A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.     

基于模运算的新颖离散差分演化算法求解多背包问题

多背包问题（MKP）是一个求解难度极大的背包问题。为了基于差分演化（DE）求解MKP,首先建立了MKP的整数规划模型,在利用模运算构造简单且有效的新型传递函数基础上,提出了一个新颖离散差分演化算法MODDE;基于贪心策略提出了消除MKP不可行解的一个有效算法GROA,由此利用MODDE给出了求解MKP的一种新方法。最后,利用MODDE求解30个国际通用的MKP实例,通过与四个代表性演化算法的比较表明,MODDE不仅计算结果优,而且算法的稳定性强,是求解MKP的一个高效算法。     

A Probabilistic Memetic Framework

Memetic algorithms (MAs) represent one of the recent growing areas in evolutionary algorithm (EA) research. The term MAs is now widely used as a synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search. Quite often, MAs are also referred to in the literature as Baldwinian EAs, Lamarckian EAs, cultural algorithms, or genetic local searches. In the last decade, MAs have been demonstrated to converge to high-quality solutions more efficiently than their conventional counterparts on a wide range of real-world problems. Despite the success and surge in interests on MAs, many of the successful MAs reported have been crafted to suit problems in very specific domains. Given the restricted theoretical knowledge available in the field of MAs and the limited progress made on formal MA frameworks, we present a novel probabilistic memetic framework that models MAs as a process involving the decision of embracing the separate actions of evolution or individual learning and analyzing the probability of each process in locating the global optimum. Further, the framework balances evolution and individual learning by governing the learning intensity of each individual according to the theoretical upper bound derived while the search progresses. Theoretical and empirical studies on representative benchmark problems commonly used in the literature are presented to demonstrate the characteristics and efficacies of the probabilistic memetic framework. Further, comparisons to recent state-of-the-art evolutionary algorithms, memetic algorithms, and hybrid evolutionary-local search demonstrate that the proposed framework yields robust and improved search performance.      

An improved fruit fly optimization algorithm for solving the multidimensional knapsack problem

This paper presents an improved fruit fly optimization algorithm (IFFOA) for solving the multidimensional knapsack problem (MKP). In IFFOA, the parallel search is employed to balance exploitation and exploration. To make full use of swarm intelligence, a modified harmony search algorithm (MHS) is proposed and applied to add cooperation among swarms in IFFOA. In MHS, novel pitch adjustment scheme and random selection rule are developed by considering specific characters of MKP and FOA. Moreover, a vertical crossover is designed to guide stagnant dimensions out of local optima and further improve the performance. Extensive numerical simulations are conducted and comparisons with other state-of-the-art algorithms verify that the proposed algorithm is an effective alternative for solving the MKP.     

Computational performance of basic state reduction based dynamic programming algorithms for bi-objective 0–1 knapsack problems

This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking.     

A spy search mechanism for memetic algorithm in dynamic environments

Searching within the sample space for optimal solutions is an important part in solving optimization problems. The motivation of this work is that today’s problem environments have increasingly become dynamic with non-stationary optima and in order to improve optima search, memetic algorithm has become a preferred search method because it combines global and local search methods to obtain good solutions. The challenge is that existing search methods perform the search during the iterations without being guided by solid information about the nature of the search environment which affects the quality of a search outcome. In this paper, a spy search mechanism is proposed for memetic algorithm in dynamic environments. The method uses a spy individual to scope out the search environment and collect information for guiding the search. The method combines hyper-mutation, random immigrants, hill climbing local search, crowding and fitness, and steepest mutation with greedy crossover hill climbing to enhance the efficiency of the search. The proposed method is tested on dynamic problems and comparisons with other methods indicate a better performance by the proposed method.     

Fast,effective heuristics for the 0–1 multi-dimensional knapsack problem

The objective of the multi-dimensional knapsack problem (MKP) is to find a subset of items with maximum value that satisfies a number of knapsack constraints. Solution methods for MKP, both heuristic and exact, have been researched for several decades. This paper introduces several fast and effective heuristics for MKP that are based on solving the LP relaxation of the problem. Improving procedures are proposed to strengthen the results of these heuristics. Additionally, the heuristics are run with appropriate deterministic or randomly generated constraints imposed on the linear relaxation that allow generating a number of good solutions. All algorithms are tested experimentally on a widely used set of benchmark problem instances to show that they compare favourably with the best-performing heuristics available in the literature.     

混合猴群算法求解折扣{0-1}背包问题

针对折扣{0-1}背包问题(D{0-1}KP),当问题规模较大时,精确算法求解比较困难.基于此,将贪心核加速算子与猴群算法融合提出一种混合猴群算法(MMA)用于求解D{0-1}KP问题.同时在MMA算法的爬过程中引入诱导因子,避免爬过程陷入局部最优,再利用修复策略对不可行解进行修复.通过仿真实验,结果表明MMA算法求解...     

Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a combinatorial optimization problem belonging to the class of NP-hard problems. This study proposes a novel self-adaptive check and repair operator (SACRO) combined with particle swarm optimization (PSO) to solve the MKP. The traditional check and repair operator (CRO) uses a unique pseudo-utility ratio, whereas SACRO dynamically and automatically changes the alternative pseudo-utility ratio as the PSO algorithm runs. Two existing PSO algorithms are used as the foundation to support the novel SACRO methods, the proposed SACRO-based algorithms were tested using 137 benchmark problems from the OR-Library to validate and demonstrate the efficiency of SACRO idea. The results were compared with those of other population-based algorithms. Simulation and evaluation results show that SACRO is more competitive and robust than the traditional CRO. The proposed SACRO-based algorithms rival other state-of-the-art PSO and other algorithms. Therefore, changing different types of pseudo-utility ratios produces solutions with better results in solving MKP. Moreover, SACRO can be combined with other population-based optimization algorithms to solve constrained optimization problems.     

基于变异和信息素扩散的多维背包问题的蚁群算法

针对蚁群算法在求解大规模多维背包问题时存在的迭代次数过多、精度不高的不足,提出一种新的高性能的蚁群求解算法.算法将信息素更新和随机搜索机制的改进相融合.首先,基于对较优解的偏爱,采用Top-k策略从每次迭代的k个解中挖掘出对象间的关联距离;其次,以对象为信源借助关联距离建立信息素的扩散模型,通过信息素扩散的耦合补偿,强化了蚂蚁间的协作和交流;最后,利用一种简单的变异策略对迭代的结果进行优化.在通用数据集上的大量实验表明:与最新的蚁群算法相比,新算法不仅能获得更好的最优解,而且收敛速度有显著的提高.     

Meta-Lamarckian learning in memetic algorithms

Over the last decade, memetic algorithms (MAs) have relied on the use of a variety of different methods as the local improvement procedure. Some recent studies on the choice of local search method employed have shown that this choice significantly affects the efficiency of problem searches. Given the restricted theoretical knowledge available in this area and the limited progress made on mitigating the effects of incorrect local search method choice, we present strategies for MA control that decide, at runtime, which local method is chosen to locally improve the next chromosome. The use of multiple local methods during a MA search in the spirit of Lamarckian learning is here termed Meta-Lamarckian learning. Two adaptive strategies for Meta-Lamarckian learning are proposed in this paper. Experimental studies with Meta-Lamarckian learning strategies on continuous parametric benchmark problems are also presented. Further, the best strategy proposed is applied to a real-world aerodynamic wing design problem and encouraging results are obtained. It is shown that the proposed approaches aid designers working on complex engineering problems by reducing the probability of employing inappropriate local search methods in a MA, while at the same time, yielding robust and improved design search performance.     

A self-adaptive Multimeme Memetic Algorithm co-evolving utility scores to control genetic operators and their parameter settings

Memetic algorithms are a class of well-studied metaheuristics which combine evolutionary algorithms and local search techniques. A meme represents contagious piece of information in an adaptive information sharing system. The canonical memetic algorithm uses a fixed meme, denoting a hill climbing operator, to improve each solution in a population during the evolutionary search process. Given global parameters and multiple parameterised operators, adaptation often becomes a crucial constituent in the design of MAs. In this study, a self-adaptive self-configuring Steady-state Multimeme Memetic Algorithm (SSMMA) variant is proposed. Along with the individuals (solutions), SSMMA co-evolves memes, encoding the utility score for each algorithmic component choice and relevant parameter setting option. An individual uses tournament selection to decide which operator and parameter setting to employ at a given step. The performance of the proposed algorithm is evaluated on six combinatorial optimisation problems from a cross-domain heuristic search benchmark. The results indicate the success of SSMMA when compared to the static MAs as well as widely used self-adaptive Multimeme Memetic Algorithm from the scientific literature.     

一种快速求解旅行商问题的蚁群算法

蚁群优化是一种元启发式的随机搜索技术,是目前解决组合优化问题最有效的工具之一.将信息素更新和随机搜索机制的改进相结合,提出一种快速求解旅行商问题的蚁群算法.首先给出了一种新的信息素增量模型,以体现蚂蚁在不同路径上行走时所产生的信息素差异;然后以蚂蚁经过的路径(直线段)作为信息素扩散浓度场的信源,改进了信息素扩散模型,强化了蚂蚁间的协作和交流;最后采用较低复杂度的变异策略对迭代的结果进行优化.在大量通用数据集上的实验表明,该算法不仅能获得更好的最优解,而且收敛速度有显著的提高.     

基于猴群算法求解0-1背包问题

0-1背包问题是一个经典的NP完全问题,该问题在实际生活中具有广泛的应用.针对现有算法在求解0-1背包问题时精度不高的缺点,提出了一种诱导因子猴群算法.所给诱导因子猴群算法的基本思想是,在基本猴群算法的爬过程中引入诱导因子,诱导其向上爬行,从而可以逃逸局部最优解,找到全局最优解.在仿真试验中,与已有方法进行比较,结果说明利用所给诱导因子猴群算法求解0-1背包问题是有效的.     

