Comparison of Searching Behaviour of Three Evolutionary Algorithms Applied to Water Distribution System Design Optimization

During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the optimal design and operation of water distribution systems. More recently, ant colony optimization algorithms (ACOAs), which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to a number of benchmark combinatorial optimization problems. In this paper, a formulation is developed which enables ACOAs to be used for the optimal design of water distribution systems. This formulation is applied to two benchmark water distribution system optimization problems and the results are compared with those obtained using genetic algorithms. The findings of this study indicate that ACOAs are an attractive alternative to GAs for the optimal design of water distribution systems, as they outperformed GAs for the two case studies considered both in terms of computational efficiency and their ability to find near global optimal solutions.

Differential evolution (DE) is a relatively new technique that has recently been used to optimize the design for water distribution systems (WDSs). Several parameters need to be determined in the use of DE, including population size, N; mutation weighting factor, F; crossover rate, CR, and a particular mutation strategy. It has been demonstrated that the search behavior of DE is especially sensitive to the F and CR values. These parameters need to be fine-tuned for different optimization problems because they are generally problem-dependent. A self-adaptive differential evolution (SADE) algorithm is proposed to optimize the design of WDSs. Three new contributions are included in the proposed SADE algorithm: (1) instead of pre-specification, the control parameters of F and CR are encoded into the chromosome of the SADE algorithm, and hence are adapted by means of evolution; (2) F and CR values of the SADE algorithm apply at the individual level rather than the generational level normally used by the traditional DE algorithm; and (3) a new convergence criterion is proposed for the SADE algorithm as the termination condition, thereby avoiding pre-specifying a fixed number of generations or computational budget to terminate the evolution. Four WDS case studies have been used to demonstrate the effectiveness of the proposed SADE algorithm. The results show that the proposed algorithm exhibits good performance in terms of solution quality and efficiency. The advantage of the proposed SADE algorithm is that it reduces the effort required to fine-tune algorithm parameter values.

Hybrid metaheuristic algorithms have become popular for solving complex problems that are very challenging to overcome with conventional methods in recent years. This paper presents a hybrid algorithm called DE-ACO that combines Differential Evolution (DE) and Ant Colony Optimization (ACO) algorithms. The main idea is to use the Differential Evolution (DE) algorithm for a good starting point for Ant Colony Optimization (ACO) algorithm. A benchmark of six well-known test functions is employed to check the performances of the proposed approach in terms of convergence rate, quality of optimum solutions and computing time. The results obtained show that the performances of the hybrid algorithm outperform significantly the DE and ACO algorithms.

Water distribution systems least cost pipe sizing/design is probably the most explored problem in water distribution systems optimization. Attracted numerous studies over the last four decades, two main approaches were employed: decomposition in which an “inner” linear programming problem is solved for a fixed set of flows/heads, while the flows/heads are altered at an “outer” problem using a gradient or a sub-gradient type technique; and the utilization of an evolutionary optimization algorithm (e.g., a genetic algorithm). In reality, however, from a broader perspective the design problem is inherently of a multiobjective nature incorporating competing objectives such as minimizing cost versus maximizing reliability. This chapter reviews some of the literature on single and multiobjective optimal design of water distribution systems and suggests a few future research directions in this area.

This parameters selection is an important issue in the research of ¿-support vector regression machine (¿-SVRM), whose nature is an optimization selection process. Motivated by the effectiveness of differential evolution (DE) algorithm on optimization problem, a new automatic searching method based on DE algorithm was proposed. Experimental results demonstrate that ¿-SVRM model optimization based on DE algorithm has better prediction capability compared with the methods based on genetic algorithm (GA), ant colony optimization (ACO) and particle swarm optimization (PSO).

A novel optimization framework for efficiently identifying high-quality Pareto-optimal solutions: maximizing resilience of water distribution systems under cost constraints

Evolutionary algorithms (EAs) have been widely used to search for optimal strategies for the planning and management of water resources systems, particularly reservoir operation. This study provides a comprehensive diagnostic assessment of state of the art of the non-animal-inspired EA applications to reservoir optimization. This type of EAs does not mimic biologic traits and group strategies of animal (wild) species. A search of pertinent papers was applied to the journal citation reports (JCRs). A bibliometric survey identified 14 pertinent non-animal-inspired EAs, such as the genetic algorithm (GA), simulated annealing (SA), and differential evolution (DE) algorithms, most of which have a number of modified versions. The characteristics of non-animal-inspired EAs and their modified versions were discussed to identify the difference between EAs and how each EA was improved. Additionally, the type of application of non-animal-inspired EAs to different case studies was investigated, and comparisons were made between the performance of the applied EAs in the studied literature. The survey revealed that the GA is the most frequently applied algorithm, followed by the DE algorithm. Non-animal-inspired EAs are superior to the classical methods of reservoir optimization (e.g., the non-linear programming and dynamic programming) due to faster convergence, diverse solution space, and efficient objective function evaluation. Several non-animal-inspired EAs of recent vintage have been shown to outperform the classic GA, which was the first evolutionary algorithm applied to reservoir operation.

