Rung-Tzuo Liaw

Effect of model complexity for estimation of distribution algorithm in NK landscapes

Evolutionary algorithms (EAs) have been widely proved to be effective in solving complex problems. Estimation of distribution algorithm (EDA) is an emerging EA, which manipulates probability models instead of genes for evolution EDA creates probability models based on the promising solution in the population and generates offspring by sampling from these models. The model complexity is a key factor in the performance of EDA. Complex models can express the relations among variables more accurately than simple models. However, for some problems with strong interaction among variables, building a model for all the relations becomes unrealistic and impractical due to its high computational cost and requirement for a large population size. This study aims to understand the behaviors of EDAs with different model complexities in NK landscapes. Specifically, this study compares the solution quality and convergence speed of univariate marginal distribution algorithm (UMDA), bivariate marginal distribution algorithm (BMDA), and estimation of Bayesian network (EBNA) in the NK landscapes with different parameter settings. The comparative results reveal that high complexity does not imply high performance: Simple model such as UMDA and BMDA can outperform complex mode like EBNA on the tested NK landscape problems. The results also show that BMDA achieves a stable high probability of generating the best solution and satisfactory solution quality; by contrast, the probability for EBNA drastically declines after some generations.

Mining fuzzy association rules using a memetic algorithm based on structure representation

The association rules render the relationship among items and have become an important target of data mining. The fuzzy association rules introduce fuzzy set theory to deal with the quantity of items in the association rules. The membership functions play a key role in the fuzzification process and, therefore, significantly affect the results of fuzzy association rule mining. This study proposes a memetic algorithm (MA) for optimizing the membership functions in fuzzy association rule mining. The MA adopts a novel chromosome representation that considers the structures of membership functions. Based on the structure representation, we develop a local search operator to improve the efficiency of the MA in exploring good membership functions. Two local search strategies for the MA are further investigated. This study conducts a series of experiments to examine the proposed MA on different amounts of transactions. The experimental results show that the MA outperforms state-of-the-art evolutionary algorithms in terms of solution quality and convergence speed. These preferable results show the advantages of the structure-based representation and the local search in improving the performance. They also validate the high capability of the proposed MA in mining fuzzy association rules.

Multi-vehicle selective pickup and delivery using metaheuristic algorithms

The pickup and delivery problem (PDP) addresses real-world problems in logistics and transportation, and establishes a critical class of vehicle routing problems. This study presents a novel variant of the PDP, called the multi-vehicle selective pickup and delivery problem (MVSPDP), and designs three metaheuristic algorithms for this problem. The MVSPDP aims to find the minimum-cost routes for a fleet of vehicles collecting and supplying commodities, subject to the constraints on vehicle capacity and travel distance. The problem formulation features relaxing the requirement of visiting all pickup nodes and enabling multiple vehicles for achieving transportation efficiency. To solve the MVSPDP, we propose three metaheuristic algorithms: tabu search (TS), genetic algorithm (GA), and scatter search (SS). A fixed-length representation is presented to indicate the varying number of vehicles used and the selection of pickup nodes. Furthermore, we devise four operators for TS, GA, and SS to handle the selection of pickup nodes, number of vehicles used, and their routes. The experimental results indicate that the three metaheuristic algorithms can effectively solve the MVSPDP. In particular, TS outperforms GA and SS in solution quality and convergence speed. In addition, the problem formulation produces substantially lower transportation costs than the PDP does, thus validating the utility of the MVSPDP.

Genetic algorithm with a structure-based representation for genetic-fuzzy data mining

Mining association rules is an important data mining technology aiming to find the relationship among items in the databases. Genetic-fuzzy data mining uses evolutionary algorithm, such as genetic algorithm (GA), to optimize the membership functions for mining fuzzy association rules, and has received considerable success. The increase in data, especially in big data analytics, poses serious challenges to GA in the effectiveness and efficiency of finding appropriate membership functions. This study proposes a GA for enhancing genetic-fuzzy mining of association rules. First, we design a novel chromosome representation considering the structures of membership functions. The representation facilitates arrangement of membership functions. Second, this study presents two heuristics in the light of overlap and coverage for removing inappropriate arrangement. A series of experiments is conducted to examine the proposed GA on different amounts of transactions. The experimental results show that GA benefits from the proposed representation. The two heuristics help to explore the structures of membership functions and achieve significant improvement on GA in terms of solution quality and convergence speed. The satisfactory outcomes validate the high capability of the proposed GA in genetic-fuzzy mining of association rules.

MOEA/D using covariance matrix adaptation evolution strategy for complex multi-objective optimization problems

Multi-objective optimization is a blooming research area since many real-world problems comprise multiple objectives. Multi-objective evolutionary algorithms (MOEAs) have been widely used to solve the multi-objective optimization problems. In particular, the decomposition based MOEA (MOEA/D) has achieved considerable successes in tackling multi-objective optimization problems. The covariance matrix adaptation evolution strategy (CMAES) is known for its effectiveness in solving complex numerical optimization problems. This study integrates CMAES into MOEA/D as the MOEA/D-CMAES for the merits of MOEA/D framework in multi-objective optimization and CMAES in complex numerical optimization. In MOEA/D-CMAES, each subproblem is handled with one CMAES. To avoid the drastic increase in the number of offspring generated and their fitness evaluations, MOEA/D-CMAES generates only one offspring in each subproblem. The multivariate normal distribution in each CMAES is updated by the collaboration of the offspring generated in the present subproblem and those of other subproblems. Experimental results show that MOEA/D-CMAES outperforms MOEA/D using differential evolution in terms of hypervolume and convergence speed, which validate the effectiveness and efficiency of MOEA/D-CMAES in multi-objective optimization.

