scholarly journals Sen's Multi Objective Optimization (MOO) Technique-An Extension

2020 ◽  
Vol 06 (09) ◽  
pp. 77-79
Author(s):  
Chandra Sen
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

Linear programming has been very popular for achieving (maximizing or minimizing) a single objective with certain constraints. However, when objectives are more than one, linear programming becomes inefficient. Sen's multi-objective optimization (MOO) technique [1] is efficient in achieving multiple objectives simultaneously. Few modifications in Sen's MOO technique are proposed for improving its applicability for solving multi-objective optimization problems.

Multi-Objective Pricing Optimization for a High-Speed Rail Network Under Competition

2019 ◽  
Vol 2673 (7) ◽  
pp. 215-226 ◽  
Author(s):  
Huizhuo Cao ◽  
Xuemei Li ◽  
Vikrant Vaze ◽  
Xueyan Li
Keyword(s):  
High Speed ◽  
Programming Model ◽  
Pareto Frontier ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
High Speed Rail ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Single Objective

Multi-objective pricing of high-speed rail (HSR) passenger fares becomes a challenge when the HSR operator needs to deal with multiple conflicting objectives. Although many studies have tackled the challenge of calculating the optimal fares over railway networks, none of them focused on characterizing the trade-offs between multiple objectives under multi-modal competition. We formulate the multi-objective HSR fare optimization problem over a linear network by introducing the epsilon-constraint method within a bi-level programming model and develop an iterative algorithm to solve this model. This is the first HSR pricing study to use an epsilon-constraint methodology. We obtain two single-objective solutions and four multi-objective solutions and compare them on a variety of metrics. We also derive the Pareto frontier between the objectives of profit and passenger welfare to enable the operator to choose the best trade-off. Our results based on computational experiments with Beijing–Shanghai regional network provide several new insights. First, we find that small changes in fares can lead to a significant improvement in passenger welfare with no reduction in profitability under multi-objective optimization. Second, multi-objective optimization solutions show considerable improvements over the single-objective optimization solutions. Third, Pareto frontier enables decision-makers to make more informed decisions about choosing the best trade-offs. Overall, the explicit modeling of multiple objectives leads to better pricing solutions, which have the potential to guide pricing decisions for the HSR operators.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

scholarly journals A NEW PROBABILISTIC ALGORITHM FOR SOLVING A CLASS OF SINGLE OR MULTI-OBJECTIVE OPTIMAL PROBLEMS

2009 ◽  
Vol 12 (11) ◽  
pp. 11-26
Author(s):  
Hao Van Tran ◽  
Thong Huu Nguyen
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Fixed Number ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Probabilistic Algorithm ◽  
Multi Objective ◽  
Single Objective

We consider a class of single-objective optimization problems which haves the character: there is a fixed number k (1≤k<n) that is independent of the size n of the problem such that if we only need to change values of k variables then it has the ability to find a better solution than the current one, let us call it Ok. In this paper, we propose a new numerical optimization technique, Search Via Probability (SVP) algorithm, for solving single objective optimization problems of the class Ok. The SVP algorithm uses probabilities to control the process of searching for optimal solutions. We calculate probabilities of the appearance of a better solution than the current one on each of iterations, and on the performance of SVP algorithm we create good conditions for its appearance. We tested this approach by implementing the SVP algorithm on some test single-objective and multi objective optimization problems, and we found good and very stable results.

scholarly journals An Overview of Few Nature Inspired Optimization Techniques and Its Reliability Applications

2020 ◽  
Vol 5 (4) ◽  
pp. 732-743
Author(s):  
Nitin Uniyal ◽  
Sangeeta Pant ◽  
Anuj Kumar
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Research Fields ◽  
Research Problems ◽  
Nature Inspired Algorithms ◽  
New Algorithms ◽  
Single Objective

Optimization has been a hot topic due to its inevitably in the development of new algorithms in almost every applied branch of Mathematics. Despite the broadness of optimization techniques in research fields, there is always an open scope of further refinement. We present here an overview of nature-inspired optimization with a subtle background of fundamentals and classification and their reliability applications. An attempt has been made to exhibit the contrast nature of multi objective optimization as compared to single objective optimization. Though there are various techniques to achieve the optimality in optimization problems but nature inspired algorithms have proved to be very efficient and gained special attention in modern research problems. The purpose of this article is to furnish the foundation of few nature inspired optimization techniques and their reliability applications to an interested researcher.

Evolutionary Multi-Objective Optimization for Assignment Problems

2011 ◽  
pp. 364-387
Author(s):  
Mark P. Kleeman ◽  
Gary B. Lamont
Keyword(s):  
Evolutionary Algorithms ◽  
Multiple Objectives ◽  
Multi Objective Optimization ◽  
Assignment Problems ◽  
Multi Objective ◽  
Advantages And Disadvantages ◽  
Single Objective

Assignment problems are used throughout many research disciplines. Most assignment problems in the literature have focused on solving a single objective. This chapter focuses on assignment problems that have multiple objectives that need to be satisfied. In particular, this chapter looks at how multi-objective evolutionary algorithms have been used to solve some of these problems. Additionally, this chapter examines many of the operators that have been utilized to solve assignment problems and discusses some of the advantages and disadvantages of using specific operators.