无限制背包问题的爬山算法

给出了一种求解整数背包问题的爬山解法 ,并对该算法的计算复杂度及最坏情形进行了理论分析 .通过与经典的求解背包问题方法的对比研究 ,给出了该算法的适用范围并展示其优越性 .数值实验表明 ,该算法简便易行 ,在其适用范围内具有计算复杂度低 ,近优程度高等优点 .     

Band selection for hyperspectral images using probabilistic memetic algorithm

Band selection plays an important role in identifying the most useful and valuable information contained in the hyperspectral images for further data analysis such as classification, clustering, etc. Memetic algorithm (MA), among other metaheuristic search methods, has been shown to achieve competitive performances in solving the NP-hard band selection problem. In this paper, we propose a formal probabilistic memetic algorithm for band selection, which is able to adaptively control the degree of global exploration against local exploitation as the search progresses. To verify the effectiveness of the proposed probabilistic mechanism, empirical studies conducted on five well-known hyperspectral images against two recently proposed state-of-the-art MAs for band selection are presented.     

A k-means binarization framework applied to multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is one of the widely known integer programming problems. The MKP has received significant attention from the operational research community for its large number of applications. Solving this NP-hard problem remains a very interesting challenge, especially when the number of constraints increases. In this paper we present a k-means transition ranking (KMTR) framework to solve the MKP. This framework has the property to binarize continuous population-based metaheuristics using a data mining k-means technique. In particular we binarize a Cuckoo Search and Black Hole metaheuristics. These techniques were chosen by the difference between their iteration mechanisms. We provide necessary experiments to investigate the role of key ingredients of the framework. Finally to demonstrate the efficiency of our proposal, MKP benchmark instances of the literature show that KMTR competes with the state-of-the-art algorithms.     

Classification of adaptive memetic algorithms: a comparative study.

Adaptation of parameters and operators represents one of the recent most important and promising areas of research in evolutionary computations; it is a form of designing self-configuring algorithms that acclimatize to suit the problem in hand. Here, our interests are on a recent breed of hybrid evolutionary algorithms typically known as adaptive memetic algorithms (MAs). One unique feature of adaptive MAs is the choice of local search methods or memes and recent studies have shown that this choice significantly affects the performances of problem searches. In this paper, we present a classification of memes adaptation in adaptive MAs on the basis of the mechanism used and the level of historical knowledge on the memes employed. Then the asymptotic convergence properties of the adaptive MAs considered are analyzed according to the classification. Subsequently, empirical studies on representatives of adaptive MAs for different type-level meme adaptations using continuous benchmark problems indicate that global-level adaptive MAs exhibit better search performances. Finally we conclude with some promising research directions in the area.     

Balancing exploration and exploitation in memetic algorithms: A learning automata approach

One of the problems with traditional genetic algorithms (GAs) is premature convergence, which makes them incapable of finding good solutions to the problem. The memetic algorithm (MA) is an extension of the GA. It uses a local search method to either accelerate the discovery of good solutions, for which evolution alone would take too long to discover, or reach solutions that would otherwise be unreachable by evolution or a local search method alone. In this paper, we introduce a new algorithm based on learning automata (LAs) and an MA, and we refer to it as LA‐MA. This algorithm is composed of 2 parts: a genetic section and a memetic section. Evolution is performed in the genetic section, and local search is performed in the memetic section. The basic idea of LA‐MA is to use LAs during the process of searching for solutions in order to create a balance between exploration performed by evolution and exploitation performed by local search. For this purpose, we present a criterion for the estimation of success of the local search at each generation. This criterion is used to calculate the probability of applying the local search to each chromosome. We show that in practice, the proposed probabilistic measure can be estimated reliably. On the basis of the relationship between the genetic section and the memetic section, 3 versions of LA‐MA are introduced. LLA‐MA behaves according to the Lamarckian learning model, BLA‐MA behaves according to the Baldwinian learning model, and HLA‐MA behaves according to both the Baldwinian and Lamarckian learning models. To evaluate the efficiency of these algorithms, they have been used to solve the graph isomorphism problem. The results of computer experimentations have shown that all the proposed algorithms outperform the existing algorithms in terms of quality of solution and rate of convergence.     

A New Heuristic for Solving the Multichoice Multidimensional Knapsack Problem

A new heuristic for solving the multichoice multidimensional knapsack problem (MMKP) is presented in this paper. The MMKP is first reduced to a multidimensional knapsack problem (MKP). A linear programming relaxation of the resulting MKP is solved, and a series of new values for the variables is computed. These values, pseudo-utility values, and resource value coefficients computed as well, are used in order to obtain a feasible solution for the original MMKP. Finally, the quality of the feasible solution is improved using the pseudo-utility values and the coefficient values of the objective function. Numerical results show that the performance of this approach is superior to that of previous techniques.