scholarly journals A Runtime Analysis of Typical Decomposition Approaches in MOEA/D Framework for Many-objective Optimization Problems

2021 ◽  
Author(s):  
Zhengxin Huang ◽  
Yuren Zhou ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Theoretical Analysis ◽  
Pareto Front ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Good Choice ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Penalty Parameter ◽  
Decomposition Approach ◽  
Popular Method

Decomposition approach is an important component in multi-objective evolutionary algorithm based on decomposition (MOEA/D), which is a popular method for handing many-objective optimization problems (MaOPs). This paper presents a theoretical analysis on the convergence ability of using the typical weighted sum (WS), Tchebycheff (TCH) or penalty-based boundary intersection (PBI) approach in a basic MOEA/D for solving two benchmark MaOPs. The results show that using WS, the algorithm can always find an optimal solution for any subproblem in polynomial expected runtime. In contrast, the algorithm needs at least exponential expected runtime for some subproblems if using TCH or PBI. Moreover, our analyses discover an obvious shortcoming of using WS, that is, the optimal solutions of different subproblems are easily corresponding to the same solution. In addition, this analysis indicates that if using PBI, a small value of the penalty parameter is a good choice for faster converging to the Pareto front, but it may lose the diversity. This study reveals some optimization behaviors of using three typical decomposition approaches in the well-known MOEA/D framework for solving MaOPs.

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.

Presorting as a method of acceleration of algorithms in multi-objective optimization problems

2016 ◽  
Vol 0 (0) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Distance Function ◽  
Pareto Front ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Minkowski Distance ◽  
Finite Set ◽  
Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

scholarly journals ON THE COMPLEXITY OF COMPUTING OPTIMAL SOLUTIONS

1991 ◽  
Vol 02 (03) ◽  
pp. 207-220 ◽  
Author(s):  
ZHI-ZHONG CHEN ◽  
SEINOSUKE TODA
Keyword(s):  
Polynomial Time ◽  
General Result ◽  
Optimization Problems ◽  
Randomized Algorithm ◽  
Optimal Solution ◽  
Maximum Clique ◽  
Optimal Solutions ◽  
Np Optimization ◽  
Parallel Queries ◽  
Class Of Functions

We study the computational complexity of computing optimal solutions (the solutions themselves, not just their cost) for NP optimization problems where the costs of feasible solutions are bounded above by a polynomial in the length of their instances (we simply denote by NPOP such an NP optimization problem). It is of particular interest to find a computational structure (or equivalently, a complexity class) which. captures that complexity, if we consider the problems of computing optimal solutions for NPOP’s as a class of functions giving those optimal solutions. In this paper, we will observe that [Formula: see text] the class of functions computable in polynomial-time with one free evaluation of unbounded parallel queries to NP oracle sets, captures that complexity. We first show that for any NPOP Π, there exists a polynomial-time bounded randomized algorithm which, given an instance of Π, uses one free evaluation of parallel queries to an NP oracle set and outputs some optimal solution of the instance with very high probability. We then show that for several natural NPOP’s, any function giving those optimal solutions is at least as computationally hard as all functions in [Formula: see text]. To show the hardness results, we introduce a property of NPOP’s, called paddability, and we show a general result that if Π is a paddable NPOP and its associated decision problem is NP-hard, then all functions in [Formula: see text] are computable in polynomial-time with one free evaluation of an arbitrary function giving optimal solutions for instances of Π. The hardness results are applications of this general result. Among the NPOP’s, we include MAXIMUM CLIQUE, MINIMUM COLORING, LONGEST PATH, LONGEST CYCLE, 0–1 TRAVELING SALESPERSON, and 0–1 INTEGER PROGRAMMING.

scholarly journals MODIFICATION OF FIREWORKS METHOD FOR MULTIOBJECTIVE OPTIMIZATION BASED ON NON-DOMINATED SORTING

2019 ◽  
Vol 22 (3) ◽  
pp. 67-78
Author(s):  
A. V. Panteleev ◽  
A. U. Krychkov
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Complex Structure ◽  
Optimal Solution ◽  
Future Research ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Equal Importance ◽  
Approximate Result