Parameters setting is an important problem of evolution algorithms, include differential evolution algorithm. It has an effect on the performance of evolution algorithms. Although there is only three control parameters in differential evolution (DE) algorithm, the parameters setting is also a difficult problem. Self-adaptation is highly beneficial for adjusting the control parameters, especially when done without any user interaction. This paper presents differential evolution algorithm, called (AdaptDE), which use self-adaptive mechanisms applied to the control parameters. It can get the optimal control parameters for different optimization problem without user interaction. Experimental results indicate that AdaptDE algorithm is efficient and feasible. It is superior to jDE algorithm and FADE algorithm on the quality of solution.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

This paper proposes an improved algorithm applied to path planning for the inspection of unmanned aerial vehicles (UAVs) in urban pipe corridors, which introduces a collaborative game between spherical vector particle swarm optimization (SPSO) and differential evolution (DE) algorithms. Firstly, a high-precision 3D grid map model of urban pipe corridors is constructed based on the actual urban situation. Secondly, the cost function is formulated, and the constraints for ensuring the safe and smooth inspection of UAVs are proposed to transform path planning into an optimization problem. Finally, a hybrid algorithm of SPSO and DE algorithms based on the Nash bargaining theory is proposed by introducing a cooperative game model for optimizing the cost function to plan the optimal path of UAV inspection in complex urban pipe corridors. To evaluate the performance of the proposed algorithm (GSPSODE), the SPSO, DE, genetic algorithm (GA), and ant colony optimization (ACO) are compared with GSPSODE, and the results show that GSPSODE is superior to other methods in UAV inspection path planning. However, the selection of algorithm parameters, the difference in the experimental environment, and the randomness of experimental results may affect the accuracy of experimental results. In addition, a high-precision urban pipe corridors scenario is constructed based on the RflySim platform to dynamically simulate the optimal path planning of UAV inspection in real urban pipe corridors.

Differential Evolution (DE) algorithm is a new heuristic approach which has been proposed particulary for numeric optimization problems. It is a population based algorithm like genetic algorithms using the similar operators; crossover, mutation and selection. In this work, DE algorithm has been applied to the design of fixed point digital Finite Impuls Response (FIR) filters and its performance has been compared to that of Genetic Algorithm (GA) and Least Squares Algorithm (LSQ).

This paper presents a new method for optimal design of controllers based on a thought and differential evolution. At first an extensible component library and a performance criteria library are established in the approach. The component library contains different types of system components which may be essential for controller structure. Appropriate components can be selected from the library and then combined to form a controller with richer structure. The performance criteria library includes some common control performance indexes. Users can choose one from it according to performance requirements. Then, the differential evolution algorithm is utilized to optimize the parameters of each component in order to find the optimal solution and ultimately obtain the controller structure and parameters which meet requirements. Simulations were done on different types of control objects. Simulation results show that the controllers designed by the proposed method for different types of control objects generally have better comprehensive performance than the PID controllers designed by conventional methods, differential evolution and genetic algorithm. Validity, stability and generalizability of the proposed method were also tested and verified.

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

Multi-objective design of Water Distribution Systems (WDSs) has received considerable attention in the past. Multi-objective evolutionary algorithms (MOEAs) are popular in tackling this problem due to their ability to approach the true Pareto-optimal front (PF) in a single run. Recently, several hybrid metaheuristics based on MOEAs have been proposed and validated on test problems. Among these algorithms, AMALGAM and MOHO are two noteworthy representatives which mix their constituent algorithms in contrasting fashion. In this paper, they are employed to solve a wide range of benchmark design problems against another state-of-the-art algorithm, namely NSGA-II. The design task is formulated as a bi-objective optimisation problem taking cost and network resilience into account. The performance of three algorithms is assessed via normalised hypervolume indicator. The results demonstrate that AMALGAM is superior to MOHO and NSGA-II in terms of convergence and diversity on the networks of small-to-medium size; however, for larger networks, the performance of hybrid algorithms deteriorates as they lose their adaptive capabilities. Future improvement and/or redesign on hybrid algorithms should not only adopt the strategies of adaptive portfolios of sub-algorithms and global information sharing, but also prevent the deterioration mainly caused by imbalance of constituent algorithms.

A local search enhanced differential evolutionary algorithm for sparse recovery