Combinatorial Optimization Method Research Articles

Optimizing Egalitarian Performance when Colocating Tasks with Types for Cloud Data Center Resource Management

In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but the performance of the tasks deteriorates, as the colocated tasks compete for shared resources. Since the tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [1] , [2] we proposed a new combinatorial optimization model that uses two parameters of a task — its size and its type — to characterize how a task influences the performance of other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: the aim is to optimize the performance of the worst-off task. This problem generalizes the classic makespan minimization on multiple processors ($P||C_{\max }$P||Cmax). We prove that polynomially-solvable variants of $P||C_{\max }$P||Cmax are NP-hard for this generalization, and that the problem is hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics. We simulate the algorithms on instances derived from a trace of one of Google clusters. Compared with baseline algorithms solving $P||C_{\max }$P||Cmax, our proposed algorithms aware of the types of the jobs lead to significantly better tasks’ performance. The notion of type enables us to extend standard combinatorial optimization methods to handle degradation of performance caused by colocation. Types add a layer of additional complexity. However, our results — approximation algorithms and good average-case performance — show that types can be handled efficiently.

The Cohesion-Based Communities of Symptoms of the Largest Component of the DSM-IV Network

Modern methods for network analytics provide an opportunity to revisit preconceived notions in the classification of diseases as “clusters of symptoms”. Curated collections which were subsequently modified, like the Diagnostic and Statistical Manuals of Mental Disorders “DSM-IV” and the most recent addition, DSM-5 allow us to introspect, using the solution provided by modern algorithms, if there exists a consensus between the clusters obtained via a data-driven approach, with the current classifications. In the case of mental disorders, the availability of a follow-up consensus collection (e.g. in this case the DSM-5), potentially allows investigating if the classification of disorders has moved closer (or away) to what a data-driven analytic approach would have unveiled by objectively inferring it from the data of DSM-IV. In this contribution, we present a new type of mathematical approach based on a global cohesion score which we introduce for the first time for the identification of communities of symptoms. Different from other approaches, this combinatorial optimization method is based on the identification of “triangles” in the network; these triads are the building block of feedback loops that can exist between groups of symptoms. We used a memetic algorithm to obtain a collection of highly connected-cohesive sets of symptoms and we compare the resulting community structure with the classification of disorders present in the DSM-IV.

A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy MAGDM

Some interval-valued intuitionistic fuzzy information MAGDM problems with combinatorial optimization characteristics have so many feasible alternatives that they can hardly be enumerated and evaluated. Moreover, due to the lack of quantitative functions, they are difficult to be solved with traditional combinatorial optimization methods. Therefore, by combining the MAGDM with combinatorial optimization, we propose a decision variable-based combinatorial optimization approach for the purpose of solving the interval-valued intuitionistic fuzzy MAGDM problems in this paper. Firstly, the utility evaluation matrix of decision maker is defined and the interval-valued intuitionistic fuzzy weighted average operator is used to aggregate utility evaluation matrices with decision makers’ preference information. Then, the 0–1 integer decision variable is introduced and a combinatorial optimization model is established for the interval-valued intuitionistic fuzzy MAGDM problem. For the purpose of comparison, a multi-attribute decision-making method based on the weighted relative distance is adopted to rank different alternatives. Besides, an artificial bee colony algorithm improved by integer encoding, ranking selection and elite guidance is used to solve the combinatorial optimization model. Finally, two applications of the approach are proposed: research group dispatch and group weapon-group target assignment. Through the comparison of the algorithms, the feasibility of the proposed approach was verified.

Cost-Oriented Mobility-Aware Caching Strategies in D2D Networks With Delay Constraint

