The success of the Particle Swarm Optimiza- tion (PSO) algorithm as a single-objective optimizer (mainly when dealing with continuous search spaces) has motivated re- searchers to extend the use of this bio-inspired technique to other areas. One of them is multi-objective optimization. De- spite the fact that the first proposal of a Multi-Objective Par- ticle Swarm Optimizer (MOPSO) is over six years old, a con- siderable number of other algorithms have been proposed since then. This paper presents a comprehensive review of the vari- ous MOPSOs reported in the specialized literature. As part of this review, we include a classification of the approaches, and we identify the main features of each proposal. In the last part of the paper, we list some of the topics within this field that we consider as promising areas of future research.

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Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art

Engineering optimisation is typically multi-objective and multidisciplinary with complex constraints, and the solution of such complex problems requires efficient optimisation algorithms. Recently, Xin-She Yang proposed a bat-inspired algorithm for solving non-linear, global optimisation problems. In this paper, we extend this algorithm to solve multi-objective optimisation problems. The proposed multi-objective bat algorithm (MOBA) is first validated against a subset of test functions, and then applied to solve multi-objective design problems such as welded beam design. Simulation results suggest that the proposed algorithm works efficiently.

Bat algorithm for multi-objective optimisation

Multiobjective cuckoo search for design optimization

Particle Swarm Optimization (PSO), in its present form, has been in existence for roughly a decade, with formative research in related domains (such as social modelling, computer graphics, simulation and animation of natural swarms or flocks) for some years before that; a relatively short time compared with some of the other natural computing paradigms such as artificial neural networks and evolutionary computation. However, in that short period, PSO has gained widespread appeal amongst researchers and has been shown to offer good performance in a variety of application domains, with potential for hybridisation and specialisation, and demonstration of some interesting emergent behaviour. This paper aims to offer a compendious and timely review of the field and the challenges and opportunities offered by this welcome addition to the optimization toolbox. Part I discusses the location of PSO within the broader domain of natural computing, considers the development of the algorithm, and refinements introduced to prevent swarm stagnation and tackle dynamic environments. Part II considers current research in hybridisation, combinatorial problems, multicriteria and constrained optimization, and a range of indicative application areas.

A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.

Multiobjective firefly algorithm for continuous optimization

An algorithm for solving multiobjective optimization problems is presented based on PSO through the improvement of the selection manner for global and individual extremum. The search for the Pareto optimal set of multiobjective optimization problems is performed. Numerical simulations show the effectiveness of the proposed algorithm.

Z.Q. Ma

Papers

Solving multi objective optimization problems using particle swarm optimization