Hybrid genetic algorithms for timetabling

Hybrid genetic algorithms are presented that use optimization heuristics and genetic techniques to outperform all existing programs for the timetabling problem. The timetabling problem is very hard (NP-complete) and a general polynomial time deterministic algorithm is not known. An artificial intelligence approach, in a logic programming environment, may be useful for such a problem. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited for this kind of problem, since there exists an easy way to assess a good timetable but not a well-structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solutions. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the problem knowledge and the heuristics, i.e., from the timetable builder. A fundamental issue and a general problem in the decision process and automated reasoning is how to efficiently obtain logic decisions under disjunctive constraints. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present article illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favorably with the best-known programs to solve decisions problems under logic constraints. Complexity of the new algorithms and results of significant experiments are reported. © 1996 John Wiley & Sons, Inc.     

Parallel hybrid method for SAT that couples genetic algorithms andlocal search

A parallel hybrid method for solving the satisfiability (SAT) problem that combines cellular genetic algorithms (GAs) and the random walk SAT (WSAT) strategy of greedy SAT (GSAT) is presented. The method, called cellular genetic WSAT (CGWSAT), uses a cellular GA to perform a global search from a random initial population of candidate solutions and a local selective generation of new strings. The global search is then specialized in local search by adopting the WSAT strategy. A main characteristic of the method is that it indirectly provides a parallel implementation of WSAT when the probability of crossover is set to zero. CGWSAT has been implemented on a Meiko CS-2 parallel machine using a 2D cellular automaton as a parallel computation model. The algorithm has been tested on randomly generated problems and some classes of problems from the DIMACS and SATLIB test set     

Hybrid genetic algorithms for feature selection

This paper proposes a novel hybrid genetic algorithm for feature selection. Local search operations are devised and embedded in hybrid GAs to fine-tune the search. The operations are parameterized in terms of their fine-tuning power, and their effectiveness and timing requirements are analyzed and compared. The hybridization technique produces two desirable effects: a significant improvement in the final performance and the acquisition of subset-size control. The hybrid GAs showed better convergence properties compared to the classical GAs. A method of performing rigorous timing analysis was developed, in order to compare the timing requirement of the conventional and the proposed algorithms. Experiments performed with various standard data sets revealed that the proposed hybrid GA is superior to both a simple GA and sequential search algorithms.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

Kalman-extended genetic algorithm for search in nonstationaryenvironments with noisy fitness evaluations

In basic genetic algorithm (GA) applications, the fitness of a solution takes a value that is certain and unchanging. This formulation does not work for ongoing searches for better solutions in a nonstationary environment in which expected solution fitness changes with time in unpredictable ways, or for fitness evaluations corrupted by noise. In such cases, the estimated fitness has an associated uncertainty. The uncertainties due to environmental changes (process noise) and to noisy evaluations (observation noise) can be reduced, at least temporarily, by re-evaluating existing solutions. The Kalman formulation provides a formal mechanism for treating uncertainty in GA. It provides the mechanics for determining the estimated fitness and uncertainty when a new solution is generated and evaluated for the first time. It also provides the mechanics for updating the estimated fitness and uncertainty after an existing solution is re-evaluated and for increasing the uncertainty with the passage of time. A Kalman-extended GA (KGA) is developed to determine when to generate a new individual, and when to re-evaluate an existing one and which to re-evaluate. This KGA is applied to the problem of maintaining a network configuration with minimized message loss, with mobile nodes and stochastic transmission. As the nodes move, the optimal network changes, but information contained within the population of solutions allows efficient discovery of better-adapted solutions. The sensitivity of the KGA to several control parameters is explored     

Interactive genetic algorithms with individual’s fuzzy fitness

Interactive genetic algorithms are effective methods to solve an optimization problem with implicit or fuzzy indices, and have been successfully applied to many real-world optimization problems in recent years. In traditional interactive genetic algorithms, many researchers adopt an accurate number to express an individual’s fitness assigned by a user. But it is difficult for this expression to reasonably reflect a user’s fuzzy and gradual cognitive to an individual. We present an interactive genetic algorithm with an individual’s fuzzy fitness in this paper. Firstly, we adopt a fuzzy number described with a Gaussian membership function to express an individual’s fitness. Then, in order to compare different individuals, we generate a fitness interval based on α-cut set, and obtain the probability of individual dominance by use of the probability of interval dominance. Finally, we determine the superior individual in tournament selection with size two based on the probability of individual dominance, and perform the subsequent evolutions. We apply the proposed algorithm to a fashion evolutionary design system, a typical optimization problem with an implicit index, and compare it with two interactive genetic algorithms, i.e., an interactive genetic algorithm with an individual’s accurate fitness and an interactive genetic algorithm with an individual’s interval fitness. The experimental results show that the proposed algorithm is advantageous in alleviating user fatigue and looking for user’s satisfactory individuals.     

