An Investigation of Generalized Differential Evolution Metaheuristic for Multiobjective Optimal Crop-Mix Planning Decision

Abstract

This paper presents an annual multiobjective crop-mix planning as a problem of concurrent maximization of net profit and maximization of crop production to determine an optimal cropping pattern. The optimal crop production in a particular planting season is a crucial decision making task from the perspectives of economic management and sustainable agriculture. A multiobjective optimal crop-mix problem is formulated and solved using the generalized differential evolution 3 (GDE3) metaheuristic to generate a globally optimal solution. The performance of the GDE3 metaheuristic is investigated by comparing its results with the results obtained using epsilon constrained and nondominated sorting genetic algorithms—being two representatives of state-of-the-art in evolutionary optimization. The performance metrics of additive epsilon, generational distance, inverted generational distance, and spacing are considered to establish the comparability. In addition, a graphical comparison with respect to the true Pareto front for the multiobjective optimal crop-mix planning problem is presented. Empirical results generally show GDE3 to be a viable alternative tool for solving a multiobjective optimal crop-mix planning problem.

Dynamics of Crop Evapotranspiration of Four Major Crops on a Large Commercial Farm: Case of the Navajo Agricultural Products Industry, New Mexico, USA

“…The best combination of land and crop that optimizes the use of farm resources is determined through the modeling approaches of the crop plan decision [77,78]. To address optimum planning issues in a commercial farm such as the NAPI, a multi-objective optimizer including planting areas, crop production, and profit should be considered [79,80]. Other optimization models of annual crop allocation have been developed based on economic factors [81,82], the uncertainly of the available water, the net benefit considering wastewater recovery [83], limited water availability [84,85], the benefit subject to a given set of ecological, financial, and food crop production selfsufficiency constraints [86], optimum production [87], crop rotation [88], intra-seasonal water allocation [89], etc.…”

Conceptual Comparison of Population Based Metaheuristics for Engineering Problems

“…The selection process based on crowding distance gives GDE3 an advantage over NSGAII. In the case of comparing feasible, incomparable, and nondominating solutions, both offspring and parent vectors are saved for the population of the next generation [ 4 ]. There is no need to remove elements, since the population size does not increase.…”

“…In the last two decades, different types of techniques aimed at effectively and efficiently exploring a search space by combining several basic heuristic methods have emerged [ 2 – 4 ]. These techniques currently referred to as “ Metaheuristics ” are used to describe heuristic methods applied to solving different practical problems.…”

Portfolio selection problem using generalized differential evolution 3

“…The selection process based on crowding distance gives GDE3 an advantage over NSGAII. In the case of comparing feasible, incomparable and non-dominating solutions, both offspring and parent vectors are saved for the population of the next generation [37]. As a result, this procedure reduces the computational costs of the Metaheuristics and improves its efficiency.…”