Pre-caching popular files at mobile users with the aid of device-to-device (D2D) communications can offload the data traffic to low-cost D2D links and reduce the network transmission cost. This leads to additional cache leasing cost brought by the lease of storage from mobile users. Besides, newly-emerging video-related applications also pose strict requirement on the network delay. Thus, it is of great significance to design caching strategies considering the transmission cost, the cache leasing cost and the delay. As the movement of mobile users can improve the communication opportunities among different users and increase the cache hit ratio, in this paper, mobility-aware caching strategies are designed to minimize the network cost including both the transmission cost and the cache leasing cost with the delay constraint. In specific, by characterizing the user mobility as an inter-contact model, analytical expressions of the average network cost and the average file delivery delay are derived and a cost-oriented mobility-aware caching problem is formulated. To handle this mixed integer nonlinear programming (MINLP) problem, we first relax the binary cache placement indicator as a continuous one and prove that both the average network cost and the average file delivery delay are convex. Hence, an iterative caching algorithm is proposed with the successive convex approximation method. Moreover, to lower the complexity, combinatorial optimization method is adopted. Firstly, to make the caching problem tractable, the average file delivery delay constraint is implicitly added in the cost objective function as a penalty term. Then, the reformulated objective function is proved to have the non-monotone submodular property and thus a modified low-complexity greedy caching strategy is proposed. Simulation results show that, compared with the most popular caching strategy, our proposed mobility-aware caching strategy can reduce the average cost by 46% when the user speed is high.

GPU-based distributed bee swarm optimisation for dynamic vehicle routing problem

Nowadays, there is still a large gap between the requirements and the performance of decision support systems for many problems such as the vehicle routing problem, consists in conceiving a set of optimal routes for a fleet of vehicles, aiming at serving a given number of customers. Nevertheless, new customer orders could be introduced while a prior plan is in progress. Therefore, routes should be recalculated in a dynamic way. In this paper, we propose a new parallel combinatorial optimisation method based on graphic processing unit (GPU) called parallel bees life algorithm (P-BLA) to solve efficiency the dynamic capacitated vehicle routing problem (DCVRP) in terms of execution time, and to reduce computational complexity often considered as the major drawback of conventional optimisation methods. P-BLA is developed using CUDA framework performed on an island-based GPU. After a set of comparisons against conventional methods namely; genetic algorithm, ant system, Tabu search and sequential BLA, P-BLA has provided efficient results reached from the most tested DCVRP benchmarks.

Multiobjective Optimization Approach for Coordinating Different DG from Distribution Network Operator

Integrating with analysis of uncertainties, this paper presented a multiobjective optimization approach for coordinating different DG from the perspective of Distribution Network Operator (DISOPER). Aiming to three uncertain factors including fuzzy variable, random variable, and interval variable, the information entropy and interval analysis methods are adopted to construct multistate models of multisource uncertainty. The information entropy method is to convert fuzzy variable into equivalent random variable. Interval analysis method is to transform random variables into interval variables by setting a confidence level. Then plenty of simulation analysis based on the small probability event and expectation are investigated to reduce the computational burden and eliminate invalid computation. Subsequently, multiobjective formulations based on multistate are built by analyzing systematical power loss, voltage quality, reliability, and environment change provide some reference for DISOPER in dealing with access of privately owned DG units. Furthermore, based on network topology analysis and modified nondominated sorting genetic algorithm (NSGA), a combinatorial optimization method is proposed to reduce search space and solve the constructed formulations efficiently. Simulations are carried out on IEEE 37-bus systems and results are presented and discussed.

Continuation methods for approximate large scale object sequencing

We propose a set of highly scalable algorithms for the combinatorial data analysis problem of seriating similarity matrices. Seriation consists of finding a permutation of data instances, such that similar instances are nearby in the ordering. Applications of the seriation problem can be found in various disciplines such as in bioinformatics for genome sequencing, data visualization and exploratory data analysis. Our algorithms attempt to minimize certain p-SUM objectives, which also arise in the problem of envelope reduction of sparse matrices. In particular, we present a set of graduated non-convexity algorithms for vector-based relaxations of the general p-SUM problem for p in left{ 2, 1, tfrac{1}{2}right} that can scale to very large problem sizes. Different choices of p emphasize global versus local similarity pattern structure. We conduct a number of experiments to compare our algorithms to various state-of-the-art combinatorial optimization methods on real and synthetic datasets. The experimental results demonstrate that compared to other approaches, the proposed algorithms are very competitive and scale well with large problem sizes.

