scholarly journals MVMOO: Mixed variable multi-objective optimisation

2021 ◽  
Author(s):  
Jamie A. Manson ◽  
Thomas W. Chamberlain ◽  
Richard A. Bourne
Keyword(s):  
Test Problems ◽  
Nsga Ii ◽  
Efficient Manner ◽  
Multi Objective ◽  
Bounded Variables ◽  
Conflicting Objectives ◽  
Efficient Data ◽  
Pareto Fronts ◽  
Continuous And Discrete Variables ◽  
Mixed Variable

AbstractIn many real-world problems there is often the requirement to optimise multiple conflicting objectives in an efficient manner. In such problems there can be the requirement to optimise a mixture of continuous and discrete variables. Herein, we propose a new multi-objective algorithm capable of optimising both continuous and discrete bounded variables in an efficient manner. The algorithm utilises Gaussian processes as surrogates in combination with a novel distance metric based upon Gower similarity. The MVMOO algorithm was compared to an existing mixed variable implementation of NSGA-II and random sampling for three test problems. MVMOO shows competitive performance on all proposed problems with efficient data acquisition and approximation of the Pareto fronts for the selected test problems.

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.

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.

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.

An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

scholarly journals Joint Optimization of Routes and Container Fleets to Design Sustainable Intermodal Chains in Chile

2020 ◽  
Vol 12 (6) ◽  
pp. 2221
Author(s):  
Alba Martínez-López ◽  
Manuel Chica
Keyword(s):  
Real Life ◽  
Decision Support Tool ◽  
Nsga Ii ◽  
Policy Makers ◽  
Support Tool ◽  
Conflicting Objectives ◽  
Objective Model ◽  
Pareto Fronts ◽  
Geographical Locations

This paper introduces a decision support tool for sustainable intermodal chains with seaborne transport, in which the optimization of a multi-objective model enables conflicting objectives to be handled simultaneously. Through the assessment of ‘door-to-door’ transport in terms of costs, time, and environmental impact, the most suitable maritime route and the optimized fleet are jointly calculated to maximize the opportunities for success of intermodal chains versus trucking. The resolution of the model through NSGA-II algorithms permits to obtain Pareto fronts that offer groups of optimized solutions. This is not only useful to make decisions in the short term, but also to establish long-term strategies through assessment of the frontiers’ behavior obtained when a sensitivity analysis is undertaken. Thus, consequences of transport policies on intermodal performance can be analyzed. A real-life case is studied to test the usefulness of the model. From the application case, not only the most suitable Motorway of the Seas with their optimized fleets are identified for Chile, but also significant general findings are provided for both policy makers and heads of ports to promote the intermodal option regardless of their geographical locations.

Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space Exploration

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mehmet Unal ◽  
Gordon P. Warn ◽  
Timothy W. Simpson
Keyword(s):  
Pareto Front ◽  
Space Exploration ◽  
Problem Formulation ◽  
Shape Index ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Complex Engineering ◽  
Trade Space Exploration ◽  
Pareto Fronts ◽  
Future Work

Recent advances in simulation and computation capabilities have enabled designers to model increasingly complex engineering problems, taking into account many dimensions, or objectives, in the problem formulation. Increasing the dimensionality often results in a large trade space, where decision-makers (DM) must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of nondominated solutions, that is, the Pareto front, onto two-objective trade spaces to help identify and negotiate tradeoffs between conflicting objectives. However, as the number of objectives increases, an exhaustive exploration of all of the two-dimensional (2D) Pareto fronts can be inefficient due to a combinatorial increase in objective pairs. Recently, an index was introduced to quantify the shape of a Pareto front without having to visualize the solution set. In this paper, a formal derivation of the Pareto Shape Index is presented and used to support multi-objective trade space exploration. Two approaches for trade space exploration are presented and their advantages are discussed, specifically: (1) using the Pareto shape index for weighting objectives and (2) using the Pareto shape index to rank objective pairs for visualization. By applying the two approaches to two multi-objective problems, the efficiency of using the Pareto shape index for weighting objectives to identify solutions is demonstrated. We also show that using the index to rank objective pairs provides DM with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed.

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.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

scholarly journals Classification of Reservoir Recovery Factor for Oil and Gas Reservoirs: A Multi-Objective Feature Selection Approach

2021 ◽  
Vol 9 (8) ◽  
pp. 888
Author(s):  
Qasem Al-Tashi ◽  
Emelia Akashah Patah Akhir ◽  
Said Jadid Abdulkadir ◽  
Seyedali Mirjalili ◽  
Tareq M. Shami ◽  
...  
Keyword(s):  
Feature Selection ◽  
Recovery Factor ◽  
Classification Error ◽  
Grey Wolf Optimizer ◽  
Small Subset ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Conflicting Objectives

The accurate classification of reservoir recovery factor is dampened by irregularities such as noisy and high-dimensional features associated with the reservoir measurements or characterization. These irregularities, especially a larger number of features, make it difficult to perform accurate classification of reservoir recovery factor, as the generated reservoir features are usually heterogeneous. Consequently, it is imperative to select relevant reservoir features while preserving or amplifying reservoir recovery accuracy. This phenomenon can be treated as a multi-objective optimization problem, since there are two conflicting objectives: minimizing the number of measurements and preserving high recovery classification accuracy. In this study, wrapper-based multi-objective feature selection approaches are proposed to estimate the set of Pareto optimal solutions that represents the optimum trade-off between these two objectives. Specifically, three multi-objective optimization algorithms—Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi-Objective Particle Swarm Optimization (MOPSO)—are investigated in selecting relevant features from the reservoir dataset. To the best of our knowledge, this is the first time multi-objective optimization has been used for reservoir recovery factor classification. The Artificial Neural Network (ANN) classification algorithm is used to evaluate the selected reservoir features. Findings from the experimental results show that the proposed MOGWO-ANN outperforms the other two approaches (MOPSO and NSGA-II) in terms of producing non-dominated solutions with a small subset of features and reduced classification error rate.

scholarly journals A Generalized SDP Multi-Objective Optimization Method for EM-Based Microwave Device Design

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3065 ◽  
Author(s):  
Ying Liu ◽  
Qingsha S. Cheng ◽  
Slawomir Koziel
Keyword(s):  
Computational Cost ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Uwb Antenna ◽  
Nsga Ii ◽  
Multi Objective ◽  
Iot Applications ◽  
Comparison Results ◽  
Pareto Fronts ◽  
Better Than

In this article, a generalized sequential domain patching (GSDP) method for efficient multi-objective optimization based on electromagnetics (EM) simulation is proposed. The GSDP method allowing fast searching for Pareto fronts for two and three objectives is elaborated in detail in this paper. The GSDP method is compared with the NSGA-II method using multi-objective problems in the DTLZ series, and the results show the GSDP method saved computational cost by more than 85% compared to NSGA-II method. A diversity comparison indicator (DCI) is used to evaluate approximate Pareto fronts. The comparison results show the diversity performance of GSDP is better than that of NSGA-II in most cases. We demonstrate the proposed GSDP method using a practical multi-objective design example of EM-based UWB antenna for IoT applications.

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