scholarly journals A Linearization to the Sum of Linear Ratios Programming Problem

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1004
Author(s):  
Mojtaba Borza ◽  
Azmin Sham Rambely
Keyword(s):  
Programming Problem ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
Straightforward Method ◽  
Global Optimal ◽  
High Computational Cost ◽  
Real World Problems

Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

scholarly journals The algorithm development based on the immune search for solving unclear problems to detect the optical flow with minimal cost

2021 ◽  
Vol 258 ◽  
pp. 06052
Author(s):  
Olga Purchina ◽  
Anna Poluyan ◽  
Dmitry Fugarov
Keyword(s):  
Multiple Solutions ◽  
Optimal Solution ◽  
Evolutionary Search ◽  
Minimal Cost ◽  
Optimal Solutions ◽  
Artificial Immune ◽  
Global Optimal Solution ◽  
Immune Algorithms ◽  
Global Optimal ◽  
Artificial Immune Algorithms

The main aim of the research is the development of effective methods and algorithms based on the hybrid principles functioning of the immune system and evolutionary search to determine a global optimal solution to optimisation problems. Artificial immune algorithms are characterised as diverse ones, extremely reliable and implicitly parallel. The integration of modified evolutionary algorithms and immune algorithms is proposed to be used for the solution of above problem. There is no exact method for the efficient solving unclear optimisation problems within the polynomial time. However, by determining close to optimal solutions within the reasonable time, the hybrid immune algorithm (HIA) is capable to offer multiple solutions, which provide compromise between several goals. Quite few researches have been focused on the optimisation of more than one goal and even fewer used to have distinctly considered diversity of solutions that plays fundamental role in good performance of any evolutionary calculation method.

A novel adaptive butterfly optimization algorithm

2018 ◽  
Vol 07 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Bhupinder Singh ◽  
Priyanka Anand
Keyword(s):  
Optimization Algorithm ◽  
Sensory Modality ◽  
Optimal Solution ◽  
Bench Mark ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
Simulation Process ◽  
Bee Colony ◽  
Global Optimal ◽  
Loss Of Diversity

Butterfly optimization algorithm (BOA) is an interesting bio-inspired algorithm that uses a nature inspired simulation model, based on the food foraging behavior of butterflies. A common problem with BOA is that in early stages of simulation process, it may converge to sub-optimal solutions due to the loss of diversity in its population. The sensory modality is the critical parameter which is responsible for searching new solutions in the nearby regions. In this work, an adaptive butterfly optimization algorithm is proposed in which a novel phenomenon of changing the sensory modality of BOA is employed during the optimization process in order to achieve better results in comparison to traditional BOA. The proposed Adaptive butterfly optimization algorithm (ABOA) is tested against seventeen standard bench mark functions. Its performance is then compared against existing standard optimization algorithms, namely artificial bee colony, firefly algorithm and standard butterfly optimization algorithm. The results indicate that the proposed adaptive BOA with improved parameter calculation mechanism produces superior results in terms of convergence and achievement of the global optimal solution efficiently.

scholarly journals Heuristic approach applied to the optimum stratification problem

2021 ◽  
Author(s):  
José André Brito ◽  
Leonardo de Lima ◽  
Pedro Henrique González ◽  
Breno Oliveira ◽  
Nelson Maculan
Keyword(s):  
Variable Neighborhood Search ◽  
Optimal Solution ◽  
Optimization Method ◽  
Neighborhood Search ◽  
Optimal Solutions ◽  
Enumeration Algorithm ◽  
Global Optimal Solution ◽  
Optimal Sample ◽  
Precision Level ◽  
Global Optimal

The problem of finding an optimal sample stratification has been extensively studied in the literature. In this paper, we propose a heuristic optimization method for solving the univariate optimum stratification problem aiming at minimizing the sample size for a given precision level. The method is based on the variable neighborhood search metaheuristic, which was combined with an exact method. Numerical experiments were performed over a dataset of 24 instances, and the results of the proposed algorithm were compared with two very well-known methods from the literature. Our results outperformed $94\%$ of  the considered cases. In addition, we developed an enumeration algorithm to find the global optimal solution in some populations and scenarios, which enabled us to validate our metaheuristic method. Furthermore, we find that our algorithm obtained the global optimal solutions for the vast majority of the cases.

scholarly journals A Review of Piecewise Linearization Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ming-Hua Lin ◽  
John Gunnar Carlsson ◽  
Dongdong Ge ◽  
Jianming Shi ◽  
Jung-Fa Tsai
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Convex Programming Problem ◽  
Nonlinear Programming Problem ◽  
Global Optimal Solution ◽  
Piecewise Linearization ◽  
Linearization Methods ◽  
Global Optimal

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

scholarly journals Performance Analysis of Parameter Estimator Based on Closed-Form Newton Method for Ultrawideband Positioning

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Chuanyang Wang ◽  
Yipeng Ning ◽  
Jian Wang ◽  
Guobiao Yao ◽  
Longping Zhang ◽  
...  
Keyword(s):  
Closed Form ◽  
Newton Method ◽  
High Efficiency ◽  
Functional Model ◽  
Computational Cost ◽  
Optimal Solution ◽  
Indoor Positioning ◽  
Initial Value ◽  
Global Optimal Solution ◽  
Global Optimal

Ultrawideband (UWB) is considered as a promising technology in indoor positioning due to its accurate time resolution and good penetration through objects. Since the functional model of UWB positioning is nonlinear, iterative algorithms are often considered for solving the nonlinear problem. With a rough initial value, we can obtain the optimal solution by the way of continuous iteration. As an iterative descent method of high efficiency, the Gauss–Newton method is widely used to estimate the position. However, in the UWB indoor positioning, since the location information of the user is rather limited, it is not easy to get a good initial value for iteration. Besides, the positioning system is prone to become ill-posed. These factors make the Gauss–Newton method not easy to converge to a global optimal solution or even diverge, especially under ill-conditioned positioning configuration. Furthermore, the linearization of the positioning functional model results in biased least-squares estimation. The Gauss–Newton method only includes the first-order Taylor expansion of distance equations. The bias comes from neglected higher order terms. In this study, the closed-form Newton method which considers the high order partial derivatives is introduced and proposed. The simulation and measurement experiments are implemented to analyze the performance of the closed-form Newton method in UWB positioning. Both the initial value factor and geometric configuration factor are discussed. Experimental results are given to demonstrate that the closed-form Newton method can converge to the global optimal solution with better convergence and higher efficiency regardless of whether the initial iteration value is reasonable or not. Meanwhile, the closed-form Newton method can improve the accuracy of positioning results, particularly when the anchors are not uniformly and symmetrically distributed, or the ranging error is relatively large. The study shows that closed-form of the Newton method has better convergence and positioning performance than the Gauss–Newton method, especially under ill-conditioned positioning configuration or relatively low measurement precision, even though it adds a little computational cost.

Hybrid Multi-Population and Adaptive Search Range Strategy With Particle Swarm Optimization for Multimodal Optimization

2021 ◽  
Vol 12 (4) ◽  
pp. 146-168
Author(s):  
Shiqi Wang ◽  
Zepeng Shen ◽  
Yao Peng
Keyword(s):  
Particle Swarm Optimization ◽  
Optimal Solution ◽  
Search Space ◽  
Multimodal Optimization ◽  
Adaptive Search ◽  
Optimal Solutions ◽  
Search Range ◽  
Global Optimal Solution ◽  
Swarm Optimization ◽  
Global Optimal

This paper proposes an algorithm named hybrid multi-population and adaptive search range strategy with particle swarm optimization (ARPSO) for solving multimodal optimization problems. The main idea of the algorithm is to divide the global search space into multiple sub-populations searching in parallel and independently. For diversity increasing, each sub-population will continuously change the search area adaptively according to whether there are local optimal solutions in its search space and the position of the global optimal solution, and in each iteration, the optimal solution in this area will be reserved. For the purpose of accelerating convergence, at the global and local levels, when the global optimal solution or local optimal solution is found, the global search space and local search space will shrink toward the optimal solution. Experiments show that ARPSO has unique advantages for solving multi-dimensional problems, especially problems with only one global optimal solution but multiple local optimal solutions.

scholarly journals On Locally and Globally Optimal Solutions in Scalar Variational Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 829 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Optimal Solution ◽  
Control Problems ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
New Class ◽  
Minimal Criterion ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Curvilinear Integral

In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion for a local optimal solution of the considered PDE and PDI-constrained variational control problem to be its global optimal solution. The effectiveness of the main result is validated by a two-dimensional non-convex scalar variational control problem.

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

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