Optimization of flapping wing mechanism of bionic eagle

The present study is focused on optimization of a double-crank-rocker flapping wing mechanism to imitate the motion of eagle wing divided into inner and outer wing with flapping, folding and twist degree of freedom, and structural flexibility. Considering the multibar dimensions of the flapping mechanism as design variables, combinatorial optimization method was applied to maximize the aerodynamic efficiency. Based on the optimization results, a bionic eagle model of 1.5 m wing span was manufactured to perform flight tests. The study results show that the optimized kinematic of motion can be achieved by using the multibar flapping mechanism; the inner wing plays the key role of producing lift while the outer wing producing thrust; as a result of the optimization, the lift was increased by 2.8% from 3.85 N up to 3.96 N and the thrust increased by 12.5% from 0.16 N up to 0.18 N, which was verified by the flight tests. The flight test also demonstrated a sustainable level flight of the bionic eagle model at a flapping frequency of 2 Hz.

Higher Structure Solution Space Based Multi-point Combinatorial Optimization Method with Diversification and Intensification Strategy

Higher Structure Solution Space Based Multi-point Combinatorial Optimization Method with Diversification and Intensification Strategy

Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

Computing maxmin edge length triangulations

In 1991, Edelsbrunner and Tan gave an $O(n^2)$ algorithm for finding the MinMax Length triangulation of a set of points in the plane, but stated the complexity of finding a MaxMin Edge Length Triangulation (MELT) as a natural open problem. We resolve this long-standing problem by showing that computing a MELT is NP-complete. Moreover, we prove that (unless P=NP), there is no polynomial-time approximation algorithm that can approximate MELT within any polynomial factor. While this may be taken as conclusive evidence from a theoretical point of view that the problem is hopelessly intractable, it still makes sense to consider powerful optimization methods, such as integer programming (IP), in order to obtain provably optimal solutions for intances of non-trivial size. A straightforward IP based on pairwise disjointness of the $\Theta(n^2)$ segments between the n points has $\Theta(n^4)$ constraints, making this IP hopelessly intractable from a practical point of view, even for relatively small $n$. The main algorithm engineering twist of this paper is to demonstrate how the combination of geometric insights with refined methods of combinatorial optimization can still help to put together an exact method capable of computing optimal MELT solutions for planar point sets up to $n = 200$. Our key idea is to exploit specific geometric properties in combination with more compact IP formulations, such that we are able to drastically reduce the IPs. On the practical side, we combine two of the most powerful software packages for the individual components: CGAL for carrying out the geometric computations, and CPLEX for solving the IPs. In addition, we discuss specific analytic aspects of the speedup for random point sets.

Heat exchanger network cleaning scheduling: From optimal control to mixed-Integer decision making

An approach for optimising the cleaning schedule in heat exchanger networks (HENs) subject to fouling is presented. This work focuses on HEN applications in crude oil preheat trains located in refineries. Previous approaches have focused on using mixed-integer nonlinear programming (MINLP) methods involving binary decision variables describing when and which unit to clean in a multi-period formulation. This work is based on the discovery that the HEN cleaning scheduling problem is in actuality a multistage optimal control problem (OCP), and further that cleaning actions are the controls which appear linearly in the system equations. The key feature is that these problems exhibit bang-bang behaviour, obviating the need for combinatorial optimisation methods. Several case studies are considered; ranging from a single unit up to 25 units. Results show that the feasible path approach adopted is stable and efficient in comparison to classical methods which sometimes suffer from failure in convergence.

Multipoint combinatorial optimization method with a search strategy in higher structure solution space

We propose a multipoint combinatorial optimization method that aims to realize efficient search in consideration of intensification and diversification in higher structure solution space by sharing information between search points. We evaluated the performance of the proposed method through numerical experiments using benchmark problems.

Generating guitar solos by integer programming

In this paper, we present a framework for computer-aided composition (CAC) that uses exact combinatorial optimisation methods to generate guitar solos from a newly proposed data-set of licks over an accompaniment based on the 12-bar blues chord progression. An integer programming formulation, which can be solved to optimality by a branch-and-cut algorithm, was developed for this problem whose objective is to determine an optimal sequence of a set of licks given a matrix of transition costs derived from user preferences. The generated solos are displayed in tablature format. Outputs of the system were evaluated in an empirical experiment with 173 participants. The results show that the solos whose licks were optimally sequenced were significantly more enjoyed than those randomly sequenced. We project that the developed framework could be of potential use to guitarists looking for original material; as an educational tool for future composers; and to support composers in discovering unique and novel compositional ideas.

