# A Multi-Objective Harmony Search Algorithm for Sustainable Design of Floating Settlements +
Evolutionary algorithms are nature-inspired processes mimicking the selection and reproduction processes in living organisms. Evolutionary and Swarm algorithms provide satisfactory good design solutions and handle the complexity of the architectural problems. In this regard, Pareto front approximation is an efficient way to distinguish between inferior and good solutions. Recently, in [4], the authors worked on identifying configurations of functions for a floating neighborhood design proposal by using multi-objective optimization. Two evolutionary algorithms are developed and their results are compared with each other. Differential evolution (DE) algorithm is a stochastic real-parameter optimization algorithm developed by [5]. DE algorithms have three parameters. These are the population size (NP), the crossover rate (CR), and the mutation rate (F). These parameters have a significant impact on the performance of DE algorithms. In [6], a self-adaptive DE algorithm, called JDE, is developed. It is a very simple and effective algorithm that converges much faster than the traditional DE, particularly when the dimensionality of the problem is high or the problem concerned is complicated. In JDE, each individual has its own \(F_{i}\) and \(CR_{i}\) values. Initially, they are assigned to \(CR_{i}=0.5\) and \(F_{i}=0.9\) and they are updated at each generation \(g\) as \(F_{i}^{g}= \begin{cases}F_{l}+r_{1}.F_{u}&if\ r_{2}<t_{1}\\ F_{i}^{g-1}&otherwise\end{cases} \) and \(CR_{i}^{g}= \begin{cases}r_{3}&if\ r_{4}<t_{2}\\ CR_{i}^{g-1}&otherwise\end{cases} \), where \(r_{j}\in\{1,2,3,4\}\) are uniform random numbers in the range \([0,1]\). \(t_{1}\) and \(t_{2}\) denote the probabilities to adjust the \(F_{i}\) and \(CR_{i}\) values. They are taken as \(t_{1}=t_{2}=0.1\) and \(F_{1}=0.1\) and \(F_{u}=0.9\). In [7], the authors investigated sustainable designs of floating settlements by using a multi-objective self-adaptive differential evolution (JDE) algorithm inspired by [6]. The main contribution of the JDE algorithm was to show that many architectural design problems are mainly multi-objective constrained real-parameter optimization problems. This paper is an extension of [7] by developing a multi-objective harmony search (MOHS) algorithm for the same benchmark instance in order to identify a set of design alternatives for decision-makers. The basic harmony search (HS) algorithm is developed in [8; 9]. Regarding the multi-objective harmony search algorithms (MOHS), [PERSON] [10; 11] proposed two MOHS algorithms for the time-cost trade-off optimization of project management and water distribution network optimization, respectively. These two MOHS algorithms employ a strict domination rule in such a way that a new solution is generated by HS operators and the new solution is replaced by the worst solution in the population if the new solution strictly dominates the worst solution. However, in the MOHS algorithm developed in this paper, a new population of solutions is generated by HS operators. Then, the old and new population are merged. To determine the population in the next generation, the fast non-dominated sorting algorithm in [12] is employed to identify the non-dominated fronts and the constrained-dominance rule in [12] is used to compare the solutions. An excellent survey of the applications of HS algorithm can be found in [13]. The rest of the paper is organized as follows: Section 2 introduces the problem through a concise definition. Section 3 presents the generative model and MOHS algorithm that have been applied in this paper. Section 4 discusses the computational results. Finally, Section 5 gives the conclusions.