A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem

The multidimensional assignment problem (MAP), also known as multi-index assignment problem, is a natural extension of the assignment problem. A MAP deals with the question of how to assign elements from s disjoint sets with n 1 ,…,n s items on each. A MAP with s dimensions is called a sAP. Local search heuristics and Memetic algorithms have been proven to be the most effective techniques to solve MAP. In this work we use an exact technique that outperforms some local searches and Memetic algorithms on several instances of MAP. Then, we design a heuristic that uses repeatedly our exact technique in order to provide high quality solutions for harder types of instances of MAP. We perform an experimental evaluation of our exact technique and of our heuristic and we show its effectiveness against more complex local searches and some Memetic algorithms for MAP.

The Multidimensional Assignment Problem (MAP) is a natural extension of the well-known assignment problem. The most studied case of the MAP is the 3-dimensional Assignment Problem (3AP), though in recent years some local search heuristics and a memetic algorithm were proposed for the general case. Until now, a memetic algorithm has been proven to be the best-known option to solve MAP instances and it uses some procedures called dimensionwise variation heuristics as part of the improvement of individuals. We propose a new local search heuristic, based on ideas from dimensionwise variation heuristics, which consider a bigger space of neighborhoods, providing higher quality solutions for the MAP. Our main contribution is a generalization of several local search heuristics known from the literature, the conceptualization of a new one, and the application of exact techniques to find local optimum solutions at its neighborhoods. The results of computational evaluation show how our heuristic outperforms the previous local search heuristics and its competitiveness against a state-of-the-art memetic algorithm.

The impact of parametrization in memetic evolutionary algorithms

The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the state-of-the art 3-AP memetic algorithm.

One important challenge of a hybrid genetic algorithm (HGA) (also called memetic algorithm) is the tradeoff between global and local searching (LS) as it is the case that the cost of an LS can be rather high. This paper proposes a novel, simplified, and efficient HGA with a new individual learning procedure that performs a LS only when the best offspring (solution) in the offspring population is also the best in the current parent population. Additionally, a new LS method is developed based on a three-directional search (TD), which is derivative-free and self-adaptive. The new HGA with two different LS methods (the TD and Neld-Mead simplex) is compared with a traditional HGA. Four benchmark functions are employed to illustrate the improvement of the proposed method with the new learning procedure. The results show that the new HGA greatly reduces the number of function evaluations and converges much faster to the global optimum than a traditional HGA. The TD local search method is a good choice in helping to locate a global “mountain” (or “valley”) but may not perform the Nelder-Mead method in the final fine tuning toward the optimal solution.

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

Memetic algorithm (MA) is widely applied to optimize routing problems as it provides one way to combine local search with global search. However, the local search in MA needs to be carefully designed according to the problem's characteristics. In this article, we consider a real-world large-scale waste collection problem with multiple depots, multiple disposal facilities, multiple trips, and working time constraints. Vehicles with a limited capacity and working time can start from different depots, collect waste at different sites, and make multiple trips to different disposal facilities to empty the waste and return to its origin. While the existing work considered problems with multiple trips and time constraints, none have tackled problems with multiple depots, multiple disposal facilities, multiple trips, as well as working time constraints. The change from "single-depot" to "multidepot" not only reflects better the situation in real life but also leads to a qualitative different and more complex problem. In this article, we first model this complex problem mathematically. Then, a novel region-focused MA is proposed to tackle this new challenge. Compared to classic MA, this region-focused one is enhanced by two major components: 1) a new heuristic-assisted solution initialization algorithm and 2) a region-focused local search with novel heuristics. Comprehensive computational studies show that our proposed approaches significantly outperform several state-of-the-arts on our real problem of thousands of tasks. The new local search procedure and solution initialization method significantly improve the search ability in combination with global search ability of MA.

We consider the maximum scatter travelling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the shortest edge in the tour that travels each city only once in the given network. It is a very complicated NP-hard problem, and hence, exact solutions are obtainable for small sizes only. For large sizes, heuristic algorithms must be applied, and genetic algorithms (GAs) are observed to be very successful in dealing with such problems. In our study, a simple GA (SGA) and four hybrid GAs (HGAs) are proposed for the MSTSP. The SGA starts with initial population produced by sequential sampling approach that is improved by 2-opt search, and then it is tried to improve gradually the population through a proportionate selection procedure, sequential constructive crossover, and adaptive mutation. A stopping condition of maximum generation is adopted. The hybrid genetic algorithms (HGAs) include a selected local search and perturbation procedure to the proposed SGA. Each HGA uses one of three local search procedures based on insertion, inversion and swap operators directly or randomly. Experimental study has been carried out among the proposed SGA and HGAs by solving some TSPLIB asymmetric and symmetric instances of various sizes. Our computational experience reveals that the suggested HGAs are very good. Finally, our best HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that our best HGA is better.

Memetic algorithm (MA) is a hybrid evolutionary algorithm (EA) that combines genetic operators with local search procedures. With global exploration and local exploitation in search process, the memetic algorithm can find near global solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a memetic algorithm based on MIHDE, called Memetic MIHDE, is proposed to solve mixed-integer optimization problems. Furthermore, in order to handle the constrained optimization problems, a Memetic MIHDE algorithm combined with Lagrange method is developed for solving the constrained optimization problems. Finally, the proposed algorithm is applied to a mechanical design optimization problem. Experimental results show that the algorithm can obtain a better optimal solution compared with some other search algorithms. This demonstrates that the Memetic MIHDE algorithm can solve mechanical design optimization problems effectively.

