Optimization on permutations: related structures, problems interrelation, heuristic compositions, applications

2017 ◽  
Vol 1 (21) ◽  
pp. 37-47
Author(s):  
Mikalai Miatselski
Keyword(s):  
Algebraic Structures ◽  
Size Problem ◽  
Network Problems ◽  
Real Size ◽  
Permutation Sets ◽  
Problem Instances ◽  
Permutation Problems ◽  
Special Case

A heuristics based approach to practical solving theoretically intractable combinatory and network problems is discussed. Compound heuristics (heuristics compositions) are suggested to be more efficient procedures for real size problem instances. Some aspects of the heuristics compositions topic are illustrated by optimum permutation problems. We describe a uniform presentation of the chief types of the problems and their interrelations, including the relation “to be a special case of a problem”. We consider a number of algebraic structures and combinatory constructions on permutation sets and present an inclusion chain of these constructions. The chain enables us to establish and clarify many interrelations for the minimum permutation problems, with algorithmic and complexity aspects taken into account. We also concern the applications of some problems as well.

scholarly journals Cloud Brokering with Bundles: Multi-objective Optimization of Services Selection

2019 ◽  
Vol 44 (4) ◽  
pp. 407-426
Author(s):  
Jedrzej Musial ◽  
Emmanuel Kieffer ◽  
Mateusz Guzek ◽  
Gregoire Danoy ◽  
Shyam S. Wagle ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Cloud Service ◽  
Optimal Choice ◽  
Cloud Services ◽  
Multi Objective Optimization ◽  
Problem Instances ◽  
The Cost ◽  
Special Case ◽  
Single Objective

Abstract Cloud computing has become one of the major computing paradigms. Not only the number of offered cloud services has grown exponentially but also many different providers compete and propose very similar services. This situation should eventually be beneficial for the customers, but considering that these services slightly differ functionally and non-functionally -wise (e.g., performance, reliability, security), consumers may be confused and unable to make an optimal choice. The emergence of cloud service brokers addresses these issues. A broker gathers information about services from providers and about the needs and requirements of the customers, with the final goal of finding the best match. In this paper, we formalize and study a novel problem that arises in the area of cloud brokering. In its simplest form, brokering is a trivial assignment problem, but in more complex and realistic cases this does not longer hold. The novelty of the presented problem lies in considering services which can be sold in bundles. Bundling is a common business practice, in which a set of services is sold together for the lower price than the sum of services’ prices that are included in it. This work introduces a multi-criteria optimization problem which could help customers to determine the best IT solutions according to several criteria. The Cloud Brokering with Bundles (CBB) models the different IT packages (or bundles) found on the market while minimizing (maximizing) different criteria. A proof of complexity is given for the single-objective case and experiments have been conducted with a special case of two criteria: the first one being the cost and the second is artificially generated. We also designed and developed a benchmark generator, which is based on real data gathered from 19 cloud providers. The problem is solved using an exact optimizer relying on a dichotomic search method. The results show that the dichotomic search can be successfully applied for small instances corresponding to typical cloud-brokering use cases and returns results in terms of seconds. For larger problem instances, solving times are not prohibitive, and solutions could be obtained for large, corporate clients in terms of minutes.

An Abstract System for Converting and Recovering Texts like Structured Information

2021 ◽  
Author(s):  
Edgardo Samuel Barraza Verdesoto ◽  
Richard de Jesus Gil Herrera ◽  
Marlly Yaneth Rojas Ortiz
Keyword(s):  
Structured Data ◽  
Spanish Language ◽  
Scientific Models ◽  
Algebraic Structures ◽  
Abstract System ◽  
Language Generation ◽  
Web Contents ◽  
Structured Information ◽  
The Brain ◽  
Special Case

Abstract This paper introduces an abstract system for converting texts into structured information. The proposed architecture incorporates several strategies based on scientific models of how the brain records and recovers memories, and approaches that convert texts into structured data. The applications of this proposal are vast because, in general, the information that can be expressed like a text way, such as reports, emails, web contents, etc., is considered unstructured and, hence, the repositories based on a SQL do not capable to deal efficiently with this kind of data. The model in which was based on this proposal divides a sentence into clusters of words which in turn are transformed into members of a taxonomy of algebraic structures. The algebraic structures must comply properties of Abelian groups. Methodologically, an incremental prototyping approach has been applied to develop a satisfactory architecture that can be adapted to any language. A special case is studied, this deals with the Spanish language. The developed abstract system is a framework that permits to implements applications that convert unstructured textual information to structured information, this can be useful in contexts such as Natural Language Generation, Data Mining, dynamically generation of theories, among others.

scholarly journals On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem

2020 ◽  
Vol 92 (1) ◽  
pp. 107-132 ◽  
Author(s):  
Britta Schulze ◽  
Michael Stiglmayr ◽  
Luís Paquete ◽  
Carlos M. Fonseca ◽  
David Willems ◽  
...  
Keyword(s):  
Knapsack Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Ratio ◽  
Experimental Results ◽  
Cardinality Constraint ◽  
Quadratic Knapsack Problem ◽  
Problem Instances ◽  
Quadratic Knapsack ◽  
Special Case

Abstract In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides a constant approximation ratio of 4.5. Our experimental results on a large number of artificially generated problem instances show that the average ratio is far from theoretical guarantee. In addition, we suggest refined versions of this approximation algorithm with the same time complexity and approximation ratio that lead to even better experimental results.

scholarly journals THE QUANDARY OF QUANDLES: A BOREL COMPLETE KNOT INVARIANT

2019 ◽  
Vol 108 (2) ◽  
pp. 262-277 ◽  
Author(s):  
ANDREW D. BROOKE-TAYLOR ◽  
SHEILA K. MILLER
Keyword(s):  
Isomorphism Problem ◽  
Algebraic Structures ◽  
Knot Invariant ◽  
Borel Reducibility ◽  
Special Case

We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as complex as possible in the sense of Borel reducibility. These algebraic structures are important for their connections with the theory of knots, links and braids. In particular, Joyce showed that a quandle can be associated with any knot, and this serves as a complete invariant for tame knots. However, such a classification of tame knots heuristically seemed to be unsatisfactory, due to the apparent difficulty of the quandle isomorphism problem. Our result confirms this view, showing that, from a set-theoretic perspective, classifying tame knots by quandles replaces one problem with (a special case of) a much harder problem.

Higher-Order Approximations to the Null Distributions of Test Statistics for Nonlinear Restrictions on Regression Coefficients

1988 ◽  
Vol 4 (2) ◽  
pp. 275-299
Author(s):  
Kimio Morimune
Keyword(s):  
Asymptotic Expansions ◽  
Simultaneous Equations ◽  
Regression Coefficients ◽  
Test Statistics ◽  
Lagrange Multiplier Test ◽  
Null Distributions ◽  
Asymptotic Size ◽  
Simultaneous Equations Models ◽  
Real Size ◽  
Special Case

Asymptotic expansions of the distributions of likelihood ratio and Lagrange multiplier test statistics for nonlinear restrictions on regression coefficients are derived under the null hypothesis. Nonlinear restrictions include, as a special case, the identifiability restrictions in the simultaneous equations models. Our analyses of simultaneous equations deal not only with single equations but also subsystems and complete systems. The asymptotic expansions we derive are informative about deviations of the real size of test from the nominal asymptotic size.

scholarly journals Bi-criteria parallel batch machine scheduling to minimize total weighted tardiness and electricity cost

2020 ◽  
Vol 90 (9) ◽  
pp. 1345-1381
Author(s):  
Jens Rocholl ◽  
Lars Mönch ◽  
John Fowler
Keyword(s):  
Genetic Algorithms ◽  
Pareto Front ◽  
Total Weighted Tardiness ◽  
Mixed Integer ◽  
Due Dates ◽  
Semiconductor Wafer ◽  
Weighted Tardiness ◽  
Electricity Cost ◽  
Problem Instances ◽  
Special Case

Abstract A bi-criteria scheduling problem for parallel identical batch processing machines in semiconductor wafer fabrication facilities is studied. Only jobs belonging to the same family can be batched together. The performance measures are the total weighted tardiness and the electricity cost where a time-of-use (TOU) tariff is assumed. Unequal ready times of the jobs and non-identical job sizes are considered. A mixed integer linear program (MILP) is formulated. We analyze the special case where all jobs have the same size, all due dates are zero, and the jobs are available at time zero. Properties of Pareto-optimal schedules for this special case are stated. They lead to a more tractable MILP. We design three heuristics based on grouping genetic algorithms that are embedded into a non-dominated sorting genetic algorithm II framework. Three solution representations are studied that allow for choosing start times of the batches to take into account the energy consumption. We discuss a heuristic that improves a given near-to-optimal Pareto front. Computational experiments are conducted based on randomly generated problem instances. The $$ \varepsilon $$ ε -constraint method is used for both MILP formulations to determine the true Pareto front. For large-sized problem instances, we apply the genetic algorithms (GAs). Some of the GAs provide high-quality solutions.

scholarly journals Generalized Reynolds operators on 3-Lie algebras and NS-3-Lie algebras

2021 ◽  
Author(s):  
Shuai Hou ◽  
Yunhe Sheng
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Group ◽  
Algebra Structure ◽  
Algebraic Structures ◽  
Reynolds Operator ◽  
Infinitesimal Deformations ◽  
Special Case

In this paper, first, we introduce the notion of a generalized Reynolds operator on a [Formula: see text]-Lie algebra [Formula: see text] with a representation on [Formula: see text]. We show that a generalized Reynolds operator induces a 3-Lie algebra structure on [Formula: see text], which represents on [Formula: see text]. By this fact, we define the cohomology of a generalized Reynolds operator and study infinitesimal deformations of a generalized Reynolds operator using the second cohomology group. Then we introduce the notion of an NS-[Formula: see text]-Lie algebra, which produces a 3-Lie algebra with a representation on itself. We show that a generalized Reynolds operator induces an NS-[Formula: see text]-Lie algebra naturally. Thus NS-[Formula: see text]-Lie algebras can be viewed as the underlying algebraic structures of generalized Reynolds operators on [Formula: see text]-Lie algebras. Finally, we show that a Nijenhuis operator on a 3-Lie algebra gives rise to a representation of the deformed 3-Lie algebra and a 2-cocycle. Consequently, the identity map will be a generalized Reynolds operator on the deformed 3-Lie algebra. We also introduce the notion of a Reynolds operator on a [Formula: see text]-Lie algebra, which can serve as a special case of generalized Reynolds operators on 3-Lie algebras.

Appendix A

2011 ◽  
pp. 244-275
Author(s):  
Goran Trajkovski
Keyword(s):  
Random Graph ◽  
Graph Structure ◽  
Fuzzy Relations ◽  
Algebraic Structures ◽  
Modeling Tool ◽  
Fuzzy Graphs ◽  
Special Case ◽  
Mathematical Graph

The first part of this appendix presents three approaches in defining the fuzzy version (generalization) of the mathematical graph structure: graphs with fuzzy vertices, graphs with fuzzy edges, and graphs with fuzzy vertices and edges. Their advantages and shortcomings are discussed briefly. Fuzzy graphs are observed in the light of fuzzy relations theory, and as a generalization of the notion of random graph. In the second part, we generalize some fuzzy algebraic structures towards not only [0, 1] valued, but lattice, poset, and relational structured valued structures. It is exciting to see how powerful a modeling tool they are, and also to see how classical results continue to hold as but a special case of the new results.

