A Computational Comparison of Evolutionary Algorithms for Water Resource Planning for Agricultural and Environmental Purposes

The use of water resources for agricultural purposes, particularly in arid and semi-arid regions, is a matter of increasing concern across the world. Optimisation techniques can play an important role in improving the allocation of land to different crops, based on a utility function (such as net revenue) and the water resources needed to support these. Recent work proposed a model formulation for an agricultural region in the Murrumbidgee Irrigation Area of the Murray-Darling River basin in Australia, and found that the well-known NSGA-II technique could produce sensible crop mixes while preserving ground and surface water for environmental purposes. In the present study we apply Differential Evolution using two different solution representations, one of which explores the restricted space in which no land is left fallow. The results improve on those of the prior NSGA-II and demonstrate that a combination of solution representations allows Differential Evolution to more thoroughly explore the multiobjective space of profit versus environment

A knee-point-based evolutionary algorithm using weighted subpopulation for many-objective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Among many-objective optimization problems (MaOPs), the proportion of nondominated solutions is too large to distinguish among different solutions, which is a great obstacle in the process of solving MaOPs. Thus, this paper proposes an algorithm which uses a weighted subpopulation knee point. The weight is used to divide the whole population into a number of subpopulations, and the knee point of each subpopulation guides other solutions to search. Besides, Additionally, the convergence of the knee point approach can be exploited, and the subpopulation-based approach improves performance by improving the diversity of the evolutionary algorithm. Therefore, these advantages can make the algorithm suitable for solving MaOPs. Experimental results show that the proposed algorithm performs better on most test problems than six other state-of-the-art many-objective evolutionary algorithms

Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones

Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to $1/2^{m-1}$, i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems

An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics