A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP

The difficulty to solve multiple objective combinatorial optimization problems with traditional techniques has urged researchers to look for alternative, better performing approaches for them. Recently, several algorithms have been proposed which are based on the ant colony optimization metaheuristic. In this contribution, the existing algorithms of this kind are reviewed and a proposal of a taxonomy for them is presented. In addition, an empirical analysis is developed by analyzing their performance on several instances of the bi-criteria traveling salesman problem in comparison with two well-known multi-objective genetic algorithms.     

Approximation algorithms for constrained generalized tree alignment problem

In generalized tree alignment problem, we are given a set S of k biologically related sequences and we are interested in a minimum cost evolutionary tree for S. In many instances of this problem partial phylogenetic tree for S is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically relevant minimum cost evolutionary tree. So, we propose the following natural generalization of the generalized tree alignment problem, a problem known to be MAX-SNP Hard, stated as follows:

Constrained Generalized Tree Alignment Problem [S. Divakaran, Algorithms and heuristics for constrained generalized alignment problem, DIMACS Technical Report 2007-21, 2007]: Given a set S of k related sequences and a phylogenetic forest comprising of node-disjoint phylogenetic trees that specify the topological constraints that an evolutionary tree of S needs to satisfy, construct a minimum cost evolutionary tree for S.

In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem. For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of 2−2/k.     

Probabilistic proximity searching algorithms based on compact partitions

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically difficult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms, where it has been shown that one can find 99% of the relevant objects at a fraction of the cost of the exact algorithm. These algorithms are welcome in most applications because resorting to metric space searching already involves a fuzziness in the retrieval requirements. In this paper, we push further in this direction by developing probabilistic algorithms on data structures whose exact versions are the best for high dimensions. As a result, we obtain probabilistic algorithms that are better than the previous ones. We give new insights on the problem and propose a novel view based on time-bounded searching. We also propose an experimental framework for probabilistic algorithms that permits comparing them in offline mode.     

Fast algorithms for identifying maximal common connected sets of interval graphs

Given a family of interval graphs F={G₁=(V,E₁),…,G_k=(V,E_k)} on the same vertices V, a set S⊂V is a maximal common connected set of F if the subgraphs of G_i,1?i?k, induced by S are connected in all G_i and S is maximal for the inclusion order. The maximal general common connected set for interval graphs problem (gen-CCPI) consists in efficiently computing the partition of V in maximal common connected sets of F. This problem has many practical applications, notably in computational biology. Let n=|V| and . For k?2, an algorithm in O((kn+m)logn) time is presented in Habib et al. [Maximal common connected sets of interval graphs, in: Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science, vol. 3109, Springer, Berlin, 2004, pp. 359-372]. In this paper, we improve this bound to O(knlogn+m). Moreover, if the interval graphs are given as k sets of n intervals, which is often the case in bioinformatics, we present a simple time algorithm.     

A comparison of sequential Delaunay triangulation algorithms

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm.

Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.     

A computational comparison of algorithms for the inventory routing problem

The inventory routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Each day a fleet of trucks is dispatched over a set of routes to resupply a subset of the customers. In this paper, we describe and compare algorithms for this problem defined over a short planning period, e.g. one week. These algorithms define the set of customers to be serviced each day and produce routes for a fleet of vehicles to service those customers. Two algorithms are compared in detail, one which first allocates deliveries to days and then solves a vehicle routing problem and a second which treats the multi-day problem as a modified vehicle routing problem. The comparison is based on a set of real data obtained from a propane distribution firm in Pennsylvania. The solutions obtained by both procedures compare quite favorably with those in use by the firm.Part of this work was performed while this author was visiting the University of Waterloo.     