scholarly journals Models and Solution Algorithms for Efficient Truck Scheduling at Cross-docking Terminals with Time-sensitive Products

2021 ◽  
Author(s):  
Oluwatosin Theophilus
Keyword(s):  
Mathematical Model ◽  
Metaheuristic Algorithms ◽  
Computational Time ◽  
Neighborhood Search ◽  
Perishable Products ◽  
Service Cost ◽  
Cross Docking ◽  
Truck Scheduling ◽  
Size Problem ◽  
Problem Instances

This dissertation focuses on the scheduling of trucks (both in- and outbound trucks) at a CDT, where some of the delivered products are perishable in nature. The short lifespan of perishable products (i.e., foods and drugs) poses critical challenges to the CDT operations management. Perishable goods are time-sensitive products that require minimal handling time to preserve their quality and profitability. Cross-docking is expected to facilitate the distribution of perishable products within supply chains. There are many challenges involved in the management of the cross-docking terminals with perishable products, including determination of the service order of the trucks (inbound and outbound) carrying perishable products, selection of preemption strategies for certain trucks (i.e., a given truck can leave the door, so another truck can be docked for service), allocation of suitable temporary storage space for products, quality loss due to late delivery or errors in temperature control.This dissertation aims to develop a mathematical model for scheduling the arriving trucks at a cross-dock terminal, taking product decay into consideration throughout the handling process. The objective of the mathematical model minimizes the total truck service cost, which includes (1) waiting cost; (2) service cost; (3) cost of product storage; (4) cost of delay in truck departure; and (5) the cost associated with the decay of products that are perishable in nature. A number of linearization techniques are discussed in order to linearize the original nonlinear mathematical model (where the nonlinearity is caused by the adopted product decay function). The complexity of the linearized model is evaluated in this dissertation. Moreover, the candidate solution approaches for the proposed mathematical model are described.The developed model was solved using the exact optimization technique. In particular, the model was solved to optimality using CPLEX. However, it was observed that the computational time increased as the problem size increased due to the model complexity. Four alternative solution approaches namely: (1) Evolutionary Algorithm (EA); (2) Variable Neighborhood Search (VNS); (3) Tabu Search (TS); and (4) Simulated Annealing (SA), which are common metaheuristic algorithms, were developed and compared with CPLEX using small-size problem instances. These metaheuristics were able to achieve optimal solutions for the small-size problem instances and required relatively low computational times. The metaheuristic algorithms were further compared, and EA was found to outperform the others (VNS, TS, and SA) based on the balance between the objective function and computational time values. A set of analyses were carried out using EA, and managerial insights that could be of interest to supply chain stakeholders were drawn. The proposed mathematical model, the developed EA, and the managerial insights could assist the CDT manager in making efficient and timely truck scheduling decisions in any planning horizon.

scholarly journals Determinants of binomial-related circulant matrices

2018 ◽  
Vol 6 (1) ◽  
pp. 262-272
Author(s):  
Trairat Jantaramas ◽  
Somphong Jitman ◽  
Pornpan Kaewsaard
Keyword(s):  
Positive Integer ◽  
Complex Number ◽  
Circulant Matrices ◽  
Algebraic Structures ◽  
Explicit Formulas ◽  
Open Problems ◽  
Left And Right ◽  
Nonzero Complex Number ◽  
Special Case

Abstract Due to their rich algebraic structures and wide applications, circulant matrices have been of interest and continuously studied. In this paper, n×n complex left and right circulant matrices whose first row consists of the coefficients in the expansion of (x + zy)n−1 are focused on, where z is a nonzero complex number and n is a positive integer. In the case where z ∈ {1, −1, i, −i}, explicit formulas for the determinants of such matrices are completely determined. Known results on the determinants of binomial circulant matrices can be viewed as the special case where z = 1. Finally, some remarks and open problems are discussed.

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