Multi-objective Genetic Local Search Algorithm Research Articles

A hybrid multi-objective genetic local search algorithm for the prize-collecting vehicle routing problem

This paper studies the prize-collecting vehicle routing problem (PCVRP), which is a new variant of the vehicle routing problem. In the PCVRP, besides the vehicle assignment and visiting sequencing, customer selection also must be determined because the available vehicles are insufficient to visit all the customers. Two types of PCVRP are often encountered in the real world, namely the PCVRP in which the number of vehicles is predetermined (PCVRP-P) and that in which the number of vehicles is not predetermined (PCVRP-NP). In general, multiple optimization objectives are required to be considered in both the PCVRP-P and PCVRP-NP. Unlike the commonly used weighted-sum method, a Pareto-based evolutionary algorithm featuring a genetic algorithm combined with a local search strategy (denoted as HGLS) is proposed for solving the multi-objective PCVRP-P. Subsequently, based on the proposed HGLS, a decomposition strategy is designed to solve the multi-objective PCVRP-NP problem by decomposing it into multiple PCVRP-P problems. In order to determine the number of PCVRP-P problems in the decomposition strategy, a vehicle-number-range determination approach is proposed to obtain a tight upper bound and lower bound of the number of vehicles. The superiority of the proposed algorithm is demonstrated by conducting several experiments on the benchmark problems.

Genetic local search algorithm for a new bi-objective arc routing problem with profit collection and dispersion of vehicles

We present a new bi-objective arc routing problem in which routes must be constructed in order to maximize collected profit and a non linear dispersion metric. A dispersion metric calculated based on instantaneous positions, suitable to capture routing characteristics found when vehicles have to travel in hostile environments, is a novelty in the routing literature. The inherent combinatorial nature of this problem makes it difficult to solve using exact methods. We propose a Multi-objective Genetic Local Search Algorithm to solve the problem and compare the results with those obtained by a well known multi-objective evolutionary algorithm. Computational experiments were performed on a new set of benchmark instances, and the results evidence that local search plays an important role in providing good approximation sets. The proposed method can be adapted to other multi-objective problems in which the exploitation provided by local search may improve the evolutionary procedures usually adopted.

A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems

This paper presents a novel discrete differential evolution (DDE) algorithm for solving the no-wait flow shop scheduling problems with makespan and maximum tardiness criteria. First, the individuals in the DDE algorithm are represented as discrete job permutations, and new mutation and crossover operators are developed based on this representation. Second, an elaborate one-to-one selection operator is designed by taking into account the domination status of a trial individual with its counterpart target individual as well as an archive set of the non-dominated solutions found so far. Third, a simple but effective local search algorithm is developed to incorporate into the DDE algorithm to stress the balance between global exploration and local exploitation. In addition, to improve the efficiency of the scheduling algorithm, several speed-up methods are devised to evaluate a job permutation and its whole insert neighborhood as well as to decide the domination status of a solution with the archive set. Computational simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is shown that the proposed DDE algorithm is superior to a recently published hybrid differential evolution (HDE) algorithm [Qian B, Wang L, Huang DX, Wang WL, Wang X. An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers & Operations Research 2009;36(1):209–33] and the well-known multi-objective genetic local search algorithm (IMMOGLS2) [Ishibuchi H, Yoshida I, Murata T. Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computation 2003;7(2):204–23] in terms of searching quality, diversity level, robustness and efficiency. Moreover, the effectiveness of incorporating the local search into the DDE algorithm is also investigated.

Genetic local search for multi-objective flowshop scheduling problems

This paper addresses flowshop scheduling problems with multiple performance criteria in such a way as to provide the decision maker with approximate Pareto optimal solutions. Genetic algorithms have attracted the attention of researchers in the nineties as a promising technique for solving multi-objective combinatorial optimization problems. We propose a genetic local search algorithm with features such as preservation of dispersion in the population, elitism, and use of a parallel multi-objective local search so as intensify the search in distinct regions. The concept of Pareto dominance is used to assign fitness to the solutions and in the local search procedure. The algorithm is applied to the flowshop scheduling problem for the following two pairs of objectives: (i) makespan and maximum tardiness; (ii) makespan and total tardiness. For instances involving two machines, the algorithm is compared with Branch-and-Bound algorithms proposed in the literature. For such instances and larger ones, involving up to 80 jobs and 20 machines, the performance of the algorithm is compared with two multi-objective genetic local search algorithms proposed in the literature. Computational results show that the proposed algorithm yields a reasonable approximation of the Pareto optimal set.

Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining

This paper shows how a small number of simple fuzzy if-then rules can be selected for pattern classification problems with many continuous attributes. Our approach consists of two phases: candidate rule generation by rule evaluation measures in data mining and rule selection by multi-objective evolutionary algorithms. In our approach, first candidate fuzzy if-then rules are generated from numerical data and prescreened using two rule evaluation measures (i.e., confidence and support) in data mining. Then a small number of fuzzy if-then rules are selected from the prescreened candidate rules using multi-objective evolutionary algorithms. In rule selection, we use three objectives: maximization of the classification accuracy, minimization of the number of selected rules, and minimization of the total rule length. Thus the task of multi-objective evolutionary algorithms is to find a number of non-dominated rule sets with respect to these three objectives. The main contribution of this paper is to propose an idea of utilizing the two rule evaluation measures as prescreening criteria of candidate rules for fuzzy rule selection. An arbitrarily specified number of candidate rules can be generated from numerical data for high-dimensional pattern classification problems. Through computer simulations, we demonstrate that such a prescreening procedure improves the efficiency of our approach to fuzzy rule selection. We also extend a multi-objective genetic algorithm (MOGA) in our former studies to a multi-objective genetic local search (MOGLS) algorithm where a local search procedure adjusts the selection (i.e., inclusion or exclusion) of each candidate rule. Furthermore, a learning algorithm of rule weights (i.e., certainty factors) is combined with our MOGLS algorithm. Such extensions to our MOGA for fuzzy rule selection are another contribution of this paper.

Medical image reconstruction using a multi-objective genetic local search algorithm

Image reconstruction from projections is a key problem in medical image analysis. In this paper, we cast image reconstruction from projections as a multi-objective problem. It is essential to choose some proper objective functions of the problem. We choose the square error, smoothness of the reconstructed image, and the maximum entropy as our objective functions of the problem. Then we introduce a hybrid algorithm comprising of multi-objective genetic and local search algorithms to reconstruct the image. Our algorithm has remarkable global performance. Our experiments show that we can get different results when we give different weights to different objective functions. We can also control the noise by giving different weights on different objective function. At the same time, we can adjust the parameter to let it have good local performance. Though the computation demands of the hybrid algorithm tends to be larger because of the random search of the GA, it is really a common feature of the global optimization method. Our results show that the hybrid algorithm is a more effective than the conventional method. We think our method is very promising for the medical imaging field.

A multi-objective genetic local search algorithm and its application to flowshop scheduling

We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems.