Computers & Operations Research 40 (2013) 1521–1523

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Computers & Operations Research

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journal homepage: www.elsevier.com/locate/caor

Editorial

Emergent nature inspired algorithms for multi-objective optimization

a r t i c l e i n f o a b s t r a c t

Keywords:

Metaheuristics

Multi-objective optimization

Nature inspired algorithms

48/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.cor.2013.01.020

Many real-world decision-making situations possess both a discrete and combinatorial structure and

involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of

large size and contains several objectives to be ‘‘optimized’’. Although Multiple Objective Optimization

is a well-established field of research, one branch, namely nature inspired metaheuristics is currently

experienced a tremendous growth. Over the last few years, developments of new methodologies,

methods, and techniques to deal with multi-objective large size problems in particular those with a

combinatorial structure and the strong improvement on computing technologies (during and after the

80s) made possible to solve very hard problems with the help of inspired nature based metaheuristics.

& 2013 Elsevier Ltd. All rights reserved.

1. Motivations

Multiple Criteria Decision Analysis (MCDA) covers a broadrange of areas such as multiple attribute utility theory, multipleobjective optimization and multiple criteria decision aiding. In allof these areas research on theoretical topics and successfulapplications in finance, economics, telecommunications, forestry,agriculture, etc. have led to a huge number of publications sincethe 1950s, but mainly for the last three decades.

One branch of MCDA has experienced particularly tremendousgrowth since some years ago: Metaheuristics for Multiple Objec-tives Discrete and Combinatorial Optimization problems. In thesefew years, developments of new methodologies, a better under-standing of the complexity and structure of this kind of problemsand better computing technology (since the 80s) made it possibleto solve previously intractable problems [2]. Nowadays, real-world applications of large scale multiple objectives discretemodels are feasible thanks to the developments of metaheuristics.

The use of metaheuristics to tackle multiple objective optimizationproblems has recently flourished giving birth to many ideas publishedin various journals. Some international OR journals and book publish-ers have already dedicated special issues to multi-objective meta-heuristics [1]. Till recently, metaheuristic methods have mainly beenapplied to continuous optimization problems with multiple objec-tives, this is in particular true for evolutionary algorithms. Now weobserve an increasing use of metaheuristics on Multiple ObjectiveDiscrete and Combinatorial Optimization. Despite the importanceand frequency of these real-world decision-making problems, thenew (metaheuristic) solution techniques and the rapidly growingnumber of publications in the field, no major OR journal has yetdevoted a special issue to this topic containing theoretical, methodo-logical, metaheuristics and application oriented papers. The mainobjective of this special issue is to fill this gap in the literature on thissubject.

ll rights reserved.

2. Contents

This special issue is devoted to publications on emergent natureinspired algorithms for multi-objective optimization. The topicsinclude

�

Emergent nature inspired algorithms: bee colony, ant colony,artificial immune systems, cellular genetic algorithms, scattersearch, cockoo search, evolutionary algorithms, simulatedannealing. � Hybrid methods such as coevolution. � Large scale multi-objective optimization: scheduling, vehicle

routing, path planning, energy networks, design optimization.

In the following, we shortly outline the content and contribu-tion of the nine papers that were finally selected for publication inthis special issue.

In the first paper, A.M. Mora, J.J. Merelo, P.A. Castillo, and M.G.Arenas propose a family of ant colony based optimization algo-rithms (hCHAC) for the resolution of the bi-criteria military unitpath planning problem. They consider two objectives: maximiza-tion of speed and safety. Each one of these objectives includesdifferent factors (such as stealth or avoidance of resource-consuming zones), that is why in this paper they generatedifferent members of the hCHAC family by aggregating the initialcost functions into a different amount of objectives (from one tofour) and considering a different parametrization set in eachcase. The hCHAC algorithms have been tested in several different(and increasingly realistic) scenarios, modelled in a simulatorand compared with some other well-known ant colony basedalgorithms. These latter algorithms have been adapted for thepurpose of this work to deal with this problem, along with anew multi-objective greedy approach that has been included asbaseline for comparisons. The experiments show that most of

Editorial / Computers & Operations Research 40 (2013) 1521–15231522

the hCHAC algorithms outperform the other approaches, yieldingat the same time very good military behaviour in the tacticalsense.

In the second paper, B. Dorronsoro, G. Danoy, A.J. Nebro, and P.Bouvry achieve super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperativecoevolution. This paper introduces three new multi-objectivecooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength ParetoEvolutionary Algorithm 2 (SPEA2) and Multi-objective CellularGenetic Algorithm (MOCell). In such a coevolutionary architec-ture, the population is split into several subpopulations orislands, each of them being in charge of optimizing a subset ofthe global solution by using the original multi-objective algo-rithm. Evaluation of complete solutions is achieved throughcooperation, i.e., all subpopulations share a subset of their currentpartial solutions. The purpose of this paper is to study how theperformance of the cooperative coevolutionary multi-objectiveapproaches can be drastically increased with respect to theircorresponding original versions. This is specially interesting forsolving complex problems involving a large number of variables,since the problem decomposition performed by the model at theisland level allows for much faster executions (the number ofvariables to handle in every island is divided by the number ofislands). The authors conduct a study about a real-world problemrelated to grid computing, the bi-objective robust schedulingproblem of independent tasks. The goal in this problem is tominimize makespan (i.e., the time when the latest machinefinishes its assigned tasks) and to maximize the robustness ofthe schedule (i.e., its tolerance to unexpected changes on theestimated time to complete the tasks). They propose a parallel,multi-threaded implementation of the coevolutionary algorithmsand analyze the results obtained in terms of both the quality ofthe Pareto front approximations yielded by the techniques as wellas the resulting speedups when running them on a multi-coremachine.

