scholarly journals A metaheuristic penalty approach for the starting point in nonlinear programming

2020 ◽  
Vol 54 (2) ◽  
pp. 451-469
Author(s):  
David R. Penas ◽  
Marcos Raydan
Keyword(s):  
Nonlinear Programming ◽  
Feasible Solution ◽  
Packing Problem ◽  
Merit Function ◽  
Test Problems ◽  
Huge Amount ◽  
Novel Approach ◽  
Starting Point ◽  
Metaheuristic Techniques ◽  
Optimization Schemes

Solving nonlinear programming problems usually involve difficulties to obtain a starting point that produces convergence to a local feasible solution, for which the objective function value is sufficiently good. A novel approach is proposed, combining metaheuristic techniques with modern deterministic optimization schemes, with the aim to solve a sequence of penalized related problems to generate convenient starting points. The metaheuristic ideas are used to choose the penalty parameters associated with the constraints, and for each set of penalty parameters a deterministic scheme is used to evaluate a properly chosen metaheuristic merit function. Based on this starting-point approach, we describe two different strategies for solving the nonlinear programming problem. We illustrate the properties of the combined schemes on three nonlinear programming benchmark-test problems, and also on the well-known and hard-to-solve disk-packing problem, that possesses a huge amount of local-nonglobal solutions, obtaining encouraging results both in terms of optimality and feasibility.

scholarly journals On the Simplex Algorithm Initializing

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Nebojša V. Stojković ◽  
Predrag S. Stanimirović ◽  
Marko D. Petković ◽  
Danka S. Milojković
Keyword(s):  
Feasible Solution ◽  
Numerical Test ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Initial Solution ◽  
Test Problems ◽  
Basic Feasible Solution ◽  
Cpu Time ◽  
Starting Point ◽  
Number Of Iterations

This paper discusses the importance of starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on theNetlibtest problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

A novel approach to Bilevel nonlinear programming

2007 ◽  
Vol 38 (4) ◽  
pp. 527-554 ◽  
Author(s):  
H. Tuy ◽  
A. Migdalas ◽  
N. T. Hoai-Phuong
Keyword(s):  
Nonlinear Programming ◽  
Novel Approach

scholarly journals Re-Constructing the Choreographic Studio of João Fiadeiro Through Animated Infographic Films

1969 ◽  
Vol 1 (1) ◽  
Author(s):  
Stephan Jürgens
Keyword(s):  
Academic Research ◽  
Contemporary Dance ◽  
Interesting Point ◽  
Creative Processes ◽  
Artistic Process ◽  
Conceptual Structures ◽  
Novel Approach ◽  
Starting Point ◽  
Interdisciplinary Arts

The starting point for this article is an artist-led practice developed by choreographer João Fiadeiro during the past two decades, which has been designated as "Composition in Real Time" (CTR). The interesting point about this methodology is that it has been applied in performance composition and in arts education by its author himself; but also in such diverse fields as anthropology, sociology, neurosciences, and economy by scientists and academics in collaboration with Fiadeiro. The authors of this article have conducted a long-lasting case study on the artistic process of Fiadeiro in the framework of an ERC-funded interdisciplinary arts and cognition project. We present our resulting novel approach to researching contemporary dance work through the creation and production of animated infographic films. Along with leading PaR theorists we argue that the utilization of adequate artistic techniques and methods in academic research can successfully reveal how unique creative ideas and conceptual structures come into being in the creative processes of today's contemporary artists. The article discusses specific excerpts of the provided animated infographic films to show how we digitally re-constructed Fiadeiro’s conceptual and imaginative universe, and how our findings can address both an academic and interested lay audience. SOLOS study: I am sitting in a different room you are in now from BlackBox Art&Cognition on Vimeo. SOLOS study: I was here from BlackBox Art&Cognition on Vimeo. Graphic models developed by João Fiadeiro from BlackBox Art&Cognition on Vimeo.

Application of Nature Inspired Algorithms to Optimize Multi-objective Two-Dimensional Rectangle Packing Problem

2019 ◽  
Vol 04 (04) ◽  
pp. 1950010
Author(s):  
Amandeep Kaur Virk ◽  
Kawaljeet Singh
Keyword(s):  
Production Process ◽  
Bin Packing ◽  
Performance Metrics ◽  
Packing Problem ◽  
Flower Pollination Algorithm ◽  
Two Dimensional ◽  
Due Dates ◽  
Utilization Factor ◽  
Multi Objective ◽  
Metaheuristic Techniques

This paper considers two-dimensional non-guillotine rectangular bin packing problem with multiple objectives in which small rectangular parts are to be arranged optimally on a large rectangular sheet. The optimization of rectangular parts is attained with respect to three objectives involving maximization of (1) utilization factor, minimization of (2) due dates of rectangles and (3) number of cuts. Three nature based metaheuristic algorithms — Cuckoo Search, Bat Algorithm and Flower Pollination Algorithm — have been used to solve the multi-objective packing problem. The purpose of this work is to consider multiple industrial objectives for improving the overall production process and to explore the potential of the recent metaheuristic techniques. Benchmark test data compare the performance of recent approaches with the popular approaches and also of the different objectives used. Different performance metrics analyze the behavior/performance of the proposed technique. Experimental results obtained in this work prove the effectiveness of the recent metaheuristic techniques used. Also, it was observed that considering multiple and independent factors as objectives for the production process does not degrade the overall performance and they do not necessarily conflict with each other.

scholarly journals Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 754 ◽  
Author(s):  
A. C. L. Ashton ◽  
A. S. Fokas
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Formal Proof ◽  
Hurwitz Zeta Function ◽  
Mean Square ◽  
Novel Approach ◽  
Starting Point ◽  
Lindelöf Hypothesis ◽  
Riemann Zeta ◽  
The Mean

In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here.

Automated element grouping and self-stress identification of tensegrities

2015 ◽  
Vol 32 (6) ◽  
pp. 1643-1660 ◽  
Author(s):  
Kambiz Koohestani
Keyword(s):  
Design Methodology ◽  
Feasible Solution ◽  
State Of The Art ◽  
The Self ◽  
Content Type ◽  
Stress Mode ◽  
Novel Approach ◽  
Minimisation Problem ◽  
Feasible Solutions

Purpose – The determination of feasible self-stress modes and grouping of elements for tensegrities with predefined geometry and multiple self-stress modes is very important, though difficult, in the design of these structures. The purpose of this paper is to present a novel approach to the automated element grouping and self-stress identification of tensegrities. Design/methodology/approach – A set of feasible solutions conforming to the unilateral behaviour of elements is obtained through an optimisation process, which is solved using a genetic algorithm. Each chromosome in the population having a negative fitness is a distinctive feasible solution with its own grouping characteristic, which is automatically determined throughout the evolution process. Findings – The self-stress identification is formulated through an unconstrained minimisation problem. The objective function of this minimisation problem is defined in such a way that takes into account both the feasibility of a solution and grouping of elements. The method generates a set of feasible self-stress modes rather than a single one and automatically and simultaneously suggests a grouping of elements for every feasible self-stress mode. A self-stress mode with a minimal/subminimal grouping of elements is also obtained. Originality/value – The method can efficiently generate sets of feasible solutions rather than a single one. The authors also address one of the challenging issues related to this identification, i.e., automated grouping of elements. These features makes the method very efficient since most of the state-of-the-art methods address the self-stress identification of tensegrities based on predefined groupings of elements whilst providing only a single corresponding solution.

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