Noisy optimization problems - a particular challenge for differential evolution?

Differential Evolution (DE) is a simple and fast population based Nature Inspired Algorithm (NIA). When it is experimented for benchmark problems as well as real world problems it outperformed other population based NIAs and other search metaheuristics in terms of rate of convergence. But it is not an exception in class of population based algorithms, it also show premature convergence and stagnates at suboptimal points. Therefore this paper tries to sustain a better convergence speed and keep away from stagnation by introducing levy flight random search process along with opposition based learning strategy in original DE algorithm. The proposed algorithm named as Opposition Based Levy Flight Search in DE (OLFDE) Algorithm. The newly proposed algorithm OLFDE tested over fourteen benchmark problems and three real world problems (Pressure Vessel Design, Parameter estimation for frequency modulated sound wave and Compression Spring problem) in order to prove its efficiency over some recent variants of DE.

Researchers can solve Simple optimization problems using various methods. But differential Evolution (DE) is a method(population based) to solve complex optimization problems in some easy steps that is not possible to handle by mathematical optimization methods. For global optimization problems DE is a probabilistic approach. DE when tested over some bench mark functions and real world problems it performed better than some evolutionary algorithms and swarm - intelligence based algorithms. Balancing between Exploration and Exploitation using DE mutation and crossover with control parameters F and CR (fine tunned) is to be done. DE does not complete demand of good convergence and stagnation. DE Explore better but this exploration capability sometimes may skip the true solution and exhibit premature convergence. To improve this we can decrease the step size but this exhibit stagnation. So for Better exploitation, another approach called Memetic algorithm based on levy flight based local search strategy is used with DE. Further to balance exploration and exploitation in local search area in this paper a population or generation based exploitation of local search area in LFDE is proposed that is called PGLFDE. To show better result proposed strategy is tested on some bench mark functions and compare with recent variants of DE.

When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.

We consider noisy optimization and some traditional variance reduction techniques aimed at improving the convergence rate, namely (i) common random numbers (CRN), which is relevant for population-based noisy optimization and (ii) stratified sampling, which is relevant for most noisy optimization problems. We present artificial models of noise for which common random numbers are very efficient, and artificial models of noise for which common random numbers are detrimental. We then experiment on a desperately expensive unit commitment problem. As expected, stratified sampling is never detrimental. Nonetheless, in practice, common random numbers nonetheless provided, by far, most of the improvement.

Many modern global optimization algorithms are inspired by natural phenomena rather than classes of mathematical functions. Theorems such as No Free Lunch imply that an algorithm's performance on an objective function is determined by the compatibility between the function and its structure. Grouping by inspiration blurs the distinction between algorithms, making it harder to study compatibility. Therefore, this work treats algorithms as sequential sampling algorithms, and groups them by sampling scheme: 1. perturb every design (e.g., Particle Swarm), 2. perturb a subset of designs (e.g., rand/1/bin Differential Evolution), 3. perturb a single design (e.g., best/2/bin Differential Evolution), 4. deterministically modify and then perturb the design (e.g., Quantum Particle Swarm). Using 295 analytical test cases, the structure and performance of 38 biologically inspired algorithms (major and minor variations of 5 algorithms) are compared by group. The groups are evaluated by 1. how performance scales with dimensionality, and 2. trends in mean convergence rates and accuracy. Controlling for sample size, number of algorithms/group, convergence criteria, and tuning parameters, Groups 2 and 3 demonstrate superior accuracy and convergence rates on 80 % of test cases combined, implying greater overall compatibility than other groups, and scale much better than other groups on 2nd and 4th order polynomials up to 100-dimensions, converging to minima 3---6 orders of magnitude lower. Statistical significance testing reveals overlap in the behavior of certain Group 2 and 3 algorithms on 52 test cases. Group 3 is a special case of Group 2, further implying structural compatibility with certain test cases.

Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints

Differential evolution with orthogonal array‐based initialization and a novel selection strategy

Due to increased search complexity in multi-objective optimization, premature convergence becomes a problem. Complex engineering problems poses high number of variables with many constraints. Hence, more difficult benchmark problems must be utilized to validate new algorithms performance. A well-known optimizer, Multi-Objective Particle Swarm Optimizer (MOPSO), has a few weakness that needs to be addressed, specifically its convergence in high dimensional problems and its constraints handling capability. For these reasons, we propose a modified MOPSO (M-MOPSO) to improve upon these aspects. M-MOPSO is compared with four other algorithms namely, MOPSO, Multi-Objective Grey Wolf Optimizer (MOGWO), Multi-Objective Evolutionary Algorithm based on Decompositions (MOEA/D) and Multi-Objective Differential Evolution (MODE). M-MOPSO emerged as the best algorithm in eight out of the ten constrained benchmark problems. It also shows promising results in bioprocess application problems and tumor treatment problems. In overall, M-MOPSO was able to solve multi-objective problems with good convergence and is suitable to be used in real world problem.

Link prediction based on temporal similarity metrics using continuous action set learning automata

We propose a new particle swarm optimization algorithm for problems where objective functions are subject to zero-mean, independent, and identically distributed stochastic noise. While particle swarm optimization has been successfully applied to solve many complex deterministic nonlinear optimization problems, straightforward applications of particle swarm optimization to noisy optimization problems are subject to failure because the noise in objective function values can lead the algorithm to incorrectly identify positions as the global/personal best positions. Instead of having the entire swarm follow a global best position based on the sample average of objective function values, the proposed new algorithm works with a set of statistically global best positions that include one or more positions with objective function values that are statistically equivalent, which is achieved using a combination of statistical subset selection and clustering analysis. The new PSO algorithm can be seamlessly integrated with adaptive resampling procedures to enhance the capability of PSO to cope with noisy objective functions. Numerical experiments demonstrate that the new algorithm is able to consistently find better solutions than the canonical particle swarm optimization algorithm in the presence of stochastic noise in objective function values with different resampling procedures.

Population statistics for particle swarm optimization: Resampling methods in noisy optimization problems

Differential evolution (DE) is significantly faster and robust for solving numerical optimization problem and is more likely to find true global optimum of functions. It has solved many real-world optimization problems. However, DE has sometimes been shown slow convergence and low accuracy of solutions when the solution space is hard to explore. Population initialization is very important to the performance of differential evolution. A good initialization method can help in finding better solutions and improving convergence rate. In this paper, a uniform-differential evolution algorithm (UDE) is proposed. It incorporates uniform design initialization method into differential evolution to accelerate its convergence speed and improve the stability. UDE is compared with other two algorithms of standard differential evolution (SDE) and orthogonal differential evolution (ODE). Experiments have been conducted on 23 benchmark problems of diverse complexities. The results indicate that our approach has the stronger ability and higher calculation accuracy to find better solutions than other two algorithms.

This paper compares the performance of the classic genetic algorithm with the more recently proposed ant colony optimisation for solving real-world pickup and delivery problems with hard time windows. A real-world problem that is present worldwide - waste collection - is used to evaluate the algorithms. As in most real-world waste collection problems, many of the waste bins have time windows. The time windows stem from such things as safety regulations and customer agreements, and must be strictly adhered to. The optimisation showed that the genetic algorithm is better than the ant colony optimisation when utilising standard implementations of both algorithms. However, when the algorithms are enhanced with a local search procedure, the ant colony optimisation immediately becomes superior and achieves improved results. Local search seems to be a drawback for the genetic algorithm when hard time windows are involved. Various implementations of the local search procedure are evaluated in this paper using five different test sets. Recommendations for future implementations are given as well as additional enhancements which could improve the performance of the ant colony optimisation.

Social learning differential evolution

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.