نمونه اولیه نرم افزار برای اعتبار سنجی ماشینکاری راه حل های بهینه به دست آمده با الگوریتم های متاهیوریستیک

Optimization of machining processes is of primary importance for increasing machining efficiency and economics. Determining optimal values of machining parameters is performed by applying optimization algorithms to mathematical models of relationships between machining parameters and machining performance measures. In recent years, there has been an increasing trend of using empirical models and meta-heuristic optimization algorithms. The use of meta-heuristic optimization algorithms is justified because of their ability to handle highly non-linear, multi-dimensional and multi-modal optimization problems. Meta-heuristic algorithms are powerful optimization tools which provide high quality solutions in a short amount of computational time. However, their stochastic nature creates the need to validate the obtained solutions. This paper presents a software prototype for single and multi-objective machining process optimization. Since it is based on an exhaustive iterative search, it guarantees the optimality of determined solution in given discrete search space. The motivation for the development of the presented software prototype was the validation of machining optimization solutions obtained by meta-heuristic algorithms. To analyze the software prototype applicability and performance, six case studies of machining optimization problems, both single and multi-objective, were considered. In each case study the optimization solutions that had been determined by past researchers using meta-heuristic algorithms were either validated or improved by using the developed software prototype.

Machining is one of the most important and widely used manufacturing processes. The technology of machining has grown substantially over time owing to the contribution from many branches of engineering with a common goal of achieving higher process efficiency (Mukherjee & Ray, 2006). Among many types of machining processes, the advancement of technology and the development of many hard-to-machine materials has led to the increasing usage of newer machining processes, known as non-conventional machining processes. All these machining processes have their own machining parameters, i.e. input variables, and performance measures (responses), i.e. outputs. For an effective utilization of the machining processes, it is very important to determine the optimal values of machining parameters to achieve an enhanced machining performance with high dimensional accuracy (Samanta & Chakraborty, 2011). Furthermore, as noted by Yildiz (2009a), finding optimal values of machining parameters is a crucial task in order to minimize the machining costs and gain competitive advantage on the market. Determining optimal values of machining parameters is required to be undertaken in two stages (Mukherjee & Ray, 2006): mathematical modeling and optimization. Modeling studies in machining are scientific ways to study system behaviors and help us to get a better understanding of this complex process. A mathematical model of a machining process is the relationship between input variables and outputs which is represented in terms of mathematical equation(s). Mathematical modeling of machining processes is based on well-known scientific principles. Basically, mathematical models can be divided into two categories: mechanistic (analytical) and empirical (Box & Draper, 1987). Complex relationships between machining parameters and responses make it difficult to generate explicit analytical models of machining processes (Karpat and Özel, 2007 and Zain et al., 2011). Many analytical models involve simplifications and approximations in relation to the real machining process and do not take into account any imperfections of the machining process. Therefore, analytical models are generally not accurate enough for practical usage (Davim, 2001). Empirical models which are less general, but more accurate, have become a preferred trend for modeling of machining processes. They integrate experimental and mathematical (statistical) methods, thus providing sufficient accuracy of calculations for the real conditions in which the machining processes take place. Empirical models are often constructed in two stages: experimental design (factorial design, Taguchi design, Box–Behnken, etc.) and regression analysis/response surface methodology (RSM). Although statistical regression technique may work well for machining process modeling, this technique may not precisely describe the underlying non-linear complex relationship between machining parameters and responses (Mukherjee & Ray, 2006). In recent years, there has been an increasing trend in developing empirical models using artificial intelligence techniques such as artificial neural networks (ANNs) and fuzzy logic which are often termed as semi-empirical models. In general, a mathematical model provides the basic mathematical relationships that are required for formulation of the optimization problem. Subsequently, the application of an optimization technique provides an optimal or acceptable near-optimal solution. A solution consists of a set of input variable values and a corresponding output. Many machining optimization problems are