A Normalized Circle Intersection Method for Bi-Objective Optimization Programming

2017 ◽  
Author(s):  
Jianhua Zhou ◽  
Tingting Xia ◽  
Mian Li ◽  
Min Xu
Keyword(s):  
Pareto Front ◽  
Method Comparison ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Pareto Point ◽  
Objective Space ◽  
Anchor Points ◽  
Intersection Method ◽  
Analytical Expressions

Multi-objective optimization (MOO) problems are encountered in many applications and a number of approaches have been proposed to deal with this kind of problems. Despite the computational efforts, the quality of the Pareto front is also a considerable issue. An evenly distributed Pareto front is desirable for developing analytical expressions. In this paper, a brand new approach called Normalized Circle Intersection (NCI) is proposed, which is able to efficiently generate a Pareto front with evenly-distributed Pareto points for bi-objective problems, no matter the feasible boundary is convex or not. Firstly, the anchor points are computed using an existing sequential MOO (SMOO) approach. Then in the normalized objective space, a circle with a radius of r centering at one of the anchor points or the latest obtained Pareto point is drawn. The intersection of the circle and the feasible boundary, which exists for sure, can be determined whether it is a Pareto point or not. For a convex or concave feasible boundary, the intersection is exactly the Pareto point to be found, while for a non-convex boundary the intersection can provide useful information for searching the true Pareto point even if it self is not a Pareto point. A novel MOO formulation is proposed for NCI correspondingly. Four examples, including two numerical and two engineering examples, are provided to demonstrate the applicability of the proposed method. Comparison of the computational results with WS, NNC and SMOO shows the effectiveness of the proposed method.

A Circle Intersection Method for Bi-Objective Optimization

2021 ◽  
pp. 1-36
Author(s):  
Jianhua Zhou ◽  
Mian Li ◽  
Xiaojin Fu
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
New Approach ◽  
Pareto Point ◽  
Objective Space ◽  
Anchor Points ◽  
Intersection Method

Abstract Multi-Objective Optimization (MOO) problems are encountered in many applications, of which bi-objective problems are frequently met. Despite the computational efforts, the quality of the Pareto front is also a considerable issue. An evenly distributed Pareto front is desirable in certain cases when a continuous representation of the Pareto front is needed. In this paper, a new approach called Circle Intersection (CI) is proposed. Firstly, the anchor points are computed. Then in the normalized objective space, a circle with a proper radius of r centering at one of the anchor points or the latest obtained Pareto point is drawn. Interestingly, the intersection of the circle and the feasible boundary can be determined whether it is a Pareto point or not. For a convex or concave feasible boundary, the intersection is exactly the Pareto point, while for other cases the intersection can provide useful information for searching the true Pareto point even if it is not a Pareto point. A novel MOO formulation is proposed for CI correspondingly. Sixteen examples are used to demonstrate the applicability of the proposed method and results are compared to those of NNC, MOGOA, and NSGA-II. Computational results show that the proposed CI method is able to obtain a well-distributed Pareto front with a better quality or with less computational cost.

scholarly journals Non-Epsilon Dominated Evolutionary Algorithm for the Set of Approximate Solutions

2020 ◽  
Vol 25 (1) ◽  
pp. 3
Author(s):  
Carlos Ignacio Hernández Castellanos ◽  
Oliver Schütze ◽  
Jian-Qiao Sun ◽  
Sina Ober-Blöbaum
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
The Novel ◽  
Multi Objective Optimization ◽  
Academic Problems ◽  
Decision Space ◽  
Objective Space ◽  
Novel Algorithm

In this paper, we present a novel evolutionary algorithm for the computation of approximate solutions for multi-objective optimization problems. These solutions are of particular interest to the decision-maker as backup solutions since they can provide solutions with similar quality but in different regions of the decision space. The novel algorithm uses a subpopulation approach to put pressure towards the Pareto front while exploring promissory areas for approximate solutions. Furthermore, the algorithm uses an external archiver to maintain a suitable representation in both decision and objective space. The novel algorithm is capable of computing an approximation of the set of interest with good quality in terms of the averaged Hausdorff distance. We underline the statements on some academic problems from literature and an application in non-uniform beams.

