Muhammad Asif Jan

A study of two penalty-parameterless constraint handling techniques in the framework of MOEA/D

Penalty functions are frequently employed for handling constraints in constrained optimization problems (COPs). In penalty function methods, penalty coefficients balance objective and penalty functions. However, finding appropriate penalty coefficients to strike the right balance is often very hard. They are problems dependent. Stochastic ranking (SR) and constraint-domination principle (CDP) are two promising penalty functions based constraint handling techniques that avoid penalty coefficients. In this paper, the extended/modified versions of SR and CDP are implemented for the first time in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. This led to two new algorithms, CMOEA/D-DE-SR and CMOEA/D-DE-CDP. The performance of these new algorithms is tested on CTP-series and CF-series test instances in terms of the HV-metric, IGD-metric, and SC-metric. The experimental results are compared with NSGA-II, IDEA, and the three best performers of CEC 2009 MOEA competition, which showed better and competitive performance of the proposed algorithms on most test instances of the two test suits. The sensitivity of the performance of proposed algorithms to parameters is also investigated. The experimental results reveal that CDP works better than SR in the MOEA/D framework.

Threshold Based Dynamic and Adaptive Penalty Functions for Constrained Multiobjective Optimization

Penalty functions are frequently used for dealing with constraints in constrained optimization. Among different types of penalty functions, dynamic and adaptive penalty functions seem effective, since the penalty coefficients in them are adjusted based on the current generation number (or number of solutions searched) and feedback from the search. In this paper, we propose dynamic and adaptive versions of our recently proposed threshold based penalty function. They are then implemented in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework to solve constrained multi objective optimization problems (CMOPs). This led to a new algorithm, denoted by CMOEA/D-DE-TDA. The performance of CMOEA/D-DE-TDA is tested on CTP-series test instances in terms of the HV-metric and SC-metric. The experimental results are compared with IDEA and NSGA-II, which show the effectiveness of the proposed algorithm.

Hybrid adaptive evolutionary algorithm based on decomposition

The performance of search operators varies across the different stages of the search/optimization process of evolutionary algorithms (EAs). In general, a single search operator may not do well in all these stages when dealing with different optimization and search problems. To mitigate this, adaptive search operator schemes have been introduced. The idea is that when a search operator hits a difficult patch (under-performs) in the search space, the EA scheme “reacts” to that by potentially calling upon a different search operator. Hence, several multiple-search operator schemes have been proposed and employed within EA. In this paper, a hybrid adaptive evolutionary algorithm based on decomposition (HAEA/D) that employs four different crossover operators is suggested. Its performance has been evaluated on the well-known IEEE CEC’09 test instances. HAEA/D has generated promising results which compare well against several well-known algorithms including MOEA/D, on a number of metrics such as the inverted generational distance (IGD), the hyper-volume, the Gamma and Delta functions. These results are included and discussed in this paper.

Hybrid non-dominated sorting genetic algorithm with adaptive operators selection

Graphical abstractThe main goal of this paper is to investigate the effect of the multiple search operators with adaptive selection strategy and to develop hybrid version of non-dominated sorting genetic algorithm (HNSGA) for solving recently developed complicated multi-objective optimization test suit for multi-objective evolutionary algorithms (MOEAs) competition in the special session of the congress on evolutionary computing held at Norway in 2009 (CEC09). The Inverted generational distance (IGD) has been used performance indicator to establish valuable comparison between the suggested algorithm and NSGA-II as shown in the figure below. A set of Pareto optimal solutions with smaller is the IGD values confirm that approximated Pareto front (PF) will cover whole part of true PF in term of proximity and diversity. The average IGD-metric values evolution obtained by HNSGA versus NSGA-II for UF1-UF5 within allowable resources of 300,000 function evaluations. Display Omitted HighlightsA novel hybrid non-dominated sorting genetic algorithm (HNSGA) for multiobjective optimization with continuous variables is developed.HNSGA includes adaptive operator selection to allocate resources to multiple search operators based on their individual performance at the subpopulation level.HNSGA is tested in classical benchmark problems taken from the ZDT and CEC09 suites.Inverted generational distance (IGD), relative hypervolume (RHV), Gamma and Delta functions are used as performance indicators.The new algorithm is very competitive with other state-of-the-art optimizers such as AMALGAM, NSGA-II, MOEA/D, Hybrid AMGA, OMOEA, PA-DDS, etc. Multiobjective optimization entails minimizing or maximizing multiple objective functions subject to a set of constraints. Many real world applications can be formulated as multi-objective optimization problems (MOPs), which often involve multiple conflicting objectives to be optimized simultaneously. Recently, a number of multi-objective evolutionary algorithms (MOEAs) were developed suggested for these MOPs as they do not require problem specific information. They find a set of non-dominated solutions in a single run. The evolutionary process on which they are based, typically relies on a single genetic operator. Here, we suggest an algorithm which uses a basket of search operators. This is because it is never easy to choose the most suitable operator for a given problem. The novel hybrid non-dominated sorting genetic algorithm (HNSGA) introduced here in this paper and tested on the ZDT (Zitzler-Deb-Thiele) and CEC09 (2009 IEEE Conference on Evolutionary Computations) benchmark problems specifically formulated for MOEAs. Numerical results prove that the proposed algorithm is competitive with state-of-the-art MOEAs.

A New Threshold Based Penalty Function Embedded MOEA/D

Recently, we proposed a new threshold based penalty function. The threshold dynamically controls the penalty to infeasible solutions. This paper implants the two different forms of the proposed penalty function in the multiobjective evo-lutionary algorithm based on decomposition (MOEA/D) frame-work to solve constrained multiobjective optimization problems. This led to a new algorithm, denoted by CMOEA/D-DE-ATP. The performance of CMOEA/D-DE-ATP is tested on hard CF-series test instances in terms of the values of IGD-metric and SC-metric. The experimental results are compared with the three best performers of CEC 2009 MOEA competition. Experimental results show that the proposed penalty function is very promising, and it works well in the MOEA/D framework.

Reflected Adaptive Differential Evolution with Two External Archives for Large-Scale Global Optimization

JADE is an adaptive scheme of nature inspired algorithm, Differential Evolution (DE). It performed considerably improved on a set of well-studied benchmark test problems. In this paper, we evaluate the performance of new JADE with two external archives to deal with unconstrained continuous large-scale global optimization problems labeled as Reflected Adaptive Differential Evolution with Two External Archives (RJADE/TA). The only archive of JADE stores failed solutions. In contrast, the proposed second archive stores superior solutions at regular intervals of the optimization process to avoid premature convergence towards local optima. The superior solutions which are sent to the archive are reflected by new potential solutions. At the end of the search process, the best solution is selected from the second archive and the current population. The performance of RJADE/TA algorithm is then extensively evaluated on two test beds. At first on 28 latest benchmark functions constructed for the 2013 Congress on Evolutionary Computation special session. Secondly on ten benchmark problems from CEC2010 Special Session and Competition on Large-Scale Global Optimization. Experimental results demonstrated a very competitive perfor-mance of the algorithm.

Evolutionary Algorithms Based on Decomposition and Indicator Functions: State-of-the-art Survey

In the last two decades, multiobjective optimization has become mainstream because of its wide applicability in a variety of areas such engineering, management, the military and other fields. Multi-Objective Evolutionary Algorithms (MOEAs) play a dominant role in solving problems with multiple conflicting objective functions. They aim at finding a set of representative Pareto optimal solutions in a single run. Classical MOEAs are broadly in three main groups: the Pareto dominance based MOEAs, the Indicator based MOEAs and the decomposition based MOEAs. Those based on decomposition and indicator functions have shown high search abilities as compared to the Pareto dominance based ones. That is possibly due to their firm theoretical background. This paper presents state-of-the-art MOEAs that employ decomposition and indicator functions as fitness evaluation techniques along with other efficient techniques including those which use preference based information, local search optimizers, multiple ensemble search operators together with self-adaptive strategies, metaheuristics, mating restriction approaches, statistical sampling techniques, integration of Fuzzy dominance concepts and many other advanced techniques for dealing with diverse optimization and search problems

Hybridization of Adaptive Differential Evolution with BFGS

Local search (LS) methods start from a point and use the gradient or objective function value to guide the search. Such methods are good in searching the neighborhood of a given solution (i.e., they are good at exploitation), but they are poor in exploration. Evolutionary Algorithms (EAs) are nature inspired populationbased search optimizers. They are good in exploration, but not as good at exploitation as LS methods. Thus, it makes sense to hybridize EAs with LS techniques to arrive at a method which benefits from both and, as a result, have good search ability. Broydon-Fletcher-Goldfarb-Shanno (BFGS) method is a gradient-based LS method designed for nonlinear optimization. It is an efficient, but expensive method. Adaptive Differential Evolution with Optional External Archive (JADE) is an efficient EA. Nonetheless, its performance decreases with the increase in problem dimension. In this paper, we present a new hybrid algorithm of JADE and BFGS, called Hybrid of Adaptive Differential Evolution and BFGS, or DEELS, to solve the unconstrained continuous optimization problems. The performance of DEELS is compared, in terms of the statistics of the function error values with JADE.

Hybridization of Adaptive Differential Evolution with an Expensive Local Search Method

Differential evolution (DE) is an effective and efficient heuristic for global optimization problems. However, it faces difficulty in exploiting the local region around the approximate solution. To handle this issue, local search (LS) techniques could be hybridized with DE to improve its local search capability. In this work, we hybridize an updated version of DE, adaptive differential evolution with optional external archive (JADE) with an expensive LS method, Broydon-Fletcher-Goldfarb-Shano (BFGS) for solving continuous unconstrained global optimization problems. The new hybrid algorithm is denoted by DEELS. To validate the performance of DEELS, we carried out extensive experiments on well known test problems suits, CEC2005 and CEC2010. The experimental results, in terms of function error values, success rate, and some other statistics, are compared with some of the state-of-the-art algorithms, self-adaptive control parameters in differential evolution (jDE), sequential DE enhanced by neighborhood search for large-scale global optimization (SDENS), and differential ant-stigmergy algorithm (DASA). These comparisons reveal that DEELS outperforms jDE and SDENS except DASA on the majority of test instances.

Threshold Based Penalty Functions for Constrained Multiobjective Optimization

This paper compares the performance of our re-cently proposed threshold based penalty function against its dynamic and adaptive variants. These penalty functions are incorporated in the update and replacement scheme of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework to solve constrained multiobjective op-timization problems (CMOPs). As a result, the capability of MOEA/D is extended to handle constraints, and a new algorithm, denoted by CMOEA/D-DE-TDA is proposed. The performance of CMOEA/D-DE-TDA is tested, in terms of the values of IGD-metric and SC-metric, on the well known CF-series test instances. The experimental results are also compared with the three best performers of CEC 2009 MOEA competition. Empirical results show the pitfalls of the proposed penalty functions.