Multiobjective Memetic Algorithm and Its Application in Robust Airfoil Shape Optimization

An important implementation issue in the design of hybrid evolutionary multiobjective optimization algorithms with local search (i.e., multiobjective memetic algorithms) is how to strike a balance between local search and global search. If local search is applied to all individuals at every generation, almost all computation time is spent by local search. As a result, global search ability of memetic algorithms is not well utilized. We can use three ideas for decreasing the computation load of local search. One idea is to apply local search to only a small number of individuals. This idea can be implemented by introducing a local search probability, which is used to choose only a small number of initial solutions for local search from the current population. Another idea is a periodical (i.e., intermittent) use of local search. This idea can be implemented by introducing a local search interval (e.g., every 10 generations), which is used to specify when local search is applied. The other idea is an early termination of local search. Local search for each initial solution is terminated after a small number of neighbors are examined. This idea can be implemented by introducing a local search length, which is the number of examined neighbors in a series of iterated local search from a single initial solution. In this paper, we discuss the use of these three ideas to strike a local-global search balance. Through computational experiments on a two-objective 500-item knapsack problem, we compare various settings of local search such as short local search from all individuals at every generation, long local search from only a few individuals at every generation, and periodical long local search from all individuals. Global search in this paper means genetic search by crossover and mutation in multiobjective memetic algorithms.

The success of local search techniques in the solution of combinatorial optimization problems has motivated their incorporation into multi-objective evolutionary algorithms, giving rise to the so-called multi-objective memetic algorithms (MOMAs). The main advantage for adopting this sort of hybridization is to speed up convergence to the Pareto front. However, the use of MOMAs introduces new issues, such as how to select the solutions to which the local search will be applied and for how long to run the local search engine (the use of such a local search engine has an extra computational cost). Here, we propose a new MOMA which switches between a hypervolume-based global optimizer and an IGD+-based local search engine. Our proposed local search engine adopts a novel clustering technique based on the IGD+ indicator for splitting the objective space into sub-regions. Since both computing the hypervolume and applying a local search engine are very costly procedures, we propose a GPU-based parallelization of our algorithm. Our preliminary results indicate that our MOMA is able to converge faster than SMS-EMOA to the true Pareto front of multi-objective problems having different degrees of difficulty.

A hybrid genetic local search algorithm for the permutation flowshop scheduling problem

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.

A multiobjective memetic algorithm with particle swarm optimization and Q-learning-based local search for energy-efficient distributed heterogeneous hybrid flow-shop scheduling problem

Multiobjective memetic optimization algorithms (MMOAs) are recently applied to solve nonlinear optimization problems with conflicting objectives. An important issue in an MMOA is how to identify the relative best solutions to guide its adaptive processes. Pareto dominance has been used extensively to find the relative relations between solutions for the fitness assessment in multiobjective optimization based on evolutionary algorithms (MOEA). However, the approach based on the Pareto dominance criterion decreases its convergence speed when the number of objectives increases. In this paper, we propose an effective information-theoretic criterion based on the multiscale relative Renyi entropy to guide the adaptive selection, clustering, and local learning processes in our framework of adaptive multiobjective memetic optimization algorithms (AMMOA). The implementation of AMMOA is applied to several benchmark test problems with remarkable results.

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.

Robust face alignment and tracking by combining local search and global fitting

Memetic algorithms arise as very effective algorithms to obtain reliable and high accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, making recommendable to test the behavior of the optimization algorithms to large-scale problems. The local search method must be applied with a higher intensity, specially to most promising solutions, to explore the higher domain space around each solution. In this work, we present a preliminar study of a memetic algorithm that assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. This algorithm have obtained good results in continuous optimization and we study whether is a good algorithm for large scale optimizations problems. We make experiments of our proposal using the benchmark problems defined in the Special Session or Competition on Large Scale Global Optimisation, on the IEEE Congress on Evolutionary Computation in 2008. First, we test different local search methods to identify the best one. Then, we compare the proposed algorithm with the algorithms used into the competition, obtaining that our proposal is a very promising algorithm for this type of high-dimensional problems: with dimension 500 our proposal is the second best of the compared algorithms, and the best memetic algorithm.

Communities have proven to be one of the important topological features of complex networks and can be discovered in various aspects of life. Understanding these community structures help the researchers to unlock distinct characteristics of networks that are not visible otherwise. In this paper, a hybrid genetic algorithm with link strength-based local search strategy (HGALS) is proposed for solving the community detection problem. The local search method presented in the algorithm is faster than the traditional modularity-based search operations. Furthermore, different variants of link strength measures are used in the local search method that is useful for various types of complex networks. The HGALS algorithm is analysed using different community structure metrics and its outcome is compared with three evolutionary algorithms and seven non-evolutionary algorithm-based approaches. The results thus obtained from the comparisons with other algorithms show good performances of HGALS in most of the cases for identifying better community structures.

Memetic algorithms (MAs) refer to hybrid methods of global search and local search, which aims to systematically balance exploitation and exploration for solving an optimization problem. This paper attempts to create a sawtooth growing exploitation framework for MAs. Under the framework, a sawtooth-wave function is used to control ratios of global search and local search, and thus the exploitation is restricted to sawtooth growing patterns. An MA instance is implemented by combining modified differential evolution and neighborhood field algorithms, named as MDE-NF. Compared with several state-of-the-art algorithms, the MDE-NF algorithm shows promising performance on several benchmark functions.

In this paper, we present a memetic algorithm which combines in a local search chaining framework, a steady-state genetic algorithm as evolutionary algorithm and a CMA-ES as local search method. It is an extension of an already presented algorithm which uses a region-based niching strategy and which has proven to be very efficient on real parameter optimisation problems. In this new version, we propose to dynamically update the niche size in order to make it less dependent to such critical parameter. In addition, we used an automatic configuration tool to optimise its parameters, and show that the optimised version of this algorithm is significantly better than with its default parameters. We tested this algorithm on the Special Session and Competition on Real-Parameter Optimization of the IEEE Congress on Evolutionary 2013 benchmark.

We aim to suggest a simple genetic algorithm (GA) and other four hybrid GAs (HGAs) for solving the asymmetric distance-constrained vehicle routing problem (ADVRP), a variant of vehicle routing problem (VRP). The VRP is a difficult NP-hard optimization problem that has numerous real-life applications. The VRP aims to find an optimal tour that has least total distance (or cost) to provide service to n customers (or nodes or cities) utilizing m vehicles so that every vehicle starts journey from and ends journey at a depot (headquarters) and visits every customer only once. The problem has many variations, and we consider the ADVRP for this study, where distance traveled by every vehicle must not exceed a predefined maximum distance. The proposed GA uses random initial population followed by sequential constructive crossover and swap mutation. The HGAs enhance the initial solution using 2-opt search method and incorporate a local search technique along with an immigration procedure to obtain effective solution to the ADVRP. Experiments have been conducted among the suggested GAs by solving several restricted and unrestricted ADVRP instances on asymmetric TSPLIB utilizing several vehicles. Our experiments claim that the suggested HGAs using local search methods are very effective. Finally, we reported a comparative study between our best HGA and a state-of-the-art algorithm on asymmetric capacitated VRP and found that our algorithm is better than the state-of-the-art algorithm for the instances.

In the paper we present a new method for solving optimal control problems of a class of hybrid systems. We describe the new effective algorithm based on memetic algorithm (MA) for optimal control of switched systems. We concentrate on a class of problems in which a pre-specified sequence of active subsystems is known. Our aim is to find both the optimal switching instants and the optimal continuous inputs. The new approach, which we propose, decomposes the cost functional of the basic optimal control problem in Bolza form in two terms. The first term depends explicitly on a value of state variables at the final time. The second term depends on state and control trajectories. In oreder to solve those two tasks we used MA as the multi-objective optimization algorithm. In this paper we considered a fundamental bi-criteria case with two mentioned before functions: the value of state variables at the final time and the state and control trajectories. In order to find an approximation of Pareto frontier, we proposed new effective method based on genetic algorithm (GA) and local search (LS). Problems properties were taken into consideration in the design of our new approach of solving it. They were used to construct new algorithm inspired by the LS NSGA-II, which performed rather well in multi-criteria scheduling problem. Since simple genetic algorithms are efficient heuristics in searching for optimal solutions, but lack the accuracy of some more computational complex algorithms, a hybrid algorithm was constructed. It uses fast non-dominated sorting, in order to evaluate child population and allocate solutions to corresponding Pareto frontiers. I addition a local search method was used, in order to find more differentiated and better solutions. Clustering solutions from Pareto frontiers also improved diversity of solutions in child population. This approach can be used as a start point for searching for algorithm for solving optimal control problems of switched systems without pre-specified sequence of active subsystems. The performance of the algorithm is illustrated by the examples: (a) a hybrid optimal control problem with nonlinear dynamics and (b) a switched linear quadratic optimal control problem with long switching time intervals.

This paper presents a multiobjective memetic algorithm based on adaptive local search chains (MMA-ALSC) for vehicle routing problem with time window (VRPTW) which is an important research area in logistics. As shown in most previous studies, VRPTW is essentially a multiobjective optimization problem and can be solved effectively by the multiobjective algorithms with various local search operators. We have observed, however, that the promising solutions obtained during the process of evolution are not fully utilized to guide the search together with different local search operators. This will lead to the discontinuous and insufficient search in the regions showing promise. To alleviate this drawback, MMA-ALSC is proposed and characterized by combining a multi-directional local search strategy (MD-LS) with an enhanced local search chain technique (eLS-Chain). In MMA-ALSC, on the one hand, with MD-LS, different local search operators are designed to perform the search towards multiple directions with distinct problem-specific knowledge of multiobjective VRPTW (MOVRPTW). On the other hand, with eLS-Chain, the promising solutions obtained during the process of evolution are adaptively selected for the subsequent local search operators. In this way, MMA-ALSC can not only effectively explore the search space in multiple directions, but also fully exploit the promising solutions in a chain-based way. Experimental results on two suites of benchmark instances have demonstrated the competitive performance of MMA-ALSC when compared with other representative algorithms.