Showing papers on "Heuristic (computer science) published in 2009"

Sensor Selection via Convex Optimization

Abstract: We consider the problem of choosing a set of k sensor measurements, from a set of m possible or potential sensor measurements, that minimizes the error in estimating some parameters. Solving this problem by evaluating the performance for each of the (m k) possible choices of sensor measurements is not practical unless m and k are small. In this paper, we describe a heuristic, based on convex optimization, for approximately solving this problem. Our heuristic gives a subset selection as well as a bound on the best performance that can be achieved by any selection of k sensor measurements. There is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small; but numerical experiments suggest that the gap is small in many cases. Our heuristic method requires on the order of m 3 operations; for m= 1000 possible sensors, we can carry out sensor selection in a few seconds on a 2-GHz personal computer.

Virtual Network Embedding with Coordinated Node and Link Mapping

Abstract: Recently network virtualization has been proposed as a promising way to overcome the current ossification of the Internet by allowing multiple heterogeneous virtual networks (VNs) to coexist on a shared infrastructure. A major challenge in this respect is the VN embedding problem that deals with efficient mapping of virtual nodes and virtual links onto the substrate network resources. Since this problem is known to be NP-hard, previous research focused on designing heuristic-based algorithms which had clear separation between the node mapping and the link mapping phases. This paper proposes VN embedding algorithms with better coordination between the two phases. We formulate the VN embedding problem as a mixed integer program through substrate network augmentation. We then relax the integer constraints to obtain a linear program, and devise two VN embedding algorithms D-ViNE and R-ViNE using deterministic and randomized rounding techniques, respectively. Simulation experiments show that the proposed algorithms increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network in the long run.

The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm

Abstract: A natural river often finds good paths among lots of possible paths in its ways from the source to destination. These near optimal or optimal paths are obtained by the actions and reactions that occur among the water drops and the water drops with the riverbeds. The intelligent water drops (IWD) algorithm is a new swarm-based optimisation algorithm inspired from observing natural water drops that flow in rivers. In this paper, the IWD algorithm is tested to find solutions of the n-queen puzzle with a simple local heuristic. The travelling salesman problem (TSP) is also solved with a modified IWD algorithm. Moreover, the IWD algorithm is tested with some more multiple knapsack problems (MKP) in which near-optimal or optimal solutions are obtained.

Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation

Abstract: In the Motion Planning research field, heuristic methods have demonstrated to outperform classical approaches gaining popularity in the last 35 years. Several ideas have been proposed to overcome the complex nature of this NP-Complete problem. Ant Colony Optimization algorithms are heuristic methods that have been successfully used to deal with this kind of problems. This paper presents a novel proposal to solve the problem of path planning for mobile robots based on Simple Ant Colony Optimization Meta-Heuristic (SACO-MH). The new method was named SACOdm, where d stands for distance and m for memory. In SACOdm, the decision making process is influenced by the existing distance between the source and target nodes; moreover the ants can remember the visited nodes. The new added features give a speed up around 10 in many cases. The selection of the optimal path relies in the criterion of a Fuzzy Inference System, which is adjusted using a Simple Tuning Algorithm. The path planner application has two operating modes, one is for virtual environments, and the second one works with a real mobile robot using wireless communication. Both operating modes are global planners for plain terrain and support static and dynamic obstacle avoidance.

General k-opt submoves for the Lin–Kernighan TSP heuristic

Abstract: Local search with k-exchange neighborhoods, k-opt, is the most widely used heuristic method for the traveling salesman problem (TSP). This paper presents an effective implementation of k-opt in LKH-2, a variant of the Lin–Kernighan TSP heuristic. The effectiveness of the implementation is demonstrated with experiments on Euclidean instances ranging from 10,000 to 10,000,000 cities. The runtime of the method increases almost linearly with the problem size. LKH-2 is free of charge for academic and non-commercial use and can be downloaded in source code.

Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming

Abstract: This paper presents a novel approach to generate data-driven regression models that not only give reliable prediction of the observed data but also have smoother response surfaces and extra generalization capabilities with respect to extrapolation. These models are obtained as solutions of a genetic programming (GP) process, where selection is guided by a tradeoff between two competing objectives - numerical accuracy and the order of nonlinearity. The latter is a novel complexity measure that adopts the notion of the minimal degree of the best-fit polynomial, approximating an analytical function with a certain precision. Using nine regression problems, this paper presents and illustrates two different strategies for the use of the order of nonlinearity in symbolic regression via GP. The combination of optimization of the order of nonlinearity together with the numerical accuracy strongly outperforms ldquoconventionalrdquo optimization of a size-related expressional complexity and the accuracy with respect to extrapolative capabilities of solutions on all nine test problems. In addition to exploiting the new complexity measure, this paper also introduces a novel heuristic of alternating several optimization objectives in a 2-D optimization framework. Alternating the objectives at each generation in such a way allows us to exploit the effectiveness of 2-D optimization when more than two objectives are of interest (in this paper, these are accuracy, expressional complexity, and the order of nonlinearity). Results of the experiments on all test problems suggest that alternating the order of nonlinearity of GP individuals with their structural complexity produces solutions that are both compact and have smoother response surfaces, and, hence, contributes to better interpretability and understanding.

MAPEL: Achieving global optimality for a non-convex wireless power control problem

Abstract: Achieving weighted throughput maximization (WTM) through power control has been a long standing open problem in interference-limited wireless networks. The complicated coupling between the mutual interferences of links gives rise to a non-convex optimization problem. Previous work has considered the WTM problem in the high signal to interference-and-noise ratio (SINR) regime, where the problem can be approximated and transformed into a convex optimization problem through proper change of variables. In the general SINR regime, however, the approximation and transformation approach does not work. This paper proposes an algorithm, MAPEL, which globally converges to a global optimal solution of the WTM problem in the general SINR regime. The MAPEL algorithm is designed based on three key observations of the WTM problem: (1) the objective function is monotonically increasing in SINR, (2) the objective function can be transformed into a product of exponentiated linear fraction functions, and (3) the feasible set of the equivalent transformed problem is always ldquonormalrdquo, although not necessarily convex. The MAPEL algorithm finds the desired optimal power control solution by constructing a series of polyblocks that approximate the feasible SINR region in an increasing precision. Furthermore, by tuning the approximation factor in MAPEL, we could engineer a desirable tradeoff between optimality and convergence time. MAPEL provides an important benchmark for performance evaluation of other heuristic algorithms targeting the same problem. With the help of MAPEL, we evaluate the performance of several existing algorithms through extensive simulations.

Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO

Abstract: In this paper an improved coordinated aggregation-based particle swarm optimization (ICA-PSO) algorithm is introduced for solving the optimal economic load dispatch (ELD) problem in power systems. In the ICA-PSO algorithm each particle in the swarm retains a memory of its best position ever encountered, and is attracted only by other particles with better achievements than its own with the exception of the particle with the best achievement, which moves randomly. Moreover, the population size is increased adaptively, the number of search intervals for the particles is selected adaptively and the particles search the decision space with accuracy up to two digit points resulting in the improved convergence of the process. The ICA-PSO algorithm is tested on a number of power systems, including the systems with 6, 13, 15, and 40 generating units, the island power system of Crete in Greece and the Hellenic bulk power system, and is compared with other state-of-the-art heuristic optimization techniques (HOTs), demonstrating improved performance over them.

Tighter Approximated MILP Formulations for Unit Commitment Problems

Abstract: The short-term unit commitment (UC) problem in hydrothermal power generation is a large-scale, mixed-integer nonlinear program, which is difficult to solve efficiently, especially for large-scale instances. It is possible to approximate the nonlinear objective function of the problem by means of piecewise-linear functions, so that UC can be approximated by an mixed-integer linear program (MILP); applying the available efficient general-purpose MILP solvers to the resulting formulations, good quality solutions can be obtained in a relatively short amount of time. We build on this approach, presenting a novel way to approximating the nonlinear objective function based on a recently developed class of valid inequalities for the problem, called ldquoperspective cuts.rdquo At least for many realistic instances of a general basic formulation of UC, an MILP-based heuristic obtains comparable or slightly better solutions in less time when employing the new approach rather than the standard piecewise linearizations, while being not more difficult to implement and use. Furthermore, ldquodynamicrdquo formulations, whereby the approximation is iteratively improved, provide even better results if the approximation is appropriately controlled.

Species tree inference by minimizing deep coalescences.

Abstract: In a 1997 seminal paper, W Maddison proposed minimizing deep coalescences, or MDC, as an optimization criterion for inferring the species tree from a set of incongruent gene trees, assuming the incongruence is exclusively due to lineage sorting In a subsequent paper, Maddison and Knowles provided and implemented a search heuristic for optimizing the MDC criterion, given a set of gene trees However, the heuristic is not guaranteed to compute optimal solutions, and its hill-climbing search makes it slow in practice In this paper, we provide two exact solutions to the problem of inferring the species tree from a set of gene trees under the MDC criterion In other words, our solutions are guaranteed to find the tree that minimizes the total number of deep coalescences from a set of gene trees One solution is based on a novel integer linear programming (ILP) formulation, and another is based on a simple dynamic programming (DP) approach Powerful ILP solvers, such as CPLEX, make the first solution appealing, particularly for very large-scale instances of the problem, whereas the DP-based solution eliminates dependence on proprietary tools, and its simplicity makes it easy to integrate with other genomic events that may cause gene tree incongruence Using the exact solutions, we analyze a data set of 106 loci from eight yeast species, a data set of 268 loci from eight Apicomplexan species, and several simulated data sets We show that the MDC criterion provides very accurate estimates of the species tree topologies, and that our solutions are very fast, thus allowing for the accurate analysis of genome-scale data sets Further, the efficiency of the solutions allow for quick exploration of sub-optimal solutions, which is important for a parsimony-based criterion such as MDC, as we show We show that searching for the species tree in the compatibility graph of the clusters induced by the gene trees may be sufficient in practice, a finding that helps ameliorate the computational requirements of optimization solutions Further, we study the statistical consistency and convergence rate of the MDC criterion, as well as its optimality in inferring the species tree Finally, we show how our solutions can be used to identify potential horizontal gene transfer events that may have caused some of the incongruence in the data, thus augmenting Maddison's original framework We have implemented our solutions in the PhyloNet software package, which is freely available at: http://bioinfocsriceedu/phylonet

An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization

Abstract: Many forecasting models based on the concept of fuzzy time series have been proposed in the past decades. Two main factors, which are the lengths of intervals and the content of forecast rules, impact the forecasted accuracy of the models. How to find the proper content of the main factors to improve the forecasted accuracy has become an interesting research topic. Some forecasting models, which combined heuristic methods or evolutionary algorithms (such as genetic algorithms and simulated annealing) with the fuzzy time series, have been proposed but their results are not satisfied. In this paper, we use the particle swarm optimization to find the proper content of the main factors. A new hybrid forecasting model which combined particle swarm optimization with fuzzy time series is proposed to improve the forecasted accuracy. The experimental results of forecasting enrollments of students of the University of Alabama show that the new model is better than any existing models, and it can get better quality solutions based on the first-order and the high-order fuzzy time series, respectively.

Cost minimization while satisfying hard/soft timing constraints for heterogeneous embedded systems

Abstract: In high-level synthesis for real-time embedded systems using heterogeneous functional units (FUs), it is critical to select the best FU type for each task. However, some tasks may not have fixed execution times. This article models each varied execution time as a probabilistic random variable and solves heterogeneous assignment with probability (HAP) problem. The solution of the HAP problem assigns a proper FU type to each task such that the total cost is minimized while the timing constraint is satisfied with a guaranteed confidence probability. The solutions to the HAP problem are useful for both hard real-time and soft real-time systems. Optimal algorithms are proposed to find the optimal solutions for the HAP problem when the input is a tree or a simple path. Two other algorithms, one is optimal and the other is near-optimal heuristic, are proposed to solve the general problem. The experiments show that our algorithms can effectively reduce the total cost while satisfying timing constraints with guaranteed confidence probabilities. For example, our algorithms achieve an average reduction of 33.0p on total cost with 0.90 confidence probability satisfying timing constraints compared with the previous work using worst-case scenario.

Memetic Algorithm With Extended Neighborhood Search for Capacitated Arc Routing Problems

Abstract: The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely Merge-Split (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of state-of-the-art algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.

Objective reduction in evolutionary multiobjective optimization: Theory and applications

Abstract: Many-objective problems represent a major challenge in the field of evolutionary multiobjective optimization---in terms of search efficiency, computational cost, decision making, visualization, and so on. This leads to various research questions, in particular whether certain objectives can be omitted in order to overcome or at least diminish the difficulties that arise when many, that is, more than three, objective functions are involved. This study addresses this question from different perspectives. First, we investigate how adding or omitting objectives affects the problem characteristics and propose a general notion of conflict between objective sets as a theoretical foundation for objective reduction. Second, we present both exact and heuristic algorithms to systematically reduce the number of objectives, while preserving as much as possible of the dominance structure of the underlying optimization problem. Third, we demonstrate the usefulness of the proposed objective reduction method in the context of both decision making and search for a radar waveform application as well as for well-known test functions.

Exact Multiple-Control Toffoli Network Synthesis With SAT Techniques

Abstract: Synthesis of reversible logic has become a very important research area in recent years. Applications can be found in the domain of low-power design, optical computing, and quantum computing. In the past, several approaches have been introduced that synthesize reversible networks with respect to a given function. Most of these methods only approximate a minimal network representation. In this paper, exact algorithms for the synthesis of multiple-control Toffoli networks are presented, i.e., algorithms that guarantee to find a network with the minimal number of gates. Our iterative algorithms formulate the synthesis problem as a sequence of decision problems. The decision problems are encoded as Boolean satisfiability (SAT) or SAT modulo theory (SMT) instances, respectively. As soon as one of these instances becomes satisfiable, a Toffoli network representation for the given function has been found. We show that choosing the encoding for synthesis is crucial for the resulting runtimes. Furthermore, we discuss the principal limits of the SAT and SMT approaches. To overcome these limits, we propose a method using problem-specific knowledge during synthesis. In addition, better embeddings to make irreversible functions reversible are considered. For the resulting synthesis problems, an improvement is presented that reduces the overall runtime by automatically setting the constant inputs to their optimal values. Experimental results on a large set of benchmarks demonstrate the differences between three exact synthesis algorithms. In addition, a comparison with the best-known heuristic results is provided. In summary, the results show that, for some benchmarks, the heuristic approaches have already found the minimal network, while for other benchmarks, significantly smaller networks exist.