The article suggests a modification for numerical fireworks method of the single-objective optimization for solving the problem of multiobjective optimization. The method is metaheuristic. It does not guarantee finding the exact solution, but can give a good approximate result. Multiobjective optimization problem is considered with numerical criteria of equal importance. A possible solution to the problem is a vector of real numbers. Each component of the vector of a possible solution belongs to a certain segment. The optimal solution of the problem is considered a Pareto optimal solution. Because the set of Pareto optimal solutions can be infinite; we consider a method for finding an approximation consisting of a finite number of Pareto optimal solutions. The modification is based on the procedure of non-dominated sorting. It is the main procedure for solutions search. Non-dominated sorting is the ranking of decisions based on the values of the numerical vector obtained using the criteria. Solutions are divided into disjoint subsets. The first subset is the Pareto optimal solutions, the second subset is the Pareto optimal solutions if the first subset is not taken into account, and the last subset is the Pareto optimal solutions if the rest subsets are not taken into account. After such a partition, the decision is made to create new solutions. The method was tested on well-known bi-objective optimization problems: ZDT2, LZ01. Structure of the location of Pareto optimal solutions differs for the problems. LZ01 have complex structure of Pareto optimal solutions. In conclusion, the question of future research and the issue of modifying the method for problems with general constraints are discussed.

scholarly journals A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cai Dai ◽  
Yuping Wang
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Experimental Studies ◽  
Evolutionary Process ◽  
Optimal Solution ◽  
Multiobjective Evolutionary Algorithm ◽  
Multiobjective Optimization Problems ◽  
Objective Space

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

Fuzzy Dynamic Programming Problem for Single Additive Constraint with Additively Separable Return by Means of Trapezoidal Membership Functions

2017 ◽  
pp. 168-187
Author(s):  
Palanivel Kaliyaperumal
Keyword(s):  
Dynamic Programming ◽  
Programming Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Optimal Arrangement ◽  
Fuzzy Membership Functions ◽  
Dynamic Programming Problem ◽  
Linear And Nonlinear

Dynamic Programming Problem (DPP) is a multivariable optimization problem is decomposed into a series of stages, optimization being done at each stage with respect to one variable only. DP stands a suitable quantitative study procedure that can be used to explain various optimization problems. It deals through reasonably large as well as complex problems; in addition, it involves creating a sequence of interconnected decisions. The technique offers an efficient procedure for defining optimal arrangement of decisions. Throughout this chapter, solving procedure completely deliberate about as Fuzzy Dynamic Programming Problem for single additive constraint with additively separable return with the support of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of Fuzzy Dynamic Programming Problem (FDPP). The fuzzified version of the problem has been stated with the support of a numerical example for both linear and nonlinear fuzzy optimal solutions and it is associated to showing that the proposed procedure offers an efficient tool for handling the dynamic programming problem instead of classical procedures. As a final point the optimal solution with in the form of fuzzy numbers and justified its solution with in the description of trapezoidal fuzzy membership functions.

Adaptive Control of Dominance Area of Solutions in Evolutionary Many-Objective Optimization

2015 ◽  
Vol 11 (02) ◽  
pp. 135-150 ◽  
Author(s):  
Kouhei Tomita ◽  
Minami Miyakawa ◽  
Hiroyuki Sato
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Search Performance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Dominance ◽  
Nsga Ii ◽  
Convergence Of Solutions

Controlling the dominance area of solutions (CDAS) relaxes the concept of Pareto dominance with an user-defined parameter S. CDAS with S < 0.5 expands the dominance area and improves the search performance of multi-objective evolutionary algorithms (MOEAs) especially in many-objective optimization problems (MaOPs) by enhancing convergence of solutions toward the optimal Pareto front. However, there is a problem that CDAS with an expanded dominance area (S < 0.5) generally cannot approximate entire Pareto front. To overcome this problem we propose an adaptive CDAS (A-CDAS) that adaptively controls the dominance area of solutions during the solutions search. Our method improves the search performance in MaOPs by approximating the entire Pareto front while keeping high convergence. In early generations, A-CDAS tries to converge solutions toward the optimal Pareto front by using an expanded dominance area with S < 0.5. When we detect convergence of solutions, we gradually increase S and contract the dominance area of solutions to obtain Pareto optimal solutions (POS) covering the entire optimal Pareto front. We verify the effectiveness and the search performance of the proposed A-CDAS on concave and convex DTLZ3 benchmark problems with 2–8 objectives, and show that the proposed A-CDAS achieves higher search performance than conventional non-dominated sorting genetic algorithm II (NSGA-II) and CDAS with an expanded dominance area.

scholarly journals Application of the Pareto front for risk control in the transport system

