Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.

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MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.

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An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http://www.ntu.edu.sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.

Comprehensive learning particle swarm optimizer for global optimization of multimodal functions

Salp Swarm Algorithm

A unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, parallel, and distributed metaheuristics Implementing metaheuristics on sequential and parallel machines Using many case studies and treating design and implementation independently, this book gives readers the skills necessary to solve large-scale optimization problems quickly and efficiently. It is a valuable reference for practicing engineers and researchers from diverse areas dealing with optimization or machine learning; and graduate students in computer science, operations research, control, engineering, business and management, and applied mathematics.

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Metaheuristics: From Design to Implementation

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.

Handling multiple objectives with particle swarm optimization

This work presents a simple mechanism to handle constraints with a particle swarm optimization algorithm. Our proposal uses a simple criterion based on closeness of a particle to the feasible region in order to select a leader. Additionally, our algorithm incorporates a turbulence operator that improves the exploratory capabilities of our particle swarm optimization algorithm. Despite its relative simplicity, our comparison of results indicates that the proposed approach is highly competitive with respect to three constraint-handling techniques representative of the state-of-the-art in the area.

A constraint-handling mechanism for particle swarm optimization

In this paper, we present an extension of the heuristic called “particle swarm optimization” (PSO) that is able to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and is based on the idea of having a set of sub-swarms instead of single particles. In each sub-swarm, a PSO algorithm is executed and, at some point, the different sub-swarms exchange information. Our proposed approach is validated using several test functions taken from the evolutionary multiobjective optimization literature. Our results indicate that the approach is highly competitive with respect to algorithms representative of the state-of-the-art in evolutionary multiobjective optimization.

Using Clustering Techniques to Improve the Performance of a Multi-objective Particle Swarm Optimizer

In this paper, we present a genetic algorithm with a very small population and a reinitialization process (a microgenetic algorithm) for solving multiobjective optimization problems. Our approach uses three forms of elitism, including an external memory (or secondary population) to keep the nondominated solutions found along the evolutionary process. We validate our proposal using several engineering optimization problems taken from the specialized literature and compare our results with respect to two other algorithms (NSGA-II and PAES) using three different metrics. Our results indicate that our approach is very efficient (computationally speaking) and performs very well in problems with different degrees of complexity.

Multiobjective structural optimization using a microgenetic algorithm

An important issue with Evolutionary Algorithms (EAs) is the way to identify the best solutions in order to guide the search process. Fitness comparisons among solutions in single-objective optimization is straightforward, but when dealing with multiple objectives, it becomes a non-trivial task. Pareto dominance has been the most commonly adopted relation to compare solutions in a multiobjective optimization context. However, it has been shown that as the number of objectives increases, the convergence ability of approaches based on Pareto dominance decreases. In this paper, we propose three novel fitness assignment methods for many-objective optimization. We also perform a comparative study in order to investigate how effective are the proposed approaches to guide the search in high-dimensional objective spaces. Results indicate that our approaches behave better than six state-of-the-art fitness assignment methods.

Gregorio Toscano Pulido

Papers

Handling multiple objectives with particle swarm optimization

A constraint-handling mechanism for particle swarm optimization

Using Clustering Techniques to Improve the Performance of a Multi-objective Particle Swarm Optimizer

Multiobjective structural optimization using a microgenetic algorithm

Ranking Methods for Many-Objective Optimization