Community detection has drawn a lot of attention as it can provide invaluable help in understanding the function and visualizing the structure of networks. Since single objective optimization methods have intrinsic drawbacks to identifying multiple significant community structures, some methods formulate the community detection as multi-objective problems and adopt population-based evolutionary algorithms to obtain multiple community structures. Evolutionary algorithms have strong global search ability, but have difficulty in locating local optima efficiently. In this study, in order to identify multiple significant community structures more effectively, a multi-objective memetic algorithm for community detection is proposed by combining multi-objective evolutionary algorithm with a local search procedure. The local search procedure is designed by addressing three issues. Firstly, nondominated solutions generated by evolutionary operations and solutions in dominant population are set as initial individuals for local search procedure. Then, a new direction vector named as pseudonormal vector is proposed to integrate two objective functions together to form a fitness function. Finally, a network specific local search strategy based on label propagation rule is expanded to search the local optimal solutions efficiently. The extensive experiments on both artificial and real-world networks evaluate the proposed method from three aspects. Firstly, experiments on influence of local search procedure demonstrate that the local search procedure can speed up the convergence to better partitions and make the algorithm more stable. Secondly, comparisons with a set of classic community detection methods illustrate the proposed method can find single partitions effectively. Finally, the method is applied to identify hierarchical structures of networks which are beneficial for analyzing networks in multi-resolution levels.

This paper addresses the problem of scheduling a set of jobs on a machine with time-varying capacity, with the goal of minimizing the total tardiness objective function. This problem arose in the context scheduling the charging times of a fleet of electric vehicles and it is NP-hard. Recent work proposed an efficient memetic algorithm for solving the problem, combining a genetic algorithm and a local search method. The local search procedure is based on swapping consecutive jobs on a C-path, defined as a sequence of consecutive jobs in a schedule. Building on it, this paper develops new memetic algorithms that stem from new local search procedures also proposed in this paper. The local search methods integrate several mechanisms to make them more effective, including a new condition for swapping pairs of jobs, a hill climbing approach, a procedure that operates on several C-paths and a method that interchanges jobs between different C-paths. As a result, the new local search methods enable the memetic algorithms to reach higher-quality solutions. Experimental results show significant improvements over existing approaches.

The multidimensional assignment problem (MAP) is a natural extension of the well known assignment problem. A problem with s dimensions is called a SAP. The most studied NP-hard case of the MAP is the 3AP. Memetic algorithms have been proven to be the most effective technique to solve MAP. The use of powerful local search heuristics in combination with a genetic algorithm, even if it has a simple structure, provides high quality solutions without a lot of effort. We perform an experimental evaluation of a basic genetic algorithm combined with a so called dimensionwise variation heuristic and show its effectiveness against a more complex state-of-the-art memetic algorithm for MAP.

In everyday life almost all problems require the help of mathematics, one of them on the transportation or on the distribution prosess. Multiple Trip Vehicle Routing Problem (MTVRP) is one of the problems related to the transportation or distribution prosess. Multiple Trip Vehicle Routing Problem (MTVRP) is defined as the problem of the Vehicle Routing Problem (VRP) with the expansion and the addition of multiple trips on the each vehicle when it distributes goods and the time window of customer service. One algorithm to solve the Multiple Trip Vehicle Routing Problem (MTVRP) is memetic algorithms. Memetic algorithm is a combination of genetic algorithm and local search procedures that intensify the search. Memetic algorithms procedures are: initialization process, evaluation process, selection, crossover process, mutation process, repair process, local search, vehicle allocation, and the best route is formed. To facilitate the search for the solution of the Multiple Trip Vehicle Routing Problem (MTVRP) especially at the time had to submit to many customers, memetic algorithms implemented in the language programming Borland Delphi. By using an program application be made, produced together with the results obtained manually route 0 – 1 – 3 – 4 – 0 – 5 – 2 – 0 with a travel time "1.1675" hours and uses a vehicle. This program is designed applications up to 50 points in the Multiple Trip Vehicle Routing Problem (MTVRP) using memetic algorithms, which is already in trials with 11 points, 22 points, and 50 points in attachment. So that the application program can be used to solve the Multiple Trip Vehicle Routing Problem (MTVRP) using memetic algorithms on the transportation or on the distribution prosess.

In this paper we address scheduling of the permutation flow shop with minimization of makespan and total flow time as the objectives. We propose a memetic algorithm (MA) to search for the set of nondominated solutions (the Pareto optimal solutions). The proposed MA adopts the permutation-based encoding and the fitness assignment mechanism of NSGAII. The main feature is the introduction of an NEH-based neighborhood function into the local search procedure. We also adjust the size of the neighborhood dynamically during the execution of the MA to strike a balance between exploration and exploitation. Forty public benchmark problem instances are used to compare the performance of our MA with that of twenty-seven existing algorithms. Our MA provides close performance for small-scale instances and much better performance for large-scale instances. It also updates more than 90% of the net set of non-dominated solutions for the large-scale instances.

In this paper, the pattern nulling of a linear array for interference cancellation is derived by phase‐only perturbations using memetic algorithms (MAs). The MAs uses improvement procedures which is obtained by incorporating local search into the genetic algorithms. It is proposed to improve the search ability of genetic algorithms. MA is a kind of an improved type of the traditional genetic algorithms. By using local search procedure, it can avoid the shortcoming of the traditional genetic algorithms, whose termination criteria are set up by using the trial and error method. The MA is applied to find the pattern nulling of the proposed adaptive antenna. This design for radiation pattern nulling of an adaptive antenna can suppress interference by placing a null at the direction of the interfering source, i.e. to increase the signal to interference ratio. This proposed method is that an innovative adaptive antenna optimization technique is also able to solve the multipath problem which exists in practical wireless communication systems. Two examples are provided to justify the proposed phase‐only perturbations approach based on MAs. Computer simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.