Comparison of Two Random Weight Generators for Multi-Objective Optimization

2016 ◽  
pp. 222-237
Author(s):  
Victor M. Carrillo ◽  
German Almanza
Keyword(s):  
Decision Maker ◽  
Optimal Solution ◽  
Multiple Objective ◽  
Heuristic Methods ◽  
Weighted Sum ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Mathematical Methods ◽  
Weighted Sum Method ◽  
Random Weight

There exist two general approaches to solve multiple objective problems. The first approach belongs to the classical mathematical methods: The weighted sum method, goal programming, or utility functions methods pertain to this approach. The output of mathematical methods is a single optimal solution. In the second approach are the heuristic methods, like the multiple objective evolutionary algorithms that offer the decision maker a set of optimal solutions usually called non- dominated or, Pareto-optimal solutions. This set is usually very large and the decision maker faces the problem of reducing the size of this set to a manageable number of solutions to analyze. In this paper the second approach is used to reduce the Pareto front using two weights generator for the non-numerical ranking preferences method and their performance is compared.

scholarly journals Multiobjective Optimal Control of HIV Dynamics

2010 ◽  
Vol 2010 ◽  
pp. 1-29 ◽  
Author(s):  
Hassan Zarei ◽  
Ali Vahidian Kamyad ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Optimal Solution ◽  
Transcriptase Inhibitor ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Human Immune System ◽  
Weighted Sum Method ◽  
Treatment Interruptions ◽  
Multiobjective Optimal Control

Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

Pareto Optimal Solution Selection for a Multi-Site Supply Chain Planning Problem Using the VIKOR and TOPSIS Methods

2017 ◽  
Vol 8 (3) ◽  
pp. 21-39 ◽  
Author(s):  
Houssem Felfel ◽  
Omar Ayadi ◽  
Faouzi Masmoudi
Keyword(s):  
Supply Chain ◽  
Optimal Solution ◽  
Quality Level ◽  
Planning Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Compromise Solution ◽  
Optimal Solutions ◽  
Pareto Solution ◽  
Solution Approach

In this paper, a multi-objective, multi-product, multi-period production and transportation planning problem in the context of a multi-site supply chain is proposed. The developed model attempts simultaneously to maximize the profit and to maximize the product quality level. The objective of this paper is to provide the decision maker with a front of Pareto optimal solutions and to help him to select the best Pareto solution. To do so, the epsilon-constraint method is adopted to generate the set of Pareto optimal solutions. Then, the technique for order preference by similarity to ideal solution (TOSIS) is used to choose the best compromise solution. The multi-criteria optimization and compromise solution (VIKOR), a commonly used method in multiple criteria analysis, is applied in order to evaluate the selected solutions using TOPSIS method. This paper offers a numerical example to illustrate the solution approach and to compare the obtained results using TOSIS and VIKOR methods.

Solving multiobjective optimal control problems using an improved scalarization method

2020 ◽  
Vol 37 (4) ◽  
pp. 1524-1547
Author(s):  
Gholam Hosein Askarirobati ◽  
Akbar Hashemi Borzabadi ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Uniform Distribution ◽  
Optimal Control Problems ◽  
Pareto Frontier ◽  
Optimal Solution ◽  
Control Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimal Control

Abstract Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights, a sequence of single objective optimal control problems is solved to achieve a uniform distribution of Pareto optimal solutions on the Pareto frontier. The aim is to achieve a more even distribution of Pareto optimal solutions on the Pareto frontier and improve the efficiency of the algorithm. It is shown that in contrast to the NBI method, where Pareto optimality of solutions is not guaranteed, the obtained optimal solution of the scalarized problem is a Pareto optimal solution of the MOCP. Finally, the ability of the proposed method is evaluated and compared with other approaches using several practical MOCPs. The numerical results indicate that the proposed method is more efficient and provides more uniform distribution of solutions on the Pareto frontier than the other methods, such a weighted sum, normalized normal constraint and NBI.

Multi-Objective Design and Selection of One Single Optimal Solution

2004 ◽  
Author(s):  
F. Levi ◽  
M. Gobbi ◽  
M. Farina ◽  
G. Mastinu
Keyword(s):  
Optimal Solution ◽  
Engineering Problem ◽  
Design Solution ◽  
Pareto Optimal ◽  
Large Set ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Final Design ◽  
Selection Of

In the paper, the problem of choosing a single final design solution among a large set of Pareto-optimal solutions is addressed. Two methods, the k-optimality approach and the more general k-ε-optimality method will be introduced. These two methods theoretically justify and mathematically define the designer’s tendency to choose solutions which are “in the middle” of the Pareto-optimal set. These two methods have been applied to the solution of a relatively simple engineering problem, i.e. the selection of the stiffness and damping of a passively suspended vehicle in order to get the best compromise between discomfort, road holding and working space. The final design solution, found by means of the k-ε-optimality approach seems consistent with the solution selected by skilled suspensions specialists. Finally the k-optimality method has proved to be very effective also when applied to complex engineering problems. The optimization of the tyre/suspension system of a sports car has been formulated as a design problem with 18 objective functions. A large set of Pareto-optimal solutions have been computed. Again, the k-optimality approach has proved to be a useful tool for the selection of a fully satisfactory final design solution.

scholarly journals Fuzzy optimization based Water Distribution Network design using Self-Adaptive Cuckoo Search Algorithm

2021 ◽  
Author(s):  
A. Vasan ◽  
K. Srinivasa Raju ◽  
B. Sriman Pankaj
Keyword(s):  
Membership Function ◽  
Water Distribution ◽  
Search Algorithm ◽  
Fuzzy Optimization ◽  
Optimal Solution ◽  
Water Distribution Network ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions

Abstract Water Distribution Network(s) (WDN) design is gaining prominence in the urban planning context. Several factors that play a significant role in design are uncertainty in data, non-linear relation of head loss & discharge, combinatorial nature of the problem, and high computational requirements. In addition, many conflicting objectives are possible and required for effective WDN design, such as cost, resilience, and leakage. Most of the research work published has used multiobjective evolutionary optimization in solving such complex WDN. However, the challenge of such population based evolutionary approaches is that they provide multiple trade-off Pareto optimal solutions to the decision-maker who will have to choose another set of techniques to arrive at a single optimal solution. The present study employs a fuzzy optimization approach that would provide a single optimal WDN design for Hanoi and Pamapur, India. Maximization of network resilience (NR) and minimization of network cost (NC) are employed in a multiobjective context. Later, minimization of network leakages (NL) is also incorporated, leading to three objective problems. Hyperbolic Membership Function (HMF), Exponential Membership Function (EMF), and Non-linear Membership Function (NMF) are employed in Self-Adaptive Cuckoo Search Algorithm based fuzzy optimization. HMF is found suitable to determine the best possible WDN design for chosen case studies based on the highest degree of satisfaction. HIGHLIGHT Most of the research conducted till now have used evolutionary multiobjective optimization in solving WDNs. But, the challenge of such evolutionary approaches is that they provide multiple trade-off pareto optimal solutions to the decision maker who will have to further choose another methodology to converge to a single optimal solution. The proposed methodology would simplify the decision-making process for an engineer.

Meta-Heuristic Structure for Multiobjective Optimization Case Study

2014 ◽  
pp. 38-58
Author(s):  
T. Ganesan ◽  
I. Elamvazuthi ◽  
K. Z. KuShaari ◽  
P. Vasant
Keyword(s):  
Performance Metrics ◽  
Heuristic Algorithms ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Green Sand ◽  
Weighted Sum Method ◽  
Real World Problem ◽  
Green Sand Mould System

In engineering optimization, one often encounters scenarios that are multiobjective (MO) where each of the objectives covers different aspects of the problem. It is hence critical for the engineer to have multiple solution choices before selecting of the best solution. In this chapter, an approach that merges meta-heuristic algorithms with the weighted sum method is introduced. Analysis on the solution set produced by these algorithms is carried out using performance metrics. By these procedures, a novel chaos-based metaheuristic algorithm, the Chaotic Particle Swarm (Ch-PSO) is developed. This method is then used generate highly diverse and optimal solutions to the green sand mould system which is a real-world problem. Some comparative analyses are then carried out with the algorithms developed and employed in this work. Analysis on the performance as well as the quality of the solutions produced by the algorithms is presented in this chapter.

Analysis and Modeling of Supply Chain Management of Fresh Products Based on Genetic Algorithm in E-commerce Environment

2020 ◽  
Author(s):  
Yaoting Chen
Keyword(s):  
Genetic Algorithm ◽  
Supply Chain ◽  
Weighted Sum ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Optimal Process ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Proposed Model ◽  
Fresh Products

Abstract BackgroundSupply chain provides the chance to enhance chain performances by decrease these uncertainties. It is a demand for some level of co-ordination of activities and processes within and between organization in the supply chain to decrease uncertainties and increase more cost for customers. Partner selection is an important issue in the supply chain management of fresh products in E-commerce environment. In this paper, we utilized a multi-objective genetic algorithm for evaluation supply chain of fresh products in E-commerce environment. ResultsThe proposed multi-objective genetic algorithm is to search the set of Pareto-optimal solutions for these conflicting objectives using by weighted sum approach. The proposed model suitable for fresh products in E-commerce environment to optimize supply chain are derived. The value of objective 1 (f1) performs approximately nonlinearly with the increasing the value of objective 2,3 and 4 (f2,f3 and f4). At the value of objective 1 of 3.2*105, f2, f3 and f4 is about 4.3*105, 86 and 5.6*104. When the value of objective 1 is increased to 7.6*105, the minimum f2, f3 and f4 is about 3.0*105, 38 and 2.56*104. It is noted that the value of objective 1 is increased from 6.4*105 to 7.6*105, the variation of f2, f3 and f4 is 11.7%, 17.4% and 3.4% respectively. It is pointed out that the variation of f2 and f3 with f1 and f4 is kept within obvious ranges. This practical result highlights the fact that the effects of the fact that effects of f2 and f3 are important factors affecting the performance supply chain network of fresh product in E-commerce environment.ConclusionsIn this paper, we utilized a multi-objective genetic algorithm for evaluation supply chain of fresh products in E-commerce environment. Four objectives for optimal process are included in the proposed model: (1) maximization of green appraisal score, (2) minimization of transportation time and total time comprised of product time, (3) maximization of average product quality, (4) minimization of transportation cost and total cost comprised of product cost. In order to evaluate optimal process, set of Pareto-optimal solutions is obtained based on the weighted sum method.

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