Hybrid genetic algorithms for structural reliability analysis

The traditional genetic algorithms (GA) involve step-by-step numerical iterations for searching the minimum reliability index of a structural system, and therefore require a relatively long computation time. In practice the size of a design problem can be very large, the limit state functions are usually implicit in terms of the random variables. When using the traditional genetic algorithms, one can encounter problems with the immense effort required in coding ones own finite element code (or for integration with other commercial finite element software) when using the traditional genetic algorithms. For convenient practical applications of the GA in engineering, two new GA methods, namely, a hybrid GA method consisting of artificial neural network (ANN) and a hybrid GA method consisting of ANN and Monte Carlo simulation with importance sampling are proposed in the present study. A distinctive feature of these proposed methods is the introduction of an explicit approximate limit state function. The explicit formulation of the approximate limit state function is derived by using the parameters of the ANN model. By introducing the derived approximate limit state function, the failure probability can be easily calculated, practically when the limit state functions are not explicitly known. These proposed methods are investigated and their accuracy and efficiency are demonstrated using numerical examples. Finally, some important parameters in these proposed methods are also discussed.     

Hybrid genetic algorithms for constrained placement problems

When solving real-world problems, often the main task is to find a proper representation for the candidate solutions. Strings of elementary data types with standard genetic operators may tend to create infeasible individuals during the search because of the discrete and often constrained search space. This article introduces a generally applicable representation for 2D combinatorial placement and packing problems. Empirical results are presented for two constrained placement problems, the facility layout problem and the generation of VLSI macro-cell layouts. For multiobjective optimization problems, common approaches often deal with the different objectives in different phases and thus are unable to efficiently solve the global problem. Due to a tree structured genotype representation and hybrid, problem-specific operators, the proposed approach is able to deal with different constraints and objectives in one optimization step     

Lossless fitness inheritance in genetic algorithms for decision trees

When genetic algorithms are used to evolve decision trees, key tree quality parameters can be recursively computed and re-used across generations of partially similar decision trees. Simply storing instance indices at leaves is sufficient for fitness to be piecewise computed in a lossless fashion. We show the derivation of the (substantial) expected speedup on two bounding case problems and trace the attractive property of lossless fitness inheritance to the divide-and-conquer nature of decision trees. The theoretical results are supported by experimental evidence.     

Guided restarting local search for production planning

Planning problems can be solved with a large variety of different approaches, and a significant amount of work has been devoted to the automation of planning processes using different kinds of methods. This paper focuses on the use of specific local search algorithms for real-world production planning based on experiments with real-world data, and presents an adapted local search guided by evolutionary metaheuristics. To make algorithms efficient, many specifics need to be considered and included in the problem solving. We demonstrate that the use of specialized local searches can significantly improve the convergence and efficiency of the algorithm. The paper also includes an experimental study of the efficiency of two memetic algorithms, and presents a real-world software implementation for the production planning.     

Hybrid genetic algorithm with adaptive local search scheme

This paper proposes a hybrid genetic algorithm (a-hGA) with adaptive local search scheme. For designing the a-hGA, a local search technique is incorporated in the loop of genetic algorithm (GA), and whether or not the local search technique is used in the GA is automatically determined by the adaptive local search scheme. Two modes of adaptive local search schemes are developed in this paper. First mode is to use the conditional local search method that can measure the average fitness values obtained from the continuous two generations of the a-hGA, while second one is to apply the similarity coefficient method that can measure a similarity among the individuals of the population of the a-hGA. These two adaptive local search schemes are included in the a-hGA loop, respectively. Therefore, the a-hGA can be divided into two types: a-hGA1 and a-hGA2. To prove the efficiency of the a-hGA1 and a-hGA2, a canonical GA (cGA) and a hybrid GA (hGA) with local search technique and without any adaptive local search scheme are also presented. In numerical example, all the algorithms (cGA, hGA, a-hGA1 and a-hGA2) are tested and analyzed. Finally, the efficiency of the proposed a-hGA1 and a-hGA2 is proved by various measures of performance.     

Hybrid methods using genetic algorithms for global optimization

This paper discusses the trade-off between accuracy, reliability and computing time in global optimization. Particular compromises provided by traditional methods (Quasi-Newton and Nelder-Mead's simplex methods) and genetic algorithms are addressed and illustrated by a particular application in the field of nonlinear system identification. Subsequently, new hybrid methods are designed, combining principles from genetic algorithms and "hill-climbing" methods in order to find a better compromise to the trade-off. Inspired by biology and especially by the manner in which living beings adapt themselves to their environment, these hybrid methods involve two interwoven levels of optimization, namely evolution (genetic algorithms) and individual learning (Quasi-Newton), which cooperate in a global process of optimization. One of these hybrid methods appears to join the group of state-of-the-art global optimization methods: it combines the reliability properties of the genetic algorithms with the accuracy of Quasi-Newton method, while requiring a computation time only slightly higher than the latter.     

Parallel best-first search algorithms for planning problems on multi-core processors

The Journal of Supercomputing - The multiplication of computing cores in modern processor units permits revisiting the design of classical algorithms to improve computational performance in complex...     

Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation

For many real-world optimization problems, the robustness of a solution is of great importance in addition to the solution's quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of quality. One way to achieve that goal is to evaluate each solution under a number of different scenarios and use the average solution quality as fitness. However, this approach is often impractical, because the cost for evaluating each individual several times is unacceptable. In this paper, we present a new and efficient approach to estimating a solution's expected quality and variance. We propose to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance. Based on a variety of test functions, we demonstrate empirically that our approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature.     

Forking genetic algorithms: GAs with search space division schemes

In this article, we propose a new type of genetic algorithm (GA), the forking GA (fGA), which divides the whole search space into subspaces, depending on the convergence status of the population and the solutions obtained so far. The fGA is intended to deal with multimodal problems that are difficult to solve using conventional GAs. We use a multipopulation scheme that includes one parent population that explores one subspace and one or more child populations exploiting the other subspace. We consider two types of fGAs, depending on the method used to divide the search space. One is the genotypic fGA (g-fGA), which defines the search subspace for each subpopulation, depending on the salient schema within the genotypic search space. The other is the phenotypic fGA (p-fGA), which defines a search subspace by a neighborhood hypercube around the current best individual in the phenotypic feature space. Empirical results on complex function optimization problems show that both the g-fGA and p-fGA perform well compared to conventional GAs. Two additional utilities of the p-fGA are also studied briefly.     

Hybrid ant colony algorithms for path planning in sparse graphs

The general problem of path planning can be modeled as a traveling salesman problem which assumes that a graph is fully connected. Such a scenario of full connectivity is however not always realistic. One such motivating example for us is the application of path planning for unmanned reconnaissance aerial vehicles (URAVs). URAVs are widely deployed for photography or imagery gathering missions of sites of interest. These sites can be targets in a combat zone to be investigated or sites inaccessible by ground transportation, such as those hit by forest fires, earthquake or other forms of natural disasters. The navigation environment is one where the overall configuration of the problem is a sparse graph. Unlike graphs that are fully connected, sparse graphs are not always Hamiltonian. In this paper, we describe hybrid ant colony algorithms (HACAs) proposed for path planning in sparse graphs since existing ant colony solvers designed for solving TSP do not apply to the present context directly. HACAs represent ant inspired algorithms incorporated with a local search procedure and some heuristic techniques for uncovering feasible route(s) or path(s) in a sparse graph within tractable time. Empirical results conducted on a set of generated sparse graphs demonstrate the excellent convergence property and robustness of HACAs in uncovering low risk and Hamiltonian visitation paths. Further, the obtained results also indicate that HACAs converge to secondary closed paths in situations where a Hamiltonian cycle does not exist theoretically or is not attainable within the bounded computational time window.     

Memory gradient method with Goldstein line search

In this paper, we present a multi-step memory gradient method with Goldstein line search for unconstrained optimization problems and prove its global convergence under some mild conditions. We also prove the linear convergence rate of the new method when the objective function is uniformly convex. Numerical results show that the new algorithm is suitable to solve large-scale optimization problems and is more stable than other similar methods in practical computation.     

A production planning problem for an industrial association

The optimal production program of an industrial enterprise is constructed by solving a block piecewise-quadratic programming problem by a two-stage algorithm. A method for long-term enterprise planning is proposed.Translated from Kibernetika, No. 5, pp. 54–58, September–October, 1989.     

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.