fast convergence to nearly optimal solutions in potential games. ACM Conference on Electronic Commerce, 2008) showed that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players n even for unweighted players and linear delay functions. Nevertheless, we show that ??(n log log W) (where W is the sum of all the players?? weights) best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every O(n) steps each player performs a constant (and non-null) number of best responses. For congestion games in which computing a best response is a polynomial time solvable problem, such a dynamics naturally implies a polynomial time distributed algorithm for the problem of computing the social optimum in congestion games, approximating the optimal solution by a constant factor.     

Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval

In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the weighted sum of completion times. No polynomial 2-approximation algorithm for this problem has been previously known. We propose a 2-approximation algorithm with O(n²) time complexity where n is the number of jobs. We show that this bound is tight. The obtained result outperforms all the previous polynomial approximation algorithms for this problem.     

Coordinate descent with arbitrary sampling I: algorithms and complexity†

We study the problem of minimizing the sum of a smooth convex function and a convex block-separable regularizer and propose a new randomized coordinate descent method, which we call ALPHA. Our method at every iteration updates a random subset of coordinates, following an arbitrary distribution. No coordinate descent methods capable to handle an arbitrary sampling have been studied in the literature before for this problem. ALPHA is a very flexible algorithm: in special cases, it reduces to deterministic and randomized methods such as gradient descent, coordinate descent, parallel coordinate descent and distributed coordinate descent—both in nonaccelerated and accelerated variants. The variants with arbitrary (or importance) sampling are new. We provide a complexity analysis of ALPHA, from which we deduce as a direct corollary complexity bounds for its many variants, all matching or improving best known bounds.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.     

Outcome aware ranking in value creation networks

In this paper, we consider a natural ranking problem that arises in settings in which a community of people (or agents) are engaged in regular interactions with an end goal of creating value. Examples of such scenarios are academic collaboration networks, creative collaborations, and interactions between agents of a service delivery organization. For instance, consider a service delivery organization which essentially resolves a sequence of service requests from its customers by deploying its agents to resolve the requests. Typically, resolving a request requires interaction between multiple agents and results in an outcome (or value). The outcome could be success or failure of problem resolution or an index of customer satisfaction. For this scenario, the ranking of the agents of the network should take into account two aspects: importance of the agents in the network structure that arises as a result of interactions and the value generated by the interactions involving the respective agents. Such a ranking can be used for several purposes such as identifying influential agents of the interaction network, effective and efficient spreading of messages in the network. In this paper, we formally model the above ranking problem and develop a novel algorithm for computing the ranking. The key aspect of our approach is creating special nodes in the interaction network corresponding to the outcomes and endowing them independent, external status. The algorithm then iteratively spreads the external status of the outcomes to the agents based on their interactions and the outcome of those interactions. This results in an eigenvector like formulation, which results in a method requiring computing the inverse of a matrix rather than the eigenvector. We present several theoretical characterizations of our algorithmic approach. We present experimental results on the public domain real-life datasets from the Internet Movie Database and a dataset constructed by retrieving impact and citation ratings for papers listed in the DBLP database.     

The single facility location problem with minimum distance constraints

We consider the problem of locating a single facility (server) in the plane, where the location of the facility is restricted to be outside a specified forbidden region (neighborhood) around each demand point. Two models are discussed. In the restricted 1-median model, the objective is to minimize the sum of the weighted rectilinear distances from the n customers to the facility. We present an O(n log n) algorithm for this model, improving upon the O(n³) complexity bound of the algorithm by Brimberg and Wesolowsky (1995). In the restricted 1-center model the objective is to minimize the maximum of the weighted rectilinear distances between the customers and the serving facility. We present an O(n log n) algorithm for finding an optimal 1-center. We also discuss some related models, involving the Euclidean norm.     

Solving a single-machine scheduling problem with maintenance,job deterioration and learning effect by simulated annealing

This paper presents a new nonlinear multi-objective mathematical model for a single-machine scheduling problem with three objectives: (1) minimizing the sum of the weighted jobs completion, (2) minimizing the sum of the weighted delay times, and (3) maximizing the sum of the job values in makespan. In addition, a number of constraints are incorporated in this presented model, such as repairing and maintenance periods, deterioration of jobs, and learning effect of the work process. Since this type of scheduling problem belongs to a class of NP-hard ones, its solution by common software packages is almost impossible, or at best very time consuming. Thus, a meta-heuristic algorithm based on simulated annealing (SA) is proposed to solve such a hard problem. At a final stage, the related results obtained by the proposed SA are compared with those results reported by the Lingo 8 software in order to demonstrate the efficiency and capability of our proposed SA algorithm.     

Glowworm swarm optimization algorithm with topsis for solving multiple objective environmental economic dispatch problem

A new glowworm swarm optimization (GSO) algorithm is proposed to find the optimal solution for multiple objective environmental economic dispatch (MOEED) problem. In this proposed approach, technique for order preference similar to an ideal solution (TOPSIS) is employed as an overall fitness ranking tool to evaluate the multiple objectives simultaneously. In addition, a time varying step size is incorporated in the GSO algorithm to get better performance. Finally, to evaluate the feasibility and effectiveness of the proposed combination of GSO algorithm with TOPSIS (GSO–T) approach is examined in four different test cases. Simulation results have revealed the capabilities of the proposed GSO–T approach to find the optimal solution for MOEED problem. The comparison with own coded weighted sum method incorporated GSO (WGSO) and other methods reported in literatures exhibit the superiority of the proposed GSO–T approach and also the results confirm the potential of the proposed GSO–T approach to solve the MOEED problem.