A comparison of heuristic algorithms for cost-oriented assembly line balancing

Two new heuristic algorithms for solving cost-oriented assembly line balancing problems -the Wage-Rate-Method (WR) and the Wage-Rate-Smoothing-Method (WRS) — are presented and compared with two known heuristics — the Positional-Weight-Method (PW) and the Positional-Weight-Wage-Rate-Difference-Method (PWWD) with respect to their solution qualities. Firstly, the heuristics are outlined and their computational effort is stated. Then, a theoretical worst-case bound for the solution quality is given and the results of an extensive performance study are reported. In the study the heuristics were investigated with respect to their solution quality by solving randomly generated line balancing problems and problems from literature. It can be concluded that PWWD and WRS are generally superior to PW and WR.Parts of this research have been supported by the Stiftung Industrieforschung.     

A multi-objective lead time control problem in multi-stage assembly systems using genetic algorithms

In this paper, we develop a multi-objective model to optimally control the lead time of a multi-stage assembly system, using genetic algorithms. The multi-stage assembly system is modelled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The optimal service control is decided at the beginning of the time horizon. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed genetic algorithm approach.     

An experimental comparison of four graph drawing algorithms

In this paper we present an extensive experimental study comparing four general-purpose graph drawing algorithms. The four algorithms take as input general graphs (with no restrictions whatsoever on connectivity, planarity, etc.) and construct orthogonal grid drawings, which are widely used in software and database visualization applications. The test data (available by anonymous ftp) are 11,582 graphs, ranging from 10 to 100 vertices, which have been generated from a core set of 112 graphs used in “real-life” software engineering and database applications. The experiments provide a detailed quantitative evaluation of the performance of the four algorithms, and show that they exhibit trade-offs between “aesthetic” properties (e.g., crossings, bends, edge length) and running time.     

A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms

This paper proposes a new crossover operator called two-part chromosome crossover (TCX) for solving the multiple travelling salesmen problem (MTSP) using a genetic algorithm (GA) for near-optimal solutions. We adopt the two-part chromosome representation technique which has been proven to minimise the size of the problem search space. Nevertheless, the existing crossover method for the two-part chromosome representation has two limitations. Firstly, it has extremely limited diversity in the second part of the chromosome, which greatly restricts the search ability of the GA. Secondly, the existing crossover approach tends to break useful building blocks in the first part of the chromosome, which reduces the GA’s effectiveness and solution quality. Therefore, in order to improve the GA search performance with the two-part chromosome representation, we propose TCX to overcome these two limitations and improve solution quality. Moreover, we evaluate and compare the proposed TCX with three different crossover methods for two MTSP objective functions, namely, minimising total travel distance and minimising longest tour. The experimental results show that TCX can improve the solution quality of the GA compared to three existing crossover approaches.     

Models and algorithms for a staff scheduling problem

We present mathematical models and solution algorithms for a family of staff scheduling problems arising in real life applications. In these problems, the daily assignments to be performed are given and the durations (in days) of the working and rest periods for each employee in the planning horizon are specified in advance, whereas the sequence in which these working and rest periods occur, as well as the daily assignment for each working period, have to be determined. The main objective is the minimization of the number of employees needed to perform all daily assignments in the horizon. We decompose the problem into two steps: the definition of the sequence of working and rest periods (called pattern) for each employee, and the definition of the daily assignment to be performed in each working period by each employee. The first step is formulated as a covering problem for which we present alternative ILP models and exact enumerative algorithms based on these models. Practical experience shows that the best approach is based on the model in which variables are associated with feasible patterns and generated either by dynamic programming or by solving another ILP. The second step is stated as a feasibility problem solved heuristically through a sequence of transportation problems. Although in general this procedure may not find a solution (even if one exists), we present sufficient conditions under which our approach is guaranteed to succeed. We also propose an iterative heuristic algorithm to handle the case in which no feasible solution is found in the second step. We present computational results on real life instances associated with an emergency call center. The proposed approach is able to determine the optimal solution of instances involving up to several hundred employees and a working period of up to 6 months. Mathematics Subject Classification (2000): 90B70, 90C10, 90C27, 90C39, 90C57, 90C59     

Theory and algorithms for linear multiple objective programs with zero–one variables

A new algorithm and theoretical results are presented for linear multiple objective programs with zero–one variables. A procedure to identify strong and weak efficient points as well as an extension of the main problem are analyzed. Extensive computational results are given and several topics for further research are discussed.     

