scholarly journals An optimization problem for continuous submodular functions

2021 ◽  
Vol 66 (1) ◽  
pp. 211-222
Author(s):  
Laszlo Csirmaz
Keyword(s):  
Optimization Problem ◽  
Submodular Functions ◽  
Minimal Cost ◽  
Open Problems ◽  
Partial Derivatives ◽  
General Optimization Problem ◽  
Function Range ◽  
The Cost ◽  
Entropy Functions ◽  
Special Case

"Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real function defined on the non-negative orthant of $\R^n$ is entropy-like (EL) if it is submodular, takes zero at zero, non-decreasing, and has the Diminishing Returns property. Motivated by problems concerning the Shannon complexity of multipartite secret sharing, a special case of the following general optimization problem is considered: find the minimal cost of those EL functions which satisfy certain constraints. In our special case the cost of an EL function is the maximal value of the $n$ partial derivatives at zero. Another possibility could be the supremum of the function range. The constraints are specified by a smooth bounded surface $S$ cutting off a downward closed subset. An EL function is feasible if at the internal points of $S$ the left and right partial derivatives of the function differ by at least one. A general lower bound for the minimal cost is given in terms of the normals of the surface $S$. The bound is tight when $S$ is linear. In the two-dimensional case the same bound is tight for convex or concave $S$. It is shown that the optimal EL function is not necessarily unique. The paper concludes with several open problems."

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.

scholarly journals An integer optimization model and algorithms to support the cost-revenue study and provisory designing warehouses or other storage objects

2018 ◽  
Vol 4 (21) ◽  
pp. 257-269
Author(s):  
Mikalai Miatselski ◽  
Bożena Staruch ◽  
Bogdan Staruch
Keyword(s):  
Exact Solution ◽  
General Problem ◽  
Optimization Model ◽  
Optimization Problem ◽  
System Analysis ◽  
Software Tools ◽  
Integer Optimization ◽  
The Cost ◽  
Special Case ◽  
Basic Constraint

An optimization model for the cost–revenue study at the stage of system analysis and preliminary designs of storage objects such as warehouses, containers, packs and similar objects are developed. Our assumptions motivated by warehouses design lead us to a nonlinear integer optimization problem with the only basic constraint. We present algorithmic methods for obtaining the exact solution to the general problem with emphasizing the special case when both the objective and the constraint functions are increasing. The results of the paper may be used in developing software tools intended for supporting designers.

scholarly journals Designing Strong Privacy Metrics Suites Using Evolutionary Optimization

2021 ◽  
Vol 24 (2) ◽  
pp. 1-35
Author(s):  
Isabel Wagner ◽  
Iryna Yevseyeva
Keyword(s):  
Optimization Problem ◽  
Evolutionary Optimization ◽  
Multiple Objectives ◽  
Shared Value ◽  
Vehicular Communications ◽  
Open Problems ◽  
Value Range ◽  
Genomic Privacy ◽  
Metaheuristic Optimization Algorithms ◽  
Selection Of

The ability to measure privacy accurately and consistently is key in the development of new privacy protections. However, recent studies have uncovered weaknesses in existing privacy metrics, as well as weaknesses caused by the use of only a single privacy metric. Metrics suites, or combinations of privacy metrics, are a promising mechanism to alleviate these weaknesses, if we can solve two open problems: which metrics should be combined and how. In this article, we tackle the first problem, i.e., the selection of metrics for strong metrics suites, by formulating it as a knapsack optimization problem with both single and multiple objectives. Because solving this problem exactly is difficult due to the large number of combinations and many qualities/objectives that need to be evaluated for each metrics suite, we apply 16 existing evolutionary and metaheuristic optimization algorithms. We solve the optimization problem for three privacy application domains: genomic privacy, graph privacy, and vehicular communications privacy. We find that the resulting metrics suites have better properties, i.e., higher monotonicity, diversity, evenness, and shared value range, than previously proposed metrics suites.

scholarly journals Inversion-free geometric mapping construction: A survey

2021 ◽  
Vol 7 (3) ◽  
pp. 289-318
Author(s):  
Xiao-Ming Fu ◽  
Jian-Ping Su ◽  
Zheng-Yu Zhao ◽  
Qing Fang ◽  
Chunyang Ye ◽  
...  
Keyword(s):  
Mesh Generation ◽  
Optimization Problem ◽  
Texture Mapping ◽  
Deformation Texture ◽  
Research Field ◽  
Combinatorial Problems ◽  
Open Problems ◽  
Nonlinear Constrained Optimization ◽  
Construction Methods ◽  
Geometric Mapping

AbstractA geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

The Calculation of Photovoltaic System Generation Access Capacity in Distribution Network Based on Probabilistic Power Flow and the PSO Optimization

2012 ◽  
Vol 529 ◽  
pp. 371-375
Author(s):  
Lu Yao Ma ◽  
Shu Jun Yao ◽  
Yan Wang ◽  
Jing Yang ◽  
Long Hui Liu
Keyword(s):  
Distributed Generation ◽  
Power Flow ◽  
Optimization Problem ◽  
Flow Model ◽  
Expansion Method ◽  
Pso Algorithm ◽  
Photovoltaic System ◽  
System Generation ◽  
Probabilistic Power Flow ◽  
The Cost

With the distributed generation such as photovoltaic power system (PVS) is largely introduced into power grid, some significant problems such as system instability problem increase seriously. In order to make full use of PVS and make sure the voltage exceeding probability is limited within a certain range to ensure the power quality, as well as consider the cost of access device, the suitable PVS access node and capacity is important. Based on this problem, this paper establishes the probabilistic power flow model of PVS by introducing the combined Cumulants and the Gram-Charlier expansion method. Also, to solve the nonlinear combinatorial optimization problem, this paper uses PSO algorithm. Finally to get the suitable PVS access node and capacity, also calculate the solution of voltage exceeding probability.