Multi-Objective Optimal Control Design With the Simple Cell Mapping Method

2013 ◽  
Author(s):  
Yousef Sardahi ◽  
Yousef Naranjani ◽  
Wei Liang ◽  
Jian-Qiao Sun ◽  
Carlos Hernandez ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Control Design ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Cell Mapping ◽  
Multi Objective ◽  
Simple Cell Mapping ◽  
Pareto Sets ◽  
Single Objective

Controls are often designed to meet different and conflicting goals. Consider the well-known LQR optimal control. The performance index contains a response measure and a control penalty, which are conflicting requirements. Proper linear or nonlinear combinations of the conflicting objective functions have led to single objective optimization problems. However, such a single objective optimization is dependent on the combination algorithm, and only provides a narrow window of all possible optimal solutions that a system may have. Multi-objective optimization provides a set of optimal solutions, known as Pareto set. There have been many studies of search algorithms for Pareto sets of multi-objective optimization problems for complex dynamical systems. Recently, the simple cell mapping (SCM) method due to C.S. Hsu has been found to be a highly effective tool to compute Pareto sets. This paper applies the SCM method to several control design problems of linear and nonlinear dynamical systems. The results of the work are very exciting to report.

MOTEO: A Novel Multi-Objective Thermal Exchange Optimization Algorithm for Optimal Design of Truss Structures

2021 ◽  
Author(s):  
Nima Khodadadi ◽  
Siamak Talatahari ◽  
Armin Dadras Eslamlou
Keyword(s):  
Structural Design ◽  
Optimization Problems ◽  
Truss Structures ◽  
Metaheuristic Algorithm ◽  
Multi Objective Optimization ◽  
Thermal Exchange ◽  
Multi Objective ◽  
Mathematical Problems ◽  
Pareto Fronts ◽  
Single Objective

Abstract In the present paper, a physics-inspired metaheuristic algorithm is presented to solve multi-objective optimization problems. The algorithm is developed based on the concept of Newtonian cooling law that recently has been employed by the Thermal Exchange Optimization (TEO) algorithm to efficiently solve single-objective optimization problems. The performance of the multi-objective version of TEO (MOTEO) is examined through bi- and tri-objective mathematical problems as well as bi-objective structural design examples. According to the comparisons between the MOTEO and several well-known algorithms, the proposed algorithm can provide quality Pareto fronts with appropriate accuracy, uniformity and coverage for multi-objective problems.

scholarly journals An integrated cuckoo search optimizer for single and multi-objective optimization problems

2021 ◽  
Vol 7 ◽  
pp. e370
Author(s):  
Xiangbo Qi ◽  
Zhonghu Yuan ◽  
Yan Song
Keyword(s):  
Optimization Problems ◽  
Cuckoo Search ◽  
Search Strategies ◽  
Comprehensive Analysis ◽  
Experimental Results ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multiple Strategies ◽  
Single Objective

Integrating heterogeneous biological-inspired strategies and mechanisms into one algorithm can avoid the shortcomings of single algorithm. This article proposes an integrated cuckoo search optimizer (ICSO) for single objective optimization problems, which incorporates the multiple strategies into the cuckoo search (CS) algorithm. The paper also considers the proposal of multi-objective versions of ICSO called MOICSO. The two algorithms presented in this paper are benchmarked by a set of benchmark functions. The comprehensive analysis of the experimental results based on the considered test problems and comparisons with other recent methods illustrate the effectiveness of the proposed integrated mechanism of different search strategies and demonstrate the performance superiority of the proposed algorithm.

scholarly journals Modelling Diversity of Solutions

2020 ◽  
Vol 34 (02) ◽  
pp. 1528-1535
Author(s):  
Linnea Ingmar ◽  
Maria Garcia de la Banda ◽  
Peter J. Stuckey ◽  
Guido Tack
Keyword(s):  
General Framework ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Solution ◽  
Single Objective

For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimization problems, as they have no single “best solution” and, thus, it is useful to find a representation of the non-dominated solutions (the Pareto frontier). However, it also applies to single objective optimization problems, where one may be interested in finding several (close to) optimal solutions that illustrate some form of diversity. The same applies to satisfaction problems. This is because models usually idealize the problem in some way, and a diverse pool of solutions may provide a better choice with respect to considerations that are omitted or simplified in the model. This paper describes a general framework for finding k diverse solutions to a combinatorial problem (be it satisfaction, single-objective or multi-objective), various approaches to solve problems in the framework, their implementations, and an experimental evaluation of their practicality.

Multi-Objective Optimization Based on Brain Storm Optimization Algorithm

2013 ◽  
Vol 4 (3) ◽  
pp. 1-21 ◽  
Author(s):  
Yuhui Shi ◽  
Jingqian Xue ◽  
Yali Wu
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Solution Space ◽  
Population Based ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Brain Storm Optimization ◽  
Objective Space ◽  
Different Characteristics ◽  
Single Objective

In recent years, many evolutionary algorithms and population-based algorithms have been developed for solving multi-objective optimization problems. In this paper, the authors propose a new multi-objective brain storm optimization algorithm in which the clustering strategy is applied in the objective space instead of in the solution space in the original brain storm optimization algorithm for solving single objective optimization problems. Two versions of multi-objective brain storm optimization algorithm with different characteristics of diverging operation were tested to validate the usefulness and effectiveness of the proposed algorithm. Experimental results show that the proposed multi-objective brain storm optimization algorithm is a very promising algorithm, at least for solving these tested multi-objective optimization problems.

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