Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing.

In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

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Evolutionary algorithms for constrained parameter optimization problems

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints

A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization

In recent years, interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) has grown due to its importance in real-world applications. Several approaches, such as the memory and multiple population schemes, have been developed for EAs to address dynamic problems. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of EAs, for DOPs. A PBIL-specific associative memory scheme, which stores best solutions as well as corresponding environmental information in the memory, is investigated to improve its adaptability in dynamic environments. In this paper, the interactions between the memory scheme and random immigrants, multipopulation, and restart schemes for PBILs in dynamic environments are investigated. In order to better test the performance of memory schemes for PBILs and other EAs in dynamic environments, this paper also proposes a dynamic environment generator that can systematically generate dynamic environments of different difficulty with respect to memory schemes. Using this generator, a series of dynamic environments are generated and experiments are carried out to compare the performance of investigated algorithms. The experimental results show that the proposed memory scheme is efficient for PBILs in dynamic environments and also indicate that different interactions exist between the memory scheme and random immigrants, multipopulation schemes for PBILs in different dynamic environments.

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Population-Based Incremental Learning With Associative Memory for Dynamic Environments

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations

Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems

Research on multiobjective optimization (MO) becomes one of the hot points of intelligent computation. Compared with evolutionary algorithm, the artificial immune system used for solving MO problems (MOPs) has shown many good performances in improving the convergence speed and maintaining the diversity of the antibody population. However, the simple clonal selection computation has some difficulties in handling some more complex MOPs. In this paper, the simple clonal selection strategy is improved and a novel immune clonal algorithm (NICA) is proposed. The improvements in NICA are mainly focus on four aspects. 1) Antibodies in the antibody population are divided into dominated ones and nondominated ones, which is suitable for the characteristic of one multiobjective optimization problem has a series Pareto-optimal solutions. 2) The entire cloning is adopted instead of different antibodies having different clonal rate. 3) The clonal selection is based on the Pareto-dominance and one antibody is selected or not depending on whether it is a nondominated one, which is different from the traditional clonal selection manner. 4) The antibody population updating operation after the clonal selection is adopted, which makes antibody population under a certain size and guarantees the convergence of the algorithm. The influences of the main parameters are analyzed empirically. Compared with the existed algorithms, simulation results on MOPs and constrained MOPs show that NICA in most problems is able to And much better spread of solutions and better convergence near the true Pareto-optimal front.

A Novel Immune Clonal Algorithm for MO Problems

One of the important issues in data warehouse development is the selection of a set of views to materialize in order to accelerate a large number of on-line analytical processing (OLAP) queries. The maintenance-cost view-selection problem is to select a set of materialized views under certain resource constraints for the purpose of minimizing the total query processing cost. However, the search space for possible materialized views may be exponentially large. A heuristic algorithm often has to be used to find a near optimal solution. In this paper, for the maintenance-cost view-selection problem, we propose a new constrained evolutionary algorithm. Constraints are incorporated into the algorithm through a stochastic ranking procedure. No penalty functions are used. Our experimental results show that the constraint handling technique, i.e., stochastic ranking, can deal with constraints effectively. Our algorithm is able to find a near-optimal feasible solution and scales with the problem size well.

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Materialized view selection as constrained evolutionary optimization

The maintenance-cost view-selection problem is one of the important issues in data warehouse design. It is to select a set of materialized views under a maintenance cost constraint (such as maintenance time), in order to minimize the total query processing cost for a given set of queries. The problem has recently received significant attention. Several greedy/heuristic algorithms were proposed. However, the quality of the greedy/heuristic algorithms has not been well analyzed. In this paper, in a multidimensional data warehouse environment, we reexamine the greedy/heuristic algorithms in various settings, and provide users with insights on the quality of these heuristic algorithms.

What Difference Heuristics Make: Maintenance-Cost View-Selection Revisited

For the purpose of satisfying different users' profiles and accelerating the subsequence OLAP (Online Analytical Processing) queries in a large data warehouse, dynamic materialized OLAP view management is highly desirable. Previous work caches data as either chunks or multidimensional range fragments. In this paper, we focus on ROLAP (Relational OLAP) in an existing relational database system. We propose a dynamic predicate-based partitioning approach, which can support a wide range of OLAP queries. We conducted extensive performance studies using TPCH benchmark data on IBM DB2 and encouraging results are obtained which indicate that our approach is highly feasible.

Dynamic materialized view management based on predicates

89 Selecting Views with Maintenance Cost Constraints: Issues, Heuristics and Performance Jeffrey Xu Yu The Chinese University of Hong Kong, Hong Kong, China email: yu@se.cuhk.edu.hk Chi-Hon Choi The Chinese University of Hong Kong, Hong Kong, China email: chchoi@se.cuhk.edu.hk Gang Gou The Chinese University of Hong Kong, Hong Kong, China email: ggou@se.cuhk.edu.hk Hongjun Lu Hong Kong Uni. of Science and Technology, Hong Kong, China email: luhj@cs.ust.hk

Selecting Views with Maintenance Cost Constraints: Issues, Heuristics and Performance

Materialized view selection with resource constraint is one of the most important issues in the management of data warehouses. In this paper, we revisit the problem of materialized view selection under disk-space constraint S. Many efficient greedy algorithms have been developed. However, we observe that when S is small, their solution quality will not be well guaranteed. In order to further improve solution quality in such cases, we develop a competitive A* algorithm. Both theory and experiment results show that our algorithm is a powerful, efficient and flexible scheme for this problem.

Chi-Hon Choi

Papers

Materialized view selection as constrained evolutionary optimization

What Difference Heuristics Make: Maintenance-Cost View-Selection Revisited

Dynamic materialized view management based on predicates

Selecting Views with Maintenance Cost Constraints: Issues, Heuristics and Performance

An efficient and interactive A*-algorithm with pruning power: materialized view selection revisited