2019 ◽  
Vol 302 ◽  
pp. 01023
Author(s):  
Agnieszka Sołtysiak ◽  
Klaudiusz Migawa
Keyword(s):  
Transport System ◽  
Pareto Front ◽  
Simulated Annealing Algorithm ◽  
Evaluation Criteria ◽  
Optimal Solution ◽  
Point Of View ◽  
Optimal Solutions ◽  
Operation Process ◽  
Markov Decision ◽  
Selection Of

The article describes the developed model of controlling the process of means of transport operation, in which the choice of control strategy is carried out using non-deterministic methods. The model presented in the paper allows one to evaluate the quality of the transport system operation from the point of view of selected evaluation criteria: the risk of occurrence of undesired events and the availability of means of transport. The article presents a description of the method for determining the optimal (quasi-optimal) strategy for controlling the process of the use of means of transport taking into account the semi-Markov decision- making processes. The selection of the optimal (quasi-optimal) solution is carried out using the genetic algorithm and the simulated annealing algorithm. As a result of numerical calculations, for the criterion functions used, a set of quasi-optimal solutions is obtained in the form of the so- called Pareto front. This applies to the selection of possible decision variants, such a strategy for controlling the operation process, for which the functions constituting the evaluation criteria achieve values belonging to the Pareto-optimal solutions set.

scholarly journals Designing a generic human-machine framework for real-time supply chain planning

2016 ◽  
Vol 4 (2) ◽  
pp. 69-85 ◽  
Author(s):  
Jonathan Gaudreault ◽  
Claude-Guy Quimper ◽  
Philippe Marier ◽  
Mathieu Bouchard ◽  
François Chéné ◽  
...  
Keyword(s):  
Decision Making ◽  
Real Time ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Real Case ◽  
Optimal Solutions ◽  
Basic Scheme ◽  
Interactive Decision Making ◽  
Mixed Initiative ◽  
Business Optimization

Abstract Mixed-Initiative-Systems (MIS) are hybrid decision-making systems in which human and machine collaborate in order to produce a solution. This paper described an MIS adapted to business optimization problems. These problems can usually be solved in less than an hour as they show a linear structure. However, this delay is unacceptable for iterative and interactive decision-making contexts where users need to provide their input. Therefore, we propose a system providing the decision-makers with a convex hull of optimal solutions that minimize/maximize the variables of interest. The users can interactively modify the value of a variable and the system is able to recompute a new optimal solution in a few milliseconds. Four real-time reoptimization methods are described and evaluated. We also propose an improvement to this basic scheme in order to allow a user to explore near-optimal solutions as well. Examples showing real case of how we have exploited this framework within interactive decision support software are given. Highlights A Mixed Initiative System adapted to business optimization problems is presented. Real-time reoptimization methods are described and evaluated. The system is able to recompute a new optimal solution in a few milliseconds. Improvement to this basic scheme allow a user to explore near-optimal solutions. Examples showing real case of exploiting this framework are given.

Environmental Adaption Method

2021 ◽  
pp. 300-327
Author(s):  
Anuj Chandila ◽  
Shailesh Tiwari ◽  
K. K. Mishra ◽  
Akash Punhani
Keyword(s):  
Particle Swarm Optimization ◽  
Randomized Algorithms ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Evolutionary Strategy ◽  
Optimal Solutions ◽  
Swarm Optimization ◽  
Local Optima ◽  
Local Optimal Solution

This article describes how optimization is a process of finding out the best solutions among all available solutions for a problem. Many randomized algorithms have been designed to identify optimal solutions in optimization problems. Among these algorithms evolutionary programming, evolutionary strategy, genetic algorithm, particle swarm optimization and genetic programming are widely accepted for the optimization problems. Although a number of randomized algorithms are available in literature for solving optimization problems yet their design objectives are same. Each algorithm has been designed to meet certain goals like minimizing total number of fitness evaluations to capture nearly optimal solutions, to capture diverse optimal solutions in multimodal solutions when needed and also to avoid the local optimal solution in multi modal problems. This article discusses a novel optimization algorithm named as Environmental Adaption Method (EAM) foable 3r solving the optimization problems. EAM is designed to reduce the overall processing time for retrieving optimal solution of the problem, to improve the quality of solutions and particularly to avoid being trapped in local optima. The results of the proposed algorithm are compared with the latest version of existing algorithms such as particle swarm optimization (PSO-TVAC), and differential evolution (SADE) on benchmark functions and the proposed algorithm proves its effectiveness over the existing algorithms in all the taken cases.

Sign in / Sign up

Export Citation Format

Share Document