Journal of Optimization

Volume 2018, Article ID 5852469, 15 pages

https://doi.org/10.1155/2018/5852469

## Multiobjective Simulation-Based Optimization Based on Artificial Immune Systems for a Distribution Center

Department of Industrial & Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong

Correspondence should be addressed to Chris S. K. Leung; moc.oohay@sirhcksl

Received 10 October 2017; Revised 27 March 2018; Accepted 19 April 2018; Published 21 May 2018

Academic Editor: Efren Mezura-Montes

Copyright © 2018 Chris S. K. Leung and Henry Y. K. Lau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Competitive market factors, such as more stringent government regulations, larger number of competitors, and shorter product life cycle, in recent years have created more significant pressure on the management in all supply chain parties. To this end, the ability of analyzing and evaluating systems and related operations involving the deployment of complex multiobjective material handling systems is vital for distribution practitioners. In this respect, simulation modeling techniques together with optimization have emerged as a very useful tool to facilitate the effective analysis of these complex operations and systems. In this paper, we apply a multiobjective simulation-based optimization framework consisting of a hybrid immune-inspired algorithm named Suppression-controlled Multiobjective Immune Algorithm (SCMIA) and a simulation model for solving a real-life multiobjective optimization problem. The results show that the framework is able to solve large scale problems with a large number of parameters, operators, and equipment involved.

#### 1. Introduction

Simulation modeling is indeed a powerful industrial engineering technique for studying the functioning, performance, and operation of complex systems. As such, it becomes an extremely useful tool for stakeholders and decision-makers in various industries and domains including multiobjective optimization. By changing input data and operating parameters of a system being studied with simulation, predictions about the system’s behaviors can be obtained through computer-aided simulation for helping management make the