The authors of the third paper, J. Taheri, Y.C. Lee, A.Y. Zomaya,and H.J. Siegel, propose a bee colony based optimization approach(JDS-BC) for simultaneous job scheduling and data replication ingrid environments. JDS-BC consists of two collaborating mechan-isms to efficiently schedule jobs onto computational nodes andreplicate datafiles on storage nodes in a system so that the twoindependent, and in many cases conflicting, objectives (i.e.,makespan and total datafile transfer time) of such heterogeneoussystems are concurrently minimized. Three benchmarks – varyingfrom small- to large-sized instances – are used to test theperformance of JDS-BC. Results are compared against otheralgorithms to show JDS-BC’s superiority under different operatingscenarios. These results also provide invaluable insights into data-centric job scheduling for grid environments.

The authors of the fourth paper, Q. Ruan, Z. Zhang, L. Miao, andH. Shen, focus on a hybrid approach for the multi-objectivevehicle routing problem with three-dimensional loading con-straints. The target problem requires a combinatorial optimiza-tion of a feasible loading and successive routing of vehicles tosatisfy customer demands, where all vehicles must start andfinish at a central depot. The goal of this combinatorial problemis to minimize the total transportation cost while serving custo-mers. Despite its clear practical significance in the real-worlddistribution management, for its high combinatorial complexity,published papers on this problem in literature are very limited.The authors present a hybrid approach that combines honey beemating optimization and six loading heuristics, one for vehiclerouting and the other for three-dimensional loading, to solve theintegrated problem. They computationally evaluate this hybrid

approach on all publicly available test instances, and obtain newbest solutions for several scenarios.

In the fifth paper, Q. Lin and J. Chen design and implement anovel micro-population immune multi-objective optimizationalgorithm. They adopt a novel adaptive mutation operator forlocal search and an efficient fine-grained selection operator forarchive update. With the external archive for storing non-dominated individuals, the population diversity can be wellpreserved by using an efficient fine-grained selection procedureperformed on the micro population. The adaptive mutationoperator is executed according to the fitness values, whichpromotes to use relative large steps for boundary and less-crowded individuals in high probability. Therefore, the explora-tory capabilities are enhanced. When comparing the proposedalgorithm with a recently proposed immune multi-objectivealgorithm and a scatter search multi-objective algorithm invarious benchmark functions, simulations show that the proposedalgorithm not only improves convergence ability but also pre-serves population diversity adequately in most cases.

The authors of the sixth paper, E. Oliveira, C.H. Antunes and A.Gomes, carry out a comparative study of different approachesusing an outranking relation in a multi-objective evolutionaryalgorithm. The decision maker’s preferences are incorporatedusing an outranking relation and preference parameters asso-ciated with the ELECTRE TRI method. The goal of this work is touse the preference information supplied by the decision maker toguide the search process to the regions where solutions more inaccordance with his/her preferences are located. This will allownarrowing the scope of the search and reducing the computa-tional effort. A real application dealing with electrical distributionnetwork is used to assess the performance of the differentapproaches.

The seventh paper, authored by X.-S. Yang and S. Deb, dealswith multi-objective cuckoo search for design optimization.Indeed, many design problems in engineering are typicallymulti-objective, under complex non-linear constraints. Comput-ing effort and the number of function evaluations may oftenincrease significantly for multi-objective problems. In this paper,the authors formulate a new cuckoo search for multi-objectiveoptimization. They validate it against a set of multi-objective testfunctions, and then apply it to solve structural design problemssuch as beam design and disc brake design. In addition, they alsoanalyze the main characteristics of the algorithm and theirimplications.

The authors of the eighth paper, S.-W. Lin and K.-C. Ying, focuson minimizing makespan and total flowtime in permutationflowshops by a bi-objective multi-start simulated-annealing algo-rithm. In this study, a bi-objective multi-start simulated-annealing algorithm (BMSA) is presented for permutationflowshop scheduling problems with the objectives of minimizingthe makespan and total flowtime of jobs. To evaluate theperformance of the BMSA, computational experiments wereconducted on the well-known benchmark problem set providedby Taillard. The non-dominated sets obtained from each of theexisting benchmark algorithms and the BMSA were compared,and then combined to form a net non-dominated front. Thecomputational results show that more than 64% of the solutionsin the net non-dominated front are contributed by theproposed BMSA.

The authors of the last paper Y-Y. Tan, Y-C. Jiao, H. Li and X-K.Wang extended a multi-objective evolutionary algorithm tohigher spaces. It is a rather difficult problem. Their new algorithmis based on a principle of decomposition and it improves MOEA/Dalgorithm. A comparison with state-of-the art NSGA II algorithmwas performed on a set of instances with five criteria. Theirmethod, named UMOEA/D, outperformed MOEA/D and NSGA II

Editorial / Computers & Operations Research 40 (2013) 1521–1523 1523

algorithms, especially in those cases where the number ofobjectives is high.

References

[1] Talbi E-G. Metaheuristics: from design to implementation. Wiley; 2009.[2] Figueira J, Greco S, Ehrgott M. Multiple criteria decision analysis—state of the

art surveys. 2nd ed.. Springer; 2013.

Jose Rui Figueira n

Instituto Superior Tecnico, Technical University of Lisbon, Portugal

E-mail address: figueira@ist.utl.pt

El-Ghazali TalbiUniversity of Lille, CNRS, INRIA, Lille, France

Available online 4 February 2013

n Corresponding author.