Pareto memetic algorithm for multiple objective optimization with an industrial application

Multiple objective combinatorial optimization problems are difficult to solve and often, exact algorithms are unable to produce optimal solutions. The development of multiple objective heuristics was inspired by the need to quickly produce acceptable solutions. In this paper, we present a new multiple objective Pareto memetic algorithm called PMS^MO. The PMS^MO algorithm incorporates an enhanced fine-grained fitness assignment, a double level archiving process and a local search procedure to improve performance. The performance of PMS^MO is benchmarked against state-of-the-art algorithms using 0–1 multi-dimensional multiple objective knapsack problem from the literature and an industrial scheduling problem from the aluminum industry.     

Using genetic algorithm for dynamic and multiple criteria web-site optimizations

In today’s competitive electronic marketplace, companies try to create long-lasting relations with their online customers. Log files and registration forms generate millions of online transactions. Companies use new techniques to “mine” these data and establish optimal online storefronts to maximize their web presence. Several criteria, such as minimization of download time, maximization of web-site visualization and product association level, can be used for the optimization of virtual storefronts. This paper introduces a genetic algorithm, to be used in a model-driven decision-support system for web-site optimizations. The algorithm ensures multiple criteria web-site optimizations, and the genetic search provides dynamic and timely solutions independent of the number of objects to be arranged.     

A comparison of multiple criteria analysis techniques for water resource management

Multiple criteria analysis (MCA) is a framework for evaluating decision options against multiple criteria. Numerous techniques for solving an MCA problem are available. This paper applies MCA to six water management decision problems. The MCA methods tested include weighted summation, range of value, PROMTHEE II, Evamix and compromise programming. We show that different MCA methods were in strong agreement with high correlations amongst rankings. In the few cases where strong disagreement between MCA methods did occur it was due to presence of mixed ordinal-cardinal data in the evaluation matrix. The results suggest that whilst selection of the MCA technique is important more emphasis is needed on the initial structuring of the decision problem, which involves choosing criteria and decision options.     

Convergence of algorithms for finding eigenvectors

1. IntroductionMethods for finding eigenvectors and eigenvalues of a matrix have importallt applications in colltrol theory, pattern recognition, signal processing and many other fields. Withthese applications the computational methods themselves have been developing rapidly. See[1--4] for some developments.For a square matriX of order n, when n is sufficiently large, it is very difficult to findits eigenvalues directly and one usually uses methods of iteration. Esseniiajly, we can evensac th…     

Separating plane algorithms for convex optimization

The equivalent formulation of a convex optimization problem is the computation of a value of a conjugate function at the origin. The latter can be achieved by approximation of the epigraph of the conjugate function around the origin and gradual refinement of the approximation. This yields a generic algorithm of convex optimization which transforms into some well-known techniques when certain strategies of approximation are employed. It also suggests new algorithmic approaches with promising computational experience and provides a uniform treatment of constrained and unconstrained optimization.     

Optimal algorithms for iterated numerical integration

Iterated (repeated, successive) integration is used for integrating functions satisfying the Lipschitz condition. To construct an optimal (minimax) algorithm, it is necessary to integrate optimally functions evaluated with indefinite errors. Such a problem is solved by generalization of an algorithm from Ref. 1 which is sequentially optimal for one-dimensional problems.     

Randomized and quantum algorithms yield a speed-up for initial-value problems

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration and approximation problems, for which a speed-up is shown in many important cases by quantum computers with respect to deterministic and randomized algorithms on a classical computer. In this paper, we deal with the randomized and quantum complexity of initial-value problems. For this nonlinear problem, we show that both randomized and quantum algorithms yield a speed-up over deterministic algorithms. Upper bounds on the complexity in the randomized and quantum settings are shown by constructing algorithms with a suitable cost, where the construction is based on integral information. Lower bounds result from the respective bounds for the integration problem.