Solving the Selective Pickup and Delivery Problem Using Max-Min Ant System

The pickup and delivery problem (PDP) is relevant to many real-world problems, e.g., logistic and transportation problems. The problem is to find the shortest route to gain commodities from the pickup nodes and supply them to the delivery nodes. The amount of commodities of pickup nodes and delivery nodes is usually assumed to be in equilibrium; thus, all pickup nodes have to be visited for collecting all commodities required. However, some real-world applications, such as rental bikes and wholesaling business, need only to gain sufficient commodities from certain pickup nodes. A variant of PDP, namely the selective pickup and delivery problem (SPDP), is formulated to address the above scenarios. The major difference of SPDP from PDP lies in the requirement of visiting all pickup nodes. The SPDP relaxes this requirement to achieve more efficient transportation. The goal of the SPDP is to seek the shortest path that satisfies the load constraint to supply the commodities demanded by all delivery nodes with some pickup nodes. This study proposes a max-min ant system (MMAS) to solve the SPDP. The ants aim to construct the shortest route for the SPDP considering the number of selected pickup nodes and all delivery nodes. This study conducts experiments to examine the performance of the proposed MMAS, in comparison with genetic algorithm and memetic algorithm. The experimental results validate the effectiveness and efficiency of the proposed MMAS in route length and convergence speed for the SPDP.

Evolutionary many-tasking based on biocoenosis through symbiosis: A framework and benchmark problems

Evolutionary multitasking is an emergent topic in evolutionary computation area. Recently, a well-known evolutionary multitasking method, the multi-factorial evolutionary algorithm (MFEA), has been proposed and applied to concurrently solve two or three problems. In MFEA, individuals of different tasks are recombined in a predefined random mating probability. As the number of tasks increases, such recombination of different tasks becomes very frequent, thereby detracting the search from any specific problems and limiting the MFEAs capability to solve many-tasking problems. This study proposes a general framework, called the evolution of biocoenosis through symbiosis (EBS), for evolutionary algorithms to deal with the many-tasking problems. The EBS has two main features: the selection of candidates from concatenate offspring and the adaptive control of information exchange among tasks. The concatenate offspring represent a set of offspring used for all tasks. Moreover, this study presents a test suite of many-tasking problems (MaTPs), modified from the CEC 2014 benchmark problems. The Spearman correlation is adopted to analyze the effect of the shifts of optima on the MaTPs. Experimental results show that the effectiveness of EBS is superior to that of single task optimization and MFEA on the four MaTPs. The results also validate that EBS is capable of exploiting the synergy of fitness landscapes.

Enhancing covariance matrix adaptation evolution strategy through fitness inheritance

Evolution strategy (ES) has shown to be effective in many search and optimization problems. In particular, the ES with covariance matrix adaptation (CMAES) achieves great successes and is viewed as a state-of-the-art evolutionary algorithm for complex numerical optimization. The CMAES models the population by a multivariate normal distribution, which requires a considerable amount of fitness evaluation results and thus degrades its efficiency. This paper proposes using fitness inheritance to reduce the computational cost at fitness evaluation. More specifically, the proposed FI-CMAES adopts fitness inheritance to approximate the fitness of offspring. The survivors are selected according to the approximated fitness; thereafter, the survival offspring are evaluated by the original fitness function. By this way, several original fitness evaluations on offspring can be saved. Experiments examine the effectiveness and efficiency of FI-CMAES on the CEC2014 test suite. The results show that FI-CMAES can outperform CMAES in terms of solution quality and convergence speed.

Considering Reputation in the Selection Strategy of Genetic Programming

Genetic programming (GP) is an evolutionary algorithm inspired by biological evolution. GP has shown to be effective to build prediction and classification model with high accuracy. Individuals in GP are evaluated by fitness, which serves as the basis of selection strategy: GP selects individuals for reproducing their offspring based on fitness. In addition to fitness, this study considers the reputation of individuals in the selection strategy of GP. Reputation is commonly used in social networks, where users earn reputation from others through recognized performance or effort. In this study, we define the reputation of an individual according to its potential to produce good offspring. Therefore, selecting parents with high reputation is expected to increase the opportunity for generating good candidate solutions. This study applies the proposed algorithm, called the RepGP, to solve the classification problems. Experimental results on four data sets show that RepGP with certain degrees of consanguinity can outperform two GP algorithms in terms of classification accuracy, precision, and recall.

An Efficient Representation for Genetic-Fuzzy Mining of Association Rules

Data mining is a blooming area in information science. Mining association rules aims to find the relationship among items in the databases and has become one of the most important data mining technologies. Previous study shows the capability of genetic algorithm (GA) to find the membership functions for fuzzy data mining. However, the chromosome representation cannot avoid the occurrence of inappropriate arrangement of membership functions, resulting in inefficiency of GA in searching for the optimal membership functions. This study proposes a novel representation that takes advantage of the structure information of membership functions to deal with the issue. In the light of overlap and coverage, we propose two heuristics for appropriate arrangement of membership functions. The experimental results show that GA using the proposed representation can achieve high fitness and suitability. The results also indicate that the two heuristics help to well exploit the structure information and therefore enhance GA in terms of solution quality and convergence speed on fuzzy association rules mining.