Wali Khan Mashwani

Multiobjective memetic algorithm based on decomposition

In recent years, hybridization of multi-objective evolutionary algorithms (MOEAs) with traditional mathematical programming techniques have received significant attention in the field of evolutionary computing (EC). The use of multiple strategies with self-adaptation manners can further improve the algorithmic performances of decomposition-based evolutionary algorithms. In this paper, we propose a new multiobjective memetic algorithm based on the decomposition approach and the particle swarm optimization (PSO) algorithm. For brevity, we refer to our developed approach as MOEA/D-DE+PSO. In our proposed methodology, PSO acts as a local search engine and differential evolution works as the main search operator in the whole process of optimization. PSO updates the position of its solution with the help of the best information on itself and its neighboring solution. The experimental results produced by our developed memtic algorithm are more promising than those of the simple MOEA/D algorithm, on most test problems. Results on the sensitivity of the suggested algorithm to key parameters such as population size, neighborhood size and maximum number of solutions to be altered for a given subproblem in the decomposition process are also included.

A decomposition-based hybrid multiobjective evolutionary algorithm with dynamic resource allocation

Different crossover operators suit different problems. It is, therefore, potentially problematic to chose the ideal crossover operator in an evolutionary optimization scheme. Using multiple crossover operators could be an effective way to address this issue. This paper reports on the implementation of this idea, i.e. the use of two crossover operators in a decomposition-based multi-objective evolutionary algorithm, but not simultaneously. After each cycle, the operator which has helped produce the better offspring is rewarded. This means that the overall algorithm uses a dynamic resource allocation to reward the better of the crossover operators in the optimization process. The operators used are the Simplex Crossover operator (SPX) and the Center of Mass Crossover operator (CMX). We report experimental results that show that this innovative use of two crossover operators improves the algorithm performance on standard test problems. Results on the sensitivity of the suggested algorithm to key parameters such as population size, neighborhood size and maximum number of solutions to be altered for a given subproblem in the the decomposition process are also included.

MOEA/D with DE and PSO: MOEA/D-DE+PSO

Hybridization is one of the important research area in evolutionary multiobjective optimization (EMO).It is a method that incorporate good merits of multiple techniques aim at to enhance the search ability of EMO algorithm. In this chapter, we combine two well-known search algorithms, DE and PSO, and developed algorithm known as MOEA/D-DE+PSO. We experimentally studied its performance on two types of continuous multi-objective optimization problems and found better improvement.

Comprehensive Survey of the Hybrid Evolutionary Algorithms

Multiobjective evolutionary algorithm based on decomposition MOEA/D and an improved non-dominating sorting multiobjective genetic algorithm NSGA-II is two well known multiobjective evolutionary algorithms MOEAs in the field of evolutionary computation. This paper mainly reviews their hybrid versions and some other algorithms which are developed for solving multiobjective optimization problems MOPs. The mathematical formulation of a MOP and some basic definitions for tackling MOPs, including Pareto optimality, Pareto optimal set PS, Pareto front PF are provided in Section 1. Section 2 presents a brief introduction to hybrid MOEAs. The authors present literature review in subsections. Subsection 2.1 provides memetic multiobjective evolutionary algorithms. Subsection 2.2 presents the hybrid versions of well-known Pareto dominance based MOEAs. Subsection 2.4 summarizes some enhanced Versions of MOEA/D paradigm. Subsection 2.5 reviews some multimethod search approaches dealing optimization problems.

A multimethod search approach based on adaptive generations level

Integration of single methods into hybrid are researched scarcely in the recent past. This paper investigates the effect of integration of single methods: MOEA/D [1] and NSGA-II [2] in a multimethod search approach, so-called, MMTD, based on self-adaptive generations level proposed in this paper. During implementation, MMTD borrows some concepts from the specialized literature of evolutionary multi-objective optimization (EMO). The synergetic combination of MOEA/D and NSGA-II can unleash their full strength and biases self-adaptively in MMTD framework and can solve efficiently two set of problems: 1) ZDT test problems [3], 2) cec09 unconstrained test instances [4], as compared to the state-of-the-art EMO methods, MOEA/D only and NSGA-II only.

Integration of NSGA-II and MOEA/D in multimethod search approach: algorithms

Integration of single methods into their hybrids are researched scarcely in the recent few years. This paper presents the feasibility study for integration of two methods: MOEA/D [7] and NSGA-II [4] in the proposed multimethod search approach (MMTD). During implementation of MMTD, we borrows some concepts from the specialized literature of EMO. In MMTD, the synergetic combination of MOEA/D and NSGA-II can unleash their full power and strength self-adaptively for tackling two set of problems: 1) ZDT test problems [6], 2) cec09 unconstrained test instances [1]. The final best approximated results illustrates the usefulness of MMTD in multiobjective optimization (MO).

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.