Multicell OFDMA Downlink Resource Allocation Using a Graphic Framework

Abstract: A novel practical low-complexity multicell orthogonal frequency-division multiple access (OFDMA) downlink channel-assignment method that uses a graphic framework is proposed in this paper. Our solution consists of two phases: 1) a coarse-scale intercell interference (ICI) management scheme and 2) a fine-scale channel-aware resource-allocation scheme. In the first phase, state-of-the-art ICI management techniques such as ICI coordination (ICIC) and base-station cooperation (BSC) are incorporated in our framework. In particular, the ICI information is acquired through inference from the diversity set of mobile stations and is presented by an interference graph. Then, ICIC or BSC is mapped to the MAX k-CUT problem in graph theory and is solved in the first phase. In the second phase, channel assignment is accomplished by taking instantaneous channel conditions into account. Heuristic algorithms are proposed to efficiently solve both phases of the problem. Extensive simulation is conducted for various practical scenarios to demonstrate the superior performance of the proposed solution compared with the conventional OFDMA allocation scheme. The proposed scheme can be used in next-generation cellular systems such as the 3GPP Long-Term Evolution and IEEE 802.16 m.

Matheuristics: Optimization, Simulation and Control

Abstract: Matheuristics are heuristic algorithms made by the interoperation of metaheuristics and mathematic programming (MP) techniques. An essential feature is the exploitation in some part of the algorithms of features derived from the mathematical model of the problems of interest, thus the definition "model-based metaheuristics" appearing in the title of some events of the conference series dedicated to matheuristics [1]. The topic has attracted the interest of a community of researchers, and this led to the publication of dedicated volumes and journal special issues, [13], [14], besides to dedicated tracks and sessions on wider scope conferences. The increasing maturity of the area permits to outline some trends and possibilities offered by matheuristic approaches. A word of caution is needed before delving into the subject, because obviously the use of MP for solving optimization problems, albeit in a heuristic way, is much older and much more widespread than matheuristics. However, this is not the case for metaheuristics, and also the very idea of designing MP methods specifically for heuristic solution has innovative traits, when opposed to exact methods which turn into heuristics when enough computational resources are not available.

Z-eigenvalue methods for a global polynomial optimization problem

Abstract: As a global polynomial optimization problem, the best rank-one approximation to higher order tensors has extensive engineering and statistical applications. Different from traditional optimization solution methods, in this paper, we propose some Z-eigenvalue methods for solving this problem. We first propose a direct Z-eigenvalue method for this problem when the dimension is two. In multidimensional case, by a conventional descent optimization method, we may find a local minimizer of this problem. Then, by using orthogonal transformations, we convert the underlying supersymmetric tensor to a pseudo-canonical form, which has the same E-eigenvalues and some zero entries. Based upon these, we propose a direct orthogonal transformation Z-eigenvalue method for this problem in the case of order three and dimension three. In the case of order three and higher dimension, we propose a heuristic orthogonal transformation Z-eigenvalue method by improving the local minimum with the lower-dimensional Z-eigenvalue methods, and a heuristic cross-hill Z-eigenvalue method by using the two-dimensional Z-eigenvalue method to find more local minimizers. Numerical experiments show that our methods are efficient and promising.

Large-scale identification of genetic design strategies using local search.

Abstract: In the past decade, computational methods have been shown to be well suited to unraveling the complex web of metabolic reactions in biological systems. Methods based on flux–balance analysis (FBA) and bi-level optimization have been used to great effect in aiding metabolic engineering. These methods predict the result of genetic manipulations and allow for the best set of manipulations to be found computationally. Bi-level FBA is, however, limited in applicability because the required computational time and resources scale poorly as the size of the metabolic system and the number of genetic manipulations increase. To overcome these limitations, we have developed Genetic Design through Local Search (GDLS), a scalable, heuristic, algorithmic method that employs an approach based on local search with multiple search paths, which results in effective, low-complexity search of the space of genetic manipulations. Thus, GDLS is able to find genetic designs with greater in silico production of desired metabolites than can feasibly be found using a globally optimal search and performs favorably in comparison with heuristic searches based on evolutionary algorithms and simulated annealing.