scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

scholarly journals An Improved Parallelized Multi-Objective Optimization Method for Complex Geographical Spatial Sampling: AMOSA-II

2020 ◽  
Vol 9 (4) ◽  
pp. 236
Author(s):  
Xiaolan Li ◽  
Bingbo Gao ◽  
Zhongke Bai ◽  
Yuchun Pan ◽  
Yunbing Gao
Keyword(s):  
Markov Chains ◽  
Optimization Problems ◽  
Optimization Method ◽  
Spatial Sampling ◽  
Computational Time ◽  
Test Problems ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Complex geographical spatial sampling usually encounters various multi-objective optimization problems, for which effective multi-objective optimization algorithms are much needed to help advance the field. To improve the computational efficiency of the multi-objective optimization process, the archived multi-objective simulated annealing (AMOSA)-II method is proposed as an improved parallelized multi-objective optimization method for complex geographical spatial sampling. Based on the AMOSA method, multiple Markov chains are used to extend the traditional single Markov chain; multi-core parallelization technology is employed based on multi-Markov chains. The tabu-archive constraint is designed to avoid repeated searches for optimal solutions. Two cases were investigated: one with six typical traditional test problems, and the other for soil spatial sampling optimization applications. Six performance indices of the two cases were analyzed—computational time, convergence, purity, spacing, min-spacing and displacement. The results revealed that AMOSA-II performed better which was more effective in obtaining preferable optimal solutions compared with AMOSA and NSGA-II. AMOSA-II can be treated as a feasible means to apply in other complex geographical spatial sampling optimizations.

scholarly journals A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

2020 ◽  
Author(s):  
Khodakaram Salimifard ◽  
Jingpeng Li ◽  
Davood Mohammadi ◽  
Reza Moghdani
Keyword(s):  
Parallel Machines ◽  
Resource Constraints ◽  
Optimization Problems ◽  
Programming Model ◽  
Total Tardiness ◽  
Test Problems ◽  
Nsga Ii ◽  
Multi Objective ◽  
Premier League ◽  
Conflicting Objectives

AbstractParallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms.

A Framework for Time-Cost-Quality Optimization in Project Management Problems Using an Exploratory Grid Concept in the Multi-Objective Simulated-Annealing

2021 ◽  
pp. 1-26
Author(s):  
Alzira Mota ◽  
Paulo Ávila ◽  
Ricardo Albuquerque ◽  
Lino Costa ◽  
João Bastos
Keyword(s):  
Decision Making ◽  
Simulated Annealing ◽  
Optimization Problems ◽  
Decision Makers ◽  
Time Cost ◽  
Trade Off ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Criteria Weights ◽  
Optimal Set

Time, cost, and quality are the three indispensable factors for the realization and success of a project. In this context, we propose a framework composed of a multi-objective approach and multi-criteria decision-making methods (MCDM) to solve time-cost-quality trade-off optimization problems. A multi-objective Simulated Annealing (MOSA) algorithm is used to compute an approximation to the Pareto optimal set. The concept of the exploratory grid is introduced in the MOSA to improve its performance. MCDM are used to assist the decision-making process. The Shannon entropy and AHP methods assign weights to criteria. The first methodology is for the inexperienced decision-makers, and the second concedes a personal and flexible weighting of the criteria weights, based on the project manager’s assessment. The TOPSIS and VIKOR methods are considered to rank the solutions. Although they have the same purpose, the rankings achieved are different. A tool is implemented to solve a time-cost-quality trade-off problem on a project activities network. The computational experiments are analyzed and the results with the exploratory grid in Simulated Annealing (SA) are promising. Despite the framework aims to solve multi-objective trade-off optimization problems, supporting the decisions of the project manager, the methodologies used can also be applied in other areas.

scholarly journals A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

2021 ◽  
Vol 26 (2) ◽  
pp. 27
Author(s):  
Alejandro Castellanos-Alvarez ◽  
Laura Cruz-Reyes ◽  
Eduardo Fernandez ◽  
Nelson Rangel-Valdez ◽  
Claudia Gómez-Santillán ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Selective Pressure ◽  
Optimization Problems ◽  
Region Of Interest ◽  
Decision Makers ◽  
Multiple Objective ◽  
Objective Functions ◽  
Multi Objective ◽  
Imperfect Knowledge ◽  
Real World Problems

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

scholarly journals Application of TOPSIS and AHP in the Multi-Objective Decision-Making Problems

2018 ◽  
Vol 228 ◽  
pp. 05002 ◽  
Author(s):  
Yihan Wang
Keyword(s):  
Decision Making ◽  
Theoretical Analysis ◽  
Optimization Problems ◽  
Basic Principles ◽  
Multi Objective ◽  
New Methods

The problems of multi-objective decision making are analysed and studied. In order to solve its optimization problems, the basic principles and application steps of TOPSIS and AHP are introduced in this paper. Then some practical examples are given to show how to apply these two new methods in multi-objective decision making problems. Finally, the advantage and feasibility of the TOPSIS and AHP methods are demonstrated by theoretical analysis.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Multi-Attribute Group Decision Making Method for Preference Conflicting with Heterogeneous Information

2018 ◽  
Vol 7 (4) ◽  
pp. 1-14 ◽  
Author(s):  
Kai-Rong Liang
Keyword(s):  
Decision Making ◽  
Objective Function ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Heterogeneous Information ◽  
Multi Objective ◽  
Attribute Weights ◽  
Relative Closeness ◽  
Decision Making Model

The aim of this article is to propose a multi-objective decision-making method for researching and solving multi-attribute heterogeneous group decision-making problems. This is in the case that the characters of the decision information and decision makers' preferences are heterogeneous, and the weight information is incomplete. In this method, the multi-objective decision-making model, which considers the alternatives decision relative closeness and the preference of heterogeneous degree of decision makers in the objective function, is put forward. In addition, this article uses the minimax method to derive the multi-objective decision-making model and obtain the attribute weights and decision makers weights, and then the optimal scheme is established. Finally, an illustrative example shows the effectiveness of the proposed method.

scholarly journals Multi-objective optimization of solar thermal photovoltaic hybrid power generation system based on NSGA-II algorithm

2021 ◽  
Vol 336 ◽  
pp. 02022
Author(s):  
Liang Meng ◽  
Wen Zhou ◽  
Yang Li ◽  
Zhibin Liu ◽  
Yajing Liu
Keyword(s):  
Power Generation ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solar Thermal ◽  
Multi Objective Optimization ◽  
Generation System ◽  
Nsga Ii ◽  
Multi Objective ◽  
Hybrid Power ◽  
Power Generation System

In this paper, NSGA-Ⅱ is used to realize the dual-objective optimization and three-objective optimization of the solar-thermal photovoltaic hybrid power generation system; Compared with the optimal solution set of three-objective optimization, optimization based on technical and economic evaluation indicators belongs to the category of multi-objective optimization. It can be considered that NSGA-Ⅱ is very suitable for multi-objective optimization of solar-thermal photovoltaic hybrid power generation system and other similar multi-objective optimization problems.

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