Combinatorial optimization of input features and learning parameters for decorrelated neural network ensemble-based soft measuring model

Abstract The decorrelated neural network ensemble (DNNE) algorithm can be used to construct an effective soft measuring model through an analytical solution comprising submodels of multiple randomized neural networks. However, DNNE exhibits one major shortcoming: the scope of the random input weights and biases is set to a default range of [−1, 1], which cannot ensure the universal approximation capability of the resulting prediction model. The three other learning parameters including the number of the ensemble submodels’ hidden nodes, ensemble size, and regularizing factor of DNNE are also data dependent. Moreover, DNNE suffers from high computation complexity when processing a high-dimensional large-scale dataset. Feature selection can improve the interpretation of the model. To address the above-mentioned problems, a combinatorial optimization method based on the adaptive genetic algorithm is used to simultaneously optimize the input features and learning parameters of the DNNE model. The evolution processes of these modeling parameters are demonstrated in detail. Simulation results based on four datasets with different dimensions and sizes validate the effectiveness of the proposed approach. The results also indicate that the random parameter scope assignment significantly influences the generalization performance and the other learning parameters of the prediction model.

Fuzzy Greedy Search

This paper presents mathematics of the so-called fuzzy greedy evaluation concept which can be integrated into approaches for hard combinatorial optimization problems. The proposed method evaluates objects in a way that combines fuzzy reasoning with a greedy mechanism, thereby exploiting a fuzzy solution space using greedy methods. Given that the greedy algorithms are computationally inexpensive compared to other more sophisticated methods for combinatorial optimization; this shows practical significance of using the proposed approach. The effectiveness and efficiency of the proposed method are demonstrated on permutation flow-shop scheduling as one of the most widely studied hard combinatorial optimization problems in the area of operational research and management science.

Irregularly Shaped Cluster Detection Using a CPSO Distribution-Free Spatial Scan Statistic

Classical spatial scan statistics are based on pre-defined shapes for scanning windows and specific distribution models and are used to detect latent cluster(s). However, the pre-defined windows (especially circularly shaped windows) may not be suitable for real situations, and the specific distribution models are inadequate for real clusters in which the exact distributions of the test statistics are only known in special cases. To generate more reasonable results, we propose a spatial scan statistic method with an irregularly shaped scanning window. A combinatorial particle swarm optimization method is used to optimize this window. A distribution-free concentration index is constructed to measure the difference between inside cluster and outside cluster. A compactness penalty function is employed to avoid generating clusters in a tree-structure. Simulation data sets are used to test the proposed method, and the results show the feasibility of our method.

解空間の確率モデルに基づいた大規模問題に対する組合せ最適化手法

解空間の確率モデルに基づいた大規模問題に対する組合せ最適化手法

Modelling railway freight traffic using the methods of graph theory and combinatorial optimization

The optimization problem of planning the railway freight traffic was presented, and approaches to reduction of problem dimension by constructing a hierarchy of the problems of train traffic planning were described. The notion of conflict graph on a set of energy-efficient standard threads was introduced. A "traveling wave" algorithm to construct the conflict-free sets of standard threads of the train schedule on the basis of the conflict graph was proposed. The problem of optimal assignments and transportations of locomotives in terms of the minimized number of utilized locomotives was formulated, an algorithm to solve to it was given, and its complexity was estimated.

Combinatorial Optimization Method Based on Hierarchical Structure in Solution Space

SUMMARYIn this paper, we introduce a new concept of hierarchical structure into solution space of a combinatorial optimization problem, and develop a novel combinatorial optimization method based on the concept. The introduction of the above new hierarchical structure concept “basin of attraction,” which is a set binding solution by utilizing properties of local optimal solutions, enables us to construe solution space as not only set of solutions but also set of basins of attraction hierarchically. It is well known that the appropriate balance of two policies, intensification and diversification, is essential in the search of metaheuristics. The proposed method clarifies the search policy by relating the hierarchical structure in solution space with intensification and diversification. With regard to diversification, we incorporate a movement strategy that has longer term or more macroscopic viewpoint than before in the algorithm by utilizing the concept basin of attraction. The performance of the proposed combinatorial optimization method is inspected by numerical experiments using some typical benchmark problems of a traveling salesman problem, a knapsack problem, a flow‐shop scheduling problem, and a quadratic assignment problem.