Optimization of the Robot Calibration Process

1992 ◽  
Author(s):  
G. Zak ◽  
R. G. Fenton ◽  
B. Benhabib
Keyword(s):  
Optimization Problem ◽  
Kinematic Model ◽  
Optimization Procedure ◽  
Calibration Procedure ◽  
Residual Error ◽  
Industrial Robots ◽  
Multiple Objective Optimization ◽  
Robot Calibration ◽  
Calibration Process ◽  
The Cost

Abstract Most industrial robots cannot be off-line programmed to carry out a task accurately, unless their kinematic model is suitably corrected through a calibration procedure. However, proper calibration is an expensive and time-consuming procedure due to the highly accurate measurement equipment required and due to the significant amount of data that must be collected. To improve the efficiency of robot calibration, an optimization procedure is proposed in this paper. The objective of minimizing the cost of the calibration is combined with the objective of minimizing the residual error after calibration in one multiple-objective optimization. Prediction of the residual error for a given calibration process presents the main difficulty for implementing the optimization. It is proposed that the residual error is expressed as a polynomial function. This function is obtained as a result of fitting a response surface to either experimental or simulated sample estimates of the residual error. The optimization problem is then solved by identifying a reduced set of possible solutions, thus greatly simplifying the decision maker’s choice of an effective calibration procedure. An application example of this method is also included.

scholarly journals On Mixed Codes with Covering Radius $1$ and Minimum Distance $2$

10.37236/969 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Wolfgang Haas ◽  
Jörn Quistorff
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Covering Radius ◽  
Minimal Cardinality ◽  
Finite Sets ◽  
Open Problems ◽  
Latin Rectangle ◽  
Mixed Codes ◽  
Special Case

Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and $|T|=t$. A code $C\subset R\times S\times T$ with covering radius $1$ and minimum distance $2$ is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality $K(r,s,t;2)$. These bounds turn out to be best possible in many instances. Focussing on the special case $t=s$ we determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when $s$ is large, relative to $r$, when $r$ is large, relative to $s$, as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally, a table with bounds on $K(r,s,s;2)$ is given.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

Optimization of Multistage Machining Systems, Part 1: Mathematical Solution

1992 ◽  
Vol 114 (4) ◽  
pp. 524-531 ◽  
Author(s):  
J. S. Agapiou
Keyword(s):  
Optimization Problem ◽  
Cutting Parameters ◽  
Optimization Method ◽  
Idle Time ◽  
Optimization Techniques ◽  
Machining Parameters ◽  
Machining Time ◽  
Physical Constraints ◽  
Time Requirements ◽  
The Cost

The optimization problem for multistage machining systems has been investigated. Due to uneven time requirements at different stages in manufacturing, there could be idle times at various stations. It may be advantageous to reduce the values of machining parameters in order to reduce the cost at stations that require less machining time. However, optimization techniques available through the literature do not effectively utilize the idle time for the different stations generated during the balancing of the system. Proposed in this paper is an optimization method which utilizes the idle time to the full extent at all machining stations, with the intention of improving tool life and thus achieving cost reduction. The mathematical analysis considers the optimization of the production cost with an equality constraint of zero idle time for the stations with idle time. Physical constraints regarding the cutting parameters, force, power, surface finish, etc., as they arise in different operations, are also considered. The aforementioned problem has been theoretically analyzed and a computational algorithm developed. The advantages and effectiveness of the proposed approach are finally established through an example.

scholarly journals Pre-Selection of the Optimal Sitting of Phase-Shifting Transformers Based on an Optimization Problem Solved within a Coordinated Cross-Border Congestion Management Process

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3748 ◽  
Author(s):  
Endika Urresti-Padrón ◽  
Marcin Jakubek ◽  
Wojciech Jaworski ◽  
Michał Kłos
Keyword(s):  
Optimization Problem ◽  
Congestion Management ◽  
Decision Makers ◽  
Phase Shifting ◽  
Management Process ◽  
European Policy ◽  
Cross Border ◽  
Remedial Actions ◽  
The Cost ◽  
Selection Of

The current European policy roadmap aims at forcing the TSOs to coordinate remedial actions used for relieving the congestions in the synchronous power system. In this paper, an optimization problem for coordinated congestion management is described and its results obtained for a real European use cases created in the H2020 EU-SysFlex project are presented. First of all, these results prove the feasibility of a central optimization problem for the coordination of the cross-border congestion management process. Next, the formulated optimization problem is used to tackle the issue of planning the investments in phase-shifting transformers (PSTs), for the purpose of increasing the efficiency/decreasing the cost of congestion management. Finally, this paper introduces two optimization-based indicators for pre-selecting the investment sites, which may be used to support the decision makers aiming at decreasing the costs of coordinated congestion management.

Sign in / Sign up

Export Citation Format

Share Document