highly non-linear, multi-dimensional and very complex in nature. It may be quite difficult or time consuming to solve these problems using algorithms based on numerical linear and nonlinear programming methods that require substantial gradient information. The gradient-based methods differ in their reliability, efficiency and sensitivity to the initial solution. Furthermore, they are inclined to obtain a local optimal solution (Yildiz, 2009a). The abovementioned inefficiency of traditional methods in solving machining optimization problems has forced researchers to search for new approaches (Yildiz, 2009b). In the past decade, the new trend in the optimization of the machining processes has been based on the use of meta-heuristic algorithms. Meta-heuristic algorithms can be defined as upper level general methodologies (templates) that can be used as guiding strategies in designing underlying heuristics to solve specific optimization problems. Modern meta-heuristic algorithms have been developed with an aim to carry out a global search with three main purposes: solving problems faster, solving large problems and obtaining robust algorithms (Talbi, 2009). The common factor in meta-heuristic algorithms is that they combine rules and randomness to imitate natural phenomena (Lee & Geem, 2005). These phenomena include the biological evolutionary process (genetic algorithm – GA), the physical annealing process (simulated annealing – SA), musical process of searching for a perfect state of harmony (harmony search algorithm – HSA), pheromone trail laying behavior of real ant colonies (ant colony optimization – ACO), social behavior of bird flocking (particle swarm optimization – PSO), lifestyle of a cuckoo bird family (cuckoo search algorithm – CSA), immune system of the human being (artificial immune algorithms – AIA), behavior of bacteria (bacteria foraging optimization – BFO), communication among the frogs (shuffled frog leaping – SFL), foraging behavior of a honey bee (artificial bee colony – ABC), etc. These algorithms have proved to be effective for solving some of the specific kinds of problems. In the field of machining process optimization, the current trend is the application of GA, SA, PSO, ABC and ACO (Yusup, Zain, & Hashim, 2012). The efficiency of meta-heuristic algorithms can be attributed to the fact that they imitate the best features in nature, especially the selection of the fittest in biological systems which have evolved by natural selection over millions of years (Gandomi, Yang, & Alavi, 2013). Besides these algorithms, the complex nature of optimization problems has forced researches to improve the existing and to seek for more efficient optimization algorithms. One such example is the recently developed teaching–learning-based-optimization (TLBO) algorithm (Venkata Rao and Kalyankar, 2011 and Venkata Rao and Savsani, 2012). The list of applications of meta-heuristic optimization algorithms and their comparisons in literature is endless (Elbeltagi et al., 2005, Rajabioun, 2011, Samanta and Chakraborty, 2011, Venkata Rao and Kalyankar, 2011, Yildiz, 2009c, Zandieh et al., 2009 and Zarei et al., 2009). Nevertheless, it can be concluded that there is no meta-heuristic algorithm which is the “best” choice for solving optimization problems. It is probably fair to say that every meta-heuristic algorithm has certain advantages and disadvantages, and that its efficiency predominantly depends on the possibility to perform fine calibration of algorithm parameters, which, on the other hand, requires a considerable knowledge in meta-heuristics and the optimization problem being solved. Moreover, there is a risk of being misled by obtained solutions if they are not validated. Although the popularity of the meta-heuristic algorithms has soared in recent years and many studies can be found in the literature where they outperform the tailored counterparts (Zarei et al., 2009), these algorithms also have certain constraints, assumptions and limitations for implementation which include the following: (i) the optimality of the determined solution is impossible to prove (in some cases, the determined solution may be far even from a near optimal solution), (ii) algorithm parameters settings have a strong influence on the final solution, (iii) there is no universal rule for setting the algorithm parameters for the optimization of mathematical model and (iv) even expert knowledge in meta-heuristics, systematical selection of the algorithm parameters, as well as understanding of the optimization problem being solved, do not guarantee the optimality of the solution. In spite of these shortcomings, in situations when it is impossible or very difficult to find optimal solution analytically, the application of meta-heuristic algorithms is justified and advisable. This is particularly valid for solving continuous optimization problems with multi-dimensional, multi-modal and highly non-linear objective functions. Apart from meta-heuristic algorithms, the potential for solving the aforementioned real optimization machining problems also has other optimization methods that are conceptually simpler, and, arguably, easier for practitioners. One of the best representatives of such methods is exhaustive “brute force” iterative search method. Capabilities of this method have been demonstrated for minimization of manufacturing cost in generative process planning (Utpal & Fang, 1997). In the above-referred work, it was then stated that exhaustive iterative search was the only manner to guarantee optimality in parameter tuning, at the expense of computational cost. The continual increase in computing power and memory size has revived interest in brute force techniques for a good reason (Nievergelt, 2000). The motivation of this paper was to develop a software prototype for single and multi-objective optimization of machining processes, based on an exhaustive iterative search in discrete space of input variable values. The main purpose of this software prototype is the validation of the machining optimization solutions obtained by meta-heuristic algorithms. The paper is organized as follows. After introduction, in the second section of this paper, an overview of the developed software prototype is given. In the third section six case studies of machining optimization problems were considered. In each case study the solutions obtained by previous researchers using meta-heuristic algorithms and the solutions obtained using the developed software prototype were compared and discussed. Furthermore, some possibilities of improving optimization solutions using the developed software prototype were presented. Findings and observations are summarized in the last section.

Numerous meta-heuristic algorithms have been increasingly applied for optimization of machining processes. These algorithms are especially useful for solving continuous optimization problems with multi-dimensional, multi-modal and highly non-linear objective functions when it is impossible or very difficult to find an optimal solution analytically. However, there are some disadvantages mutual to all of these algorithms: strong influence of algorithm parameter settings on the obtained solution, necessity of expert knowledge for fine parameter tuning, inability to prove the optimality of the determined solution, etc. In recent years, due to a continual increase in computing power and memory size, brute force techniques have again gained the attention of researchers. These techniques are especially suitable for the use in machining optimization domain, where techno-technological limitations of machine tools impose that some or all input variables take values from the order set of discrete values. Negative practice implies that optimal solution, determined by using a meta-heuristic algorithm, is being rounded to the nearest possible discrete value that could be achieved on a given machine tool. Although there is no guarantee that a good solution can be obtained this way, this process can be used along with an appropriate experimental verification. This paper presents a software prototype for single and multi-objective optimization of machining processes, based on an exhaustive iterative search of discrete space of input variable values. The main characteristics of the developed software prototype include the following: (i) simple XML based definition of discrete set of possible values for each input variable, (ii) simple XML based definition of mathematical models, (iii) for a defined discrete search space, the optimality of the determined solution is guaranteed, (iv) application of the software prototype requires no expert knowledge and setting of algorithm parameters, and (v) the software prototype has the possibility to find user defined number of best solutions and to rank them. Initially developed for the validation of optimization solutions obtained by using meta-heuristic algorithms, the software prototype proved to be a very efficient tool for solving machining optimization problems. From the analysis of the obtained results from the six case studies considered, the following conclusions can be made: • Solutions that had been determined by past researchers using meta-heuristic algorithms were either validated or improved. Although in most cases very small improvements are obtained, the optimality of the determined solutions using developed software prototype, for given discrete optimization space, is guaranteed. • In several case studies (case studies 1, 2 and 5), the obtained solution is actually the boundary point of the covered experimental hyperspace. This may indicate a need for deeper consideration of boundary points when using meta-heuristic algorithms. • Although based on an iterative search, the software prototype can be very efficiently used for finding optimal solutions in the multi-dimensional dense discretized optimization space. • Successive runs of the software prototype using smaller search intervals and smaller steps in the vicinity of the previous best solution enable further improvement of optimization solutions (case study 4). Since empirical models for machining processes do not include large numbers of input variables, it seems that in many cases it may be better to use simpler brute force optimization techniques, instead of using meta-heuristics. Alternatively, when meta-heuristic algorithms for solving machining optimization problems are used, the validation of obtained solutions is advisable, and the software prototype presented in this paper provides an efficient tool for this purpose.