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Multi-objective optimization with cross entropy method: Stochastic learning with clustered pareto fronts

This paper presents a novel multiobjective optimization strategy based on the cross entropy method (MOCE). The cross-entropy method (CE) is a stochastic learning algorithm inspired from rare event simulations and proved to be successful in the solution of difficult single objective real-valued optimization problems. The presented work extends the use of cross-entropy method to real-valued multiobjective optimization. For this purpose, parameters of CE search are adapted using the information collected from clustered nondominated solutions on the Pareto front. Comparison with well known multiobjective optimization algorithms on the solution of provably difficult benchmark problem instances demonstrated that CEMO performs at least as good as its competitors.

Probability collectives hybridised with differential evolution for global optimisation

Probability collectives PC is a recent agent-based search framework for function optimisation through optimising parameters of a collection of probability distributions. Differential evolution DE is a successful metaheuristic method particularly for real-parameter global optimisation. This paper presents a hybrid computational model based on a modified PC and DE algorithms for the purpose of improved solutions for real-valued optimisation problems. In the proposed model, PC performs a first phase local search and explores promising search areas through updating parameters of probability distributions over the solution space while DE uses the extracted PC-based knowledge to guide its search with adaptive heuristics. A novel distance-based adaptive mutation scheme is designed within DE to guide the search towards better regions of the solution space. Experimental results reveal that the proposed hybrid algorithm is able to integrate the PCs collective learning methodology and DEs adaptive search strategy effectively to generate improved solutions for difficult problems.

A genetic algorithm with multiple crossover operators for optimal frequency assignment problem

A genetic algorithm employing multiple crossover operators in its implementation is presented. A set of available crossover operators is established initially and a particular crossover operator is probabilistically selected from this set for recombination. Each crossover operator is assigned a fitness value based on the amount of fitness improvements they achieve over a number of previous generations. Hence, a randomized dynamic operator selection scheme is followed. This approach is used for the solution for which optimal results are achieved in reasonable computation times even for the very difficult problem instances.

A two-stage memory powered Great Deluge algorithm for global optimization

A two-stage memory architecture and search operators exploiting the accumulated experience in memory are maintained within the framework of a Great DeLuge algorithm for real-valued global optimization. The level-based acceptance criterion of the Great DeLuge algorithm is applied for each best solution extracted in a particular iteration. The use of memory-based search supported by effective move operators results in a powerful optimization algorithm. The success of the presented approach is illustrated using three sets of well-known benchmark functions including problems of varying sizes and difficulties. Performance of the presented approach is evaluated and in comparison to well-known algorithms and their published results. Except for a few large-scale optimization problems, experimental evaluations demonstrated that the presented approach performs at least as good as its competitors.

Evolutionary multiobjective optimization with a segment based external memory support for the multiobjective quadratic assignment problem

Multiobjective evolutionary optimization has been demonstrated to be an efficient method for some difficult multiobjective optimization problems; particularly the quadratic assignment problem which is a provably difficult NP-complete problem with a multitude of real-world applications. This paper introduces the use of a segment-based external memory in evolutionary multiobjective optimization. In principle, variable-size solution segments taken from a number of previously promising solutions are stored in an external memory whose elements are used in the construction of new solutions. In the construction of a solution, a solution segment is retrieved from the external memory and used in the construction of complete solutions through evolutionary recombination operators. The aim is to provide further intensification around promising solutions without weakening the exploration capabilities. Different instances of the multiobjective quadratic assignment problem are used for performance evaluations and, almost in all trials, the proposed external memory strategy provided significantly better results than the multiobjective genetic algorithm (MOGA).

A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem

Graphical abstractDisplay Omitted HighlightsA hybrid method combining great deluge and tabu search algorithms is proposed.This hybrid is supported with a two-stage external memory.First stage of acts as a short term memory that is frequently updated.Second stage acts as a long term memory that is updated less frequently.Elements of the second stage are maximally dissimilar in variable space. A two-stage memory architecture is maintained within the framework of great deluge algorithm for the solution of single-objective quadratic assignment problem. Search operators exploiting the accumulated experience in memory are also implemented to direct the search towards more promising regions of the solution space. The level-based acceptance criterion of the great deluge algorithm is applied for each best solution extracted in a particular iteration. The use of short- and long-term memory-based search supported by effective move operators resulted in a powerful combinatorial optimization algorithm. A successful variant of tabu search is employed as the local search method that is only applied over a few randomly selected memory elements when the second stage memory is updated. The success of the presented approach is illustrated using sets of well-known benchmark problems and evaluated in comparison to well-known combinatorial optimization algorithms. Experimental evaluations clearly demonstrate that the presented approach is a competitive and powerful alternative for solving quadratic assignment problems.

A memory-based colonization scheme for particle swarm optimization

A novel memory-based particle swarm optimization algorithm employing externally implemented global (shared) and particle-based (local) memories and a colonization approach similar to artificial immune system algorithms is presented. At any iteration, particle-based memories keep a number of previously best performing personal positions for each particle and the global memory keeps a number of globally best positions found so far. A set of velocities is computed for each particle using each of the personal best positions within its local memory and a number of randomly selected positions from the global memory. This way, a colony of new positions is obtained for each particle and the one with the best fitness is selected and put within the new swarm. Global and local memories are also updated using the solutions within each colony. This new memory-based strategy is used for the solution of problems within the CEC2005 test suit. Experimental evaluations demonstrated that the proposed strategy outperformed the conventional and other known memory-based PSO algorithms for all problem instances.

An evolutionary multi-objective modeling and solution approach for fuzzy vehicle routing problem

In this paper an evolutionary multi-objective optimization approach is applied to extend fuzzy multi objective problem considered by Jeng-Jong Lin [1] and Gupta et al [2, 3]. In our extended work, the concept of fuzzy [6, 8] due time is applied to increase satisfaction grade of customers and to meet their demands much better as well as to decrease the delay times of vehicles, which service customers during their desired period of times, so the objectives are as follows: maximize the loading capacity of vehicles, minimize the distance travelled by vehicles, minimize the waiting time of customers, maximize the satisfaction grade of customers, minimize the delay times of vehicles.

Evolutionary Multi-Objective optimization for nurse scheduling problem

Nurse scheduling problem (NSP) is the problem of determining a reasonable and efficient work schedule for nurses. This paper presents a new external memory-based approach along with Multi-Objective Genetic Algorithms (MOGA) to solve multiobjective NSPs. In multiobjective modeling of NSPs, there are several objectives which are in conflict with each other, and there are some hard constraints that should be satisfied in any solution. The presented approach can solve multiobjective NSPs in an efficient way. As demonstrated by the experimental results, MOGA together with the maintained external memory extracted significantly more nondominated solutions compared to MOGA without a memory.

Reduction of Generalization Error in Fuzzy System Modeling

This paper proposes a technique to reduce the overfitting of the fuzzy models to the training data set during the supervised training phase. Typically a training data set is employed in extraction of the unsupervised fuzzy rule base (FRB) of a fuzzy model (FM), and in supervised training of the FRB to reduce the output error of FM for the training data set. However, recently developed optimization tools usually results in the overfitting of the FM to the training data set, which causes unacceptable rise in the output error for the verification data set. The proposed approach is based on dynamic construction of synthetic training data sets with similar statistical features to the verification data set. The proposed technique is tested on simple single-input and several multi-input benchmark data sets for the commonly used TS fuzzy inference method. The test results indicated that the proposed method is successful in reducing the verification error.