**1. Introduction**

Contour cutting is one of the processes applied in metal fabrication industries. There are several non-traditional technologies employed for contour cutting, such as electro discharge machining, laser beam machining and electrochemical discharge machining, that have been noted to provide exemplary performance [1]. Accordingly, Abrasive Water Jet Machining (AWJM) is an advanced manufacturing techniques that demonstrated advantages to non-traditional machining technology owing to: its capability in cutting complex geometries, its absence of tool wear, its absence of thermal distortion, and it being environmentally friendly [2, 3]. The cutting process in AWJM is based on removing materials from a target workpiece via erosion [4]. Within this process, contour profiles in various types of programs are downloaded in a computer-based controller, where subsequently a high-pressure pump releases pressurised water in the nozzle system. The pressurised water, moving with a high velocity, is released from the orifice in a very thin stream structure [5]. The highspeed water jet that contains abrasive particles is then accelerated to generate an abrasive waterjet. Finally, the focusing tube drives the abrasive waterjet to its target point for cutting the material [4, 6]. The compounded granular abrasive and highpressure waterjet stream makes the abrasive waterjet capable of machining various workpieces, such as metals.

The performance of AWJM is influenced by several process parameters, which can be varied constantly within a period. In general, the primary goal of the metal fabrication industry is to manufacture high quality products in a shortened period. To attain productivity and economy objectives, it is imperative to select an optimum combination of process parameters within the abrasive waterjet cutting processes. Conventionally, the identification of the most suitable values of process parameters is accomplished by the execution of many experiments. Hence, to establish the optimum combination of process parameters in the absence of extensive experimental exertion, researchers have utilised advanced modelling techniques and optimisation in progressing the performance of abrasive waterjet cutting. For instance, Rao et al. [7] have investigated the impacts of traverse speed, standoff distance and abrasive mass flow rate in AWJM of AA631-T6. They have considered single-objective and multiobjective optimisation attributes to achieve optimum solutions by utilising Jaya and MO-Jaya algorithms, which were a posterior optimisation used to solve constrained and unconstrained conditions. The objectives of maximising material removal and minimising kerf taper angle and surface roughness were achieved by lower traverse speed and standoff distance and higher abrasive mass flow rate. Moreover, they determined that multi-objective Jaya algorithm achieved better results as compared with other algorithms, such as simulated annealing (SA), particle swam optimization (PSO), firefly algorithm (FA), cuckoo search (CS) algorithm, blackhole (BH) algorithm, bio-geography-based optimization (BBO) algorithm, non-dominated sorting genetic algorithm (NSGA), non-dominated sorting teaching-learning-based optimization (NSTLBO) algorithm and sequential approximation optimization (SAQ). Nair and Kumanan [8] have similarly applied weighted principal components analysis (WPCA) for optimising AWJM process parameters in machining Inconel 617. These authors evaluated the impacts of abrasive mass flow rate, standoff distance, table feed and waterjet pressure against material removal rate and geometric accuracy. The WPCA method uses internal tests and training samples to calculate the 'weighted' covariance matrix, establishing that an increase in standoff distance enhances the abrasive flow volume, leading to less geometric errors and a higher rate of material removal. Equivalently, Chakraborty and Mitra [9] have applied the grey wolf optimiser (GWO) technique for AWJM cutting of AL6061to maximise material removal rate and minimise surface roughness, simultaneously considering the constrained values of input parameters i.e., nozzle diameter and titled angle, jet feed speed, surface speed, waterjet pressure and abrasive mass flow rate. This algorithm demonstrated a faster hunting of prey (discovering the optimum parameter settings), due to the existence of a social hierarchy of grey wolves. They achieved maximum MRR via higher rate of nozzle titled angle, surface speed, waterjet pressure and abrasive mass flow rate. In the case of surface roughness, it attained its minimum value at lower rate of waterjet pressure, jet feed and surface speed and higher rate of abrasive mass flow. Trivedi et al. [10] have examined the impacts of process parameters such as pressure, traverse rate and standoff distance on surface integrity in AWJM *Multi-objective Optimisation in Abrasive Waterjet Contour Cutting of AISI 304L DOI: http://dx.doi.org/10.5772/intechopen.106817*

of AISI 316 L. Analysis of variance was employed to develop an empirical model by regression analysis for surface roughness. These authors concluded traverse speed to be the most significant parameter influencing surface roughness, whereby increasing pressure improved the surface quality of the target workpiece. Additionally, they established standoff distances, as the least contributing parameter. Research focused on optimisation of cutting operations is being continuously undertaken by researchers, where varied methods have been employed to solve different single and multi-objective optimisation problems [11–14]. Whereas single-objective optimisation problems have conventionally been applied, the performance of AWJM has mainly been measured based on multiple responses. In accordance, a multi-objective approach is required in order to optimise several categories of objective functions simultaneously. Several methods have been developed to date, and are continuously being progressed, in order to solve single-objective problems. Advances in optimisation techniques, such as: genetic algorithms (GA), simulated annealing (SA), artificial bee colony (ABC), ant colony optimization (ACO), particle swarm optimization (PSO) and teaching-learning-based optimization (TLBO), and others, have been demonstrated to be remarkably efficient in defining the optimum value of AWJM process parameters [15].

In abrasive waterjet contour-cutting, it has been realised that the impacts of most influencing factors, such as waterjet pressure, abrasive mass flow rate, standoff distance and traverse speed in straight-slit cutting, are similar with contour cutting. These research studies have shown the application of computational approaches for optimising process parameters in abrasive waterjet contour cutting requires further investigation. Therefore, this research considers the optimisation of relevant process parameters, including traverse speed, abrasive mass flow rate, and waterjet pressure on surface roughness, material removal rate and kerf taper angle in abrasive waterjet contour cutting of AISI 304L of varied thicknesses.

In this work, the experiment was designed using Taguchi orthogonal array, where a regression model has been developed to formulate the optimisation fitness function. This modelling technique has been applied to predict the response and determine optimum process parameters. In addition, response surface methodology (RSM) has been employed for multi-objective optimization, in order to obtain optimum values of input process parameters and to investigate the impacts and interactions against response parameters.