scholarly journals Multi-objective Optimization of a Hybrid Nanogrid/Microgrid: Application to Desert Camps in Hafr Al-Batin

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1245
Author(s):  
Houssem Rafik Al-Hana Bouchekara ◽  
Mohammad Shoaib Shahriar ◽  
Muhammad Sharjeel Javaid ◽  
Yusuf Abubakar Sha’aban ◽  
Makbul Anwari Muhammad Ramli
Keyword(s):  
Pareto Front ◽  
Operation Mode ◽  
Multi Objective Optimization ◽  
Nondominated Solutions ◽  
Multi Objective ◽  
Storage Batteries ◽  
The Cost ◽  
Component Models ◽  
The City

This paper presents an optimal design for a nanogrid/microgrid for desert camps in the city of Hafr Al-Batin in Saudi Arabia. The camps were designed to operate as separate nanogrids or to operate as an interconnected microgrid. The hybrid nanogrid/microgrid considered in this paper consists of a solar system, storage batteries, diesel generators, inverter, and load components. To offer the designer/operator various choices, the problem was formulated as a multi-objective optimization problem considering two objective functions, namely: the cost of electricity (COE) and the loss of power supply probability (LPSP). Furthermore, various component models were implemented, which offer a variety of equipment compilation possibilities. The formulated problem was then solved using the multi-objective evolutionary algorithm, based on both dominance and decomposition (MOEA/DD). Two cases were investigated corresponding to the two proposed modes of operation, i.e., nanogrid operation mode and microgrid operation mode. The microgrid was designed considering the interconnection of four nanogrids. The obtained Pareto front (PF) was reported for each case and the solutions forming this front were discussed. Based on this investigation, the designer/operator can select the most appropriate solution from the available set of solutions using his experience and other factors, e.g., budget, availability of equipment and customer-specific requirements. Furthermore, to assess the quality of the solutions found using the MOEA/DD, three different methods were used, and their results compared with the MOEA/DD. It was found that the MOEA/DD obtained better results (nondominated solutions), especially for the microgrid operation mode.

scholarly journals Non-dominated sorting Harris’s hawk multi-objective optimizer based on reference point approach

2019 ◽  
Vol 15 (3) ◽  
pp. 1603 ◽  
Author(s):  
Shaymah Akram Yasear ◽  
Ku Ruhana Ku-Mahamud
Keyword(s):  
Reference Point ◽  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Experimental Results ◽  
Multi Objective Optimization ◽  
Next Generation ◽  
Multi Objective ◽  
Objective Space ◽  
Reference Point Approach

A non-dominated sorting Harris’s hawk multi-objective optimizer (NDSHHMO) algorithm is presented in this paper. The algorithm is able to improve the population diversity, convergence of non-dominated solutions toward the Pareto front, and prevent the population from trapping into local optimal. This was achieved by integrating fast non-dominated sorting with the original Harris’s hawk multi-objective optimizer (HHMO).  Non-dominated sorting divides the objective space into levels based on fitness values and then selects non-dominated solutions to produce the next generation of hawks. A set of well-known multi-objective optimization problems has been used to evaluate the performance of the proposed NDSHHMO algorithm. The results of the NDSHHMO algorithm were verified against the results of an HHMO algorithm. Experimental results demonstrate the efficiency of the proposed NDSHHMO algorithm in terms of enhancing the ability of convergence toward the Pareto front and significantly improve the search ability of the HHMO.

scholarly journals Search Acceleration of Evolutionary Multi-Objective Optimization Using an Estimated Convergence Point

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 129 ◽  
Author(s):  
Yan Pei ◽  
Jun Yu ◽  
Hideyuki Takagi
Keyword(s):  
Parameter Space ◽  
Statistical Tests ◽  
Distribution Characteristic ◽  
Multi Objective Optimization ◽  
Pareto Improvement ◽  
Pareto Solutions ◽  
Pareto Solution ◽  
Multi Objective ◽  
Objective Space ◽  
Convergence Point

We propose a method to accelerate evolutionary multi-objective optimization (EMO) search using an estimated convergence point. Pareto improvement from the last generation to the current generation supports information of promising Pareto solution areas in both an objective space and a parameter space. We use this information to construct a set of moving vectors and estimate a non-dominated Pareto point from these moving vectors. In this work, we attempt to use different methods for constructing moving vectors, and use the convergence point estimated by using the moving vectors to accelerate EMO search. From our evaluation results, we found that the landscape of Pareto improvement has a uni-modal distribution characteristic in an objective space, and has a multi-modal distribution characteristic in a parameter space. Our proposed method can enhance EMO search when the landscape of Pareto improvement has a uni-modal distribution characteristic in a parameter space, and by chance also does that when landscape of Pareto improvement has a multi-modal distribution characteristic in a parameter space. The proposed methods can not only obtain more Pareto solutions compared with the conventional non-dominant sorting genetic algorithm (NSGA)-II algorithm, but can also increase the diversity of Pareto solutions. This indicates that our proposed method can enhance the search capability of EMO in both Pareto dominance and solution diversity. We also found that the method of constructing moving vectors is a primary issue for the success of our proposed method. We analyze and discuss this method with several evaluation metrics and statistical tests. The proposed method has potential to enhance EMO embedding deterministic learning methods in stochastic optimization algorithms.

scholarly journals A New Approach to Group Multi-Objective Optimization under Imperfect Information and Its Application to Project Portfolio Optimization

2021 ◽  
Vol 11 (10) ◽  
pp. 4575
Author(s):  
Eduardo Fernández ◽  
Nelson Rangel-Valdez ◽  
Laura Cruz-Reyes ◽  
Claudia Gomez-Santillan
Keyword(s):  
Portfolio Optimization ◽  
Imperfect Information ◽  
Model Parameters ◽  
Final Decision ◽  
Project Portfolio ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Multi Objective ◽  
Group Member

This paper addresses group multi-objective optimization under a new perspective. For each point in the feasible decision set, satisfaction or dissatisfaction from each group member is determined by a multi-criteria ordinal classification approach, based on comparing solutions with a limiting boundary between classes “unsatisfactory” and “satisfactory”. The whole group satisfaction can be maximized, finding solutions as close as possible to the ideal consensus. The group moderator is in charge of making the final decision, finding the best compromise between the collective satisfaction and dissatisfaction. Imperfect information on values of objective functions, required and available resources, and decision model parameters are handled by using interval numbers. Two different kinds of multi-criteria decision models are considered: (i) an interval outranking approach and (ii) an interval weighted-sum value function. The proposal is more general than other approaches to group multi-objective optimization since (a) some (even all) objective values may be not the same for different DMs; (b) each group member may consider their own set of objective functions and constraints; (c) objective values may be imprecise or uncertain; (d) imperfect information on resources availability and requirements may be handled; (e) each group member may have their own perception about the availability of resources and the requirement of resources per activity. An important application of the new approach is collective multi-objective project portfolio optimization. This is illustrated by solving a real size group many-objective project portfolio optimization problem using evolutionary computation tools.

Guideline for the management of long tunnelled external ventricular drains in chronic hydrocephalus

2021 ◽  
Vol 30 (7) ◽  
pp. 416-421
Author(s):  
Phillip Correia Copley ◽  
John Emelifeonwu ◽  
Pasquale Gallo ◽  
Drahoslav Sokol ◽  
Jothy Kandasamy ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Nursing Care ◽  
Pilocytic Astrocytoma ◽  
Parental Education ◽  
Chronic Hydrocephalus ◽  
Treatment Protocols ◽  
New Approach ◽  
Viable Treatment

This article reports on the journey of a child with an inoperable hypothalamic-origin pilocytic astrocytoma causing hydrocephalus, which was refractory to treatment with shunts, and required a new approach. With multidisciplinary support, excellent nursing care and parental education, the child's hydrocephalus was managed long term in the community with bilateral long-tunnelled external ventricular drains (LTEVDs). This article describes the patient's journey and highlights the treatment protocols that were created to achieve this feat. Despite the difficulties in initially setting up these protocols, they proved successful and thus the team managing the patient proposed that LTEVDs are a viable treatment option for children with hydrocephalus in the context of inoperable tumours to help maximise quality of life.

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