Metaheuristics in large-scale global continues optimization

Differential evolution (DE) has been proven to be one of the most powerful global numerical optimization algorithms in the evolutionary algorithm family. The core operator of DE is the differential mutation operator. Generally, the parents in the mutation operator are randomly chosen from the current population. In nature, good species always contain good information, and hence, they have more chance to be utilized to guide other species. Inspired by this phenomenon, in this paper, we propose the ranking-based mutation operators for the DE algorithm, where some of the parents in the mutation operators are proportionally selected according to their rankings in the current population. The higher ranking a parent obtains, the more opportunity it will be selected. In order to evaluate the influence of our proposed ranking-based mutation operators on DE, our approach is compared with the jDE algorithm, which is a highly competitive DE variant with self-adaptive parameters, with different mutation operators. In addition, the proposed ranking-based mutation operators are also integrated into other advanced DE variants to verify the effect on them. Experimental results indicate that our proposed ranking-based mutation operators are able to enhance the performance of the original DE algorithm and the advanced DE algorithms.

Differential Evolution With Ranking-Based Mutation Operators

A comparison of methods to avoid overfitting in neural networks training in the case of catchment runoff modelling

Population size of Differential Evolution (DE) algorithms is often specified by user and remains fixed during run. During the first decade since the introduction of DE the opinion that its population size should be related to the problem dimensionality prevailed, later the approaches to DE population size setting diversified. In large number of recently introduced DE algorithms the population size is considered to be problem-independent and often fixed to 100 or 50 individuals, but alongside a number of DE variants with flexible population size have been proposed. The present paper briefly reviews the opinions regarding DE population size setting and verifies the impact of the population size on the performance of DE algorithms. Ten DE algorithms with fixed population size, each with at least five different population size settings, and four DE algorithms with flexible population size are tested on CEC2005 benchmarks and CEC2011 real-world problems. It is found that the inappropriate choice of the population size may severely hamper the performance of each DE algorithm. Although the best choice of the population size depends on the specific algorithm, number of allowed function calls and problem to be solved, some rough guidelines may be sketched. When the maximum number of function calls is set to classical values, i.e. those specified for CEC2005 and CEC2011 competitions, for low-dimensional problems (with dimensionality below 30) the population size equal to 100 individuals is suggested; population sizes smaller than 50 are rarely advised. For higher-dimensional artificial problems the population size should often depend on the problem dimensionality d and be set to 3d–5d. Unfortunately, setting proper population size for higher-dimensional real-world problems (d>40) turns out too problem and algorithm-dependent to give any general guide; 200 individuals may be a first guess, but many DE approaches would need a much different choice, ranging from 50 to 10d. However, quite clear relation between the population size and the convergence speed has been found, showing that the fewer function calls are available, the lower population sizes perform better. Based on the extensive experimental results the use of adaptive population size is highly recommended, especially for higher-dimensional and real-world problems. However, which specific algorithms with population size adaptation perform better depends on the number of function calls allowed.

Review of Differential Evolution population size

The ability of an Evolutionary Algorithm (EA) to find a global optimal solution depends on its capacity to find a good rate between exploitation of found-so-far elements and exploration of the search space. Inspired by natural phenomena, researchers have developed many successful evolutionary algorithms which, at original versions, define operators that mimic the way nature solves complex problems, with no actual consideration of the exploration-exploitation balance. In this paper, a novel nature-inspired algorithm called the States of Matter Search (SMS) is introduced. The SMS algorithm is based on the simulation of the states of matter phenomenon. In SMS, individuals emulate molecules which interact to each other by using evolutionary operations which are based on the physical principles of the thermal-energy motion mechanism. The algorithm is devised by considering each state of matter at one different exploration---exploitation ratio. The evolutionary process is divided into three phases which emulate the three states of matter: gas, liquid and solid. In each state, molecules (individuals) exhibit different movement capacities. Beginning from the gas state (pure exploration), the algorithm modifies the intensities of exploration and exploitation until the solid state (pure exploitation) is reached. As a result, the approach can substantially improve the balance between exploration---exploitation, yet preserving the good search capabilities of an evolutionary approach. To illustrate the proficiency and robustness of the proposed algorithm, it is compared to other well-known evolutionary methods including novel variants that incorporate diversity preservation schemes. The comparison examines several standard benchmark functions which are commonly considered within the EA field. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration---exploitation balance.

An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation

Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

. The derivation of the flood risk maps requires an estimation of maximum inundation extent for a flood with a given return period, e.g. 100 or 500 yr. The results of numerical simulations of flood wave propagation are used to overcome the lack of relevant observations. In practice, deterministic 1-D models are used for that purpose. The solution of a 1-D model depends on the initial and boundary conditions and estimates of model parameters based on the available noisy observations. Therefore, there is a large uncertainty involved in the derivation of flood risk maps using a single realisation of a flow model. Bayesian conditioning based on multiple model simulations can be used to quantify this uncertainty; however, it is too computer-time demanding to be applied in flood risk assessment in practice, without further flow routing model simplifications. We propose robust and feasible methodology for estimating flood risk. In order to decrease the computation times the assumption of a gradually varied flow and the application of a steady state flow routing model is introduced. The aim of this work is an analysis of the influence of those simplifying assumptions and uncertainty of observations and modelling errors on flood inundation mapping and a quantitative comparison with deterministic flood extent maps. Apart from the uncertainty related to the model structure and its parameters, the uncertainty of the estimated flood wave with a specified probability of return period (so-called 1-in-10 yr, or 1-in-100 yr flood) is also taken into account. In order to derive the uncertainty of inundation extent conditioned on the design flood, the probabilities related to the design wave and flow model uncertainties are integrated. In the present paper that integration is done whilst taking into account the dependence of roughness coefficients on discharge. The roughness is parameterised based on maximum annual discharges. This approach allows for the relationship between flood extent and flow values to be derived, thus giving a cumulative assessment of flood risk. The methods are illustrated using the Warsaw reach of the River Vistula as a case study. The results indicate that deterministic and stochastic flood inundation maps cannot be quantitatively compared. We show that the proposed simplified approach to flood risk assessment can be applied even when breaching of the embankment occurs, with the condition that the flooded area is small enough to be filled rapidly.

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Maximising the usefulness of flood risk assessment for the River Vistula in Warsaw

An event simulation approach to the assessment of flood level frequencies: risk maps for the Warsaw reach of the River Vistula

Stormwater reservoirs are used to control the runoff volume and to attenuate the peak flow rate from urban catchments. The required capacity of a stormwater reservoir and its dimensions are...

Optimal Capacity of a Stormwater Reservoir for Flood Peak Reduction

The paper addresses the problem of determination of the energy and momentum coefficients for flows through a partly vegetated channel. These coefficients are applied to express the fluid kinetic energy and momentum equations as functions of a mean velocity. The study is based on laboratory measurements of water velocity distributions in a straight rectangular flume with stiff and flexible stems and plastic imitations of the Canadian waterweed. The coefficients were established for the vegetation layer, surface layer and the whole flow area. The results indicate that the energy and momentum coefficients increase significantly with water depth and the number of stems per unit channel area. New regression relationships for both coefficients are given.

/pdf/experimental-investigation-of-kinetic-energy-and-momentum-2l6iycvm4w.pdf

Experimental Investigation of Kinetic Energy and Momentum Coefficients in Regular Channels with Stiff and Flexible Elements Simulating Submerged Vegetation

Adam Kiczko

Papers

Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

Maximising the usefulness of flood risk assessment for the River Vistula in Warsaw

An event simulation approach to the assessment of flood level frequencies: risk maps for the Warsaw reach of the River Vistula

Optimal Capacity of a Stormwater Reservoir for Flood Peak Reduction

Experimental Investigation of Kinetic Energy and Momentum Coefficients in Regular Channels with Stiff and Flexible Elements Simulating Submerged Vegetation