scholarly journals Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2018
Author(s):  
Mohammed Mahrach ◽  
Gara Miranda ◽  
Coromoto León ◽  
Eduardo Segredo
Keyword(s):  
Evolutionary Algorithms ◽  
Knapsack Problem ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Problem Formulation ◽  
Travelling Salesman ◽  
Multi Objective ◽  
Main Components ◽  
Pareto Fronts ◽  
Single Objective

One of the main components of most modern Multi-Objective Evolutionary Algorithms (MOEAs) is to maintain a proper diversity within a population in order to avoid the premature convergence problem. Due to this implicit feature that most MOEAs share, their application for Single-Objective Optimization (SO) might be helpful, and provides a promising field of research. Some common approaches to this topic are based on adding extra—and generally artificial—objectives to the problem formulation. However, when applying MOEAs to implicit Multi-Objective Optimization Problems (MOPs), it is not common to analyze how effective said approaches are in relation to optimizing each objective separately. In this paper, we present a comparative study between MOEAs and Single-Objective Evolutionary Algorithms (SOEAs) when optimizing every objective in a MOP, considering here the bi-objective case. For the study, we focus on two well-known and widely studied optimization problems: the Knapsack Problem (KNP) and the Travelling Salesman Problem (TSP). The experimental study considers three MOEAs and two SOEAs. Each SOEA is applied independently for each optimization objective, such that the optimized values obtained for each objective can be compared to the multi-objective solutions achieved by the MOEAs. MOEAs, however, allow optimizing two objectives at once, since the resulting Pareto fronts can be used to analyze the endpoints, i.e., the point optimizing objective 1 and the point optimizing objective 2. The experimental results show that, although MOEAs have to deal with several objectives simultaneously, they can compete with SOEAs, especially when dealing with strongly correlated or large instances.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

Evolutionary algorithms for solving multi-objective travelling salesman problem

2011 ◽  
Vol 23 (2) ◽  
pp. 207-241 ◽  
Author(s):  
Vui Ann Shim ◽  
Kay Chen Tan ◽  
Jun Yong Chia ◽  
Jin Kiat Chong
Keyword(s):  
Evolutionary Algorithms ◽  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
Multi Objective

MOTEO: A Novel Multi-Objective Thermal Exchange Optimization Algorithm for Optimal Design of Truss Structures

2021 ◽  
Author(s):  
Nima Khodadadi ◽  
Siamak Talatahari ◽  
Armin Dadras Eslamlou
Keyword(s):  
Structural Design ◽  
Optimization Problems ◽  
Truss Structures ◽  
Metaheuristic Algorithm ◽  
Multi Objective Optimization ◽  
Thermal Exchange ◽  
Multi Objective ◽  
Mathematical Problems ◽  
Pareto Fronts ◽  
Single Objective

Abstract In the present paper, a physics-inspired metaheuristic algorithm is presented to solve multi-objective optimization problems. The algorithm is developed based on the concept of Newtonian cooling law that recently has been employed by the Thermal Exchange Optimization (TEO) algorithm to efficiently solve single-objective optimization problems. The performance of the multi-objective version of TEO (MOTEO) is examined through bi- and tri-objective mathematical problems as well as bi-objective structural design examples. According to the comparisons between the MOTEO and several well-known algorithms, the proposed algorithm can provide quality Pareto fronts with appropriate accuracy, uniformity and coverage for multi-objective problems.

Multi-Objective Evolutionary Algorithms

2011 ◽  
pp. 1145-1151 ◽  
Author(s):  
Sanjoy Das ◽  
Bijaya K. Panigrahi
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Population Based ◽  
Stochastic Methods ◽  
Local Minima ◽  
Multi Objective ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Complex Optimization ◽  
Single Objective

Real world optimization problems are often too complex to be solved through analytical means. Evolutionary algorithms, a class of algorithms that borrow paradigms from nature, are particularly well suited to address such problems. These algorithms are stochastic methods of optimization that have become immensely popular recently, because they are derivative-free methods, are not as prone to getting trapped in local minima (as they are population based), and are shown to work well for many complex optimization problems. Although evolutionary algorithms have conventionally focussed on optimizing single objective functions, most practical problems in engineering are inherently multi-objective in nature. Multi-objective evolutionary optimization is a relatively new, and rapidly expanding area of research in evolutionary computation that looks at ways to address these problems. In this chapter, we provide an overview of some of the most significant issues in multi-objective optimization (Deb, 2001).

A Meta-Objective Approach for Many-Objective Evolutionary Optimization

2020 ◽  
Vol 28 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Dunwei Gong ◽  
Yiping Liu ◽  
Gary G. Yen
Keyword(s):  
Evolutionary Algorithms ◽  
Selection Criteria ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Problem Formulation ◽  
Multi Objective ◽  
Objective Space ◽  
Convergence Performance ◽  
Poor Convergence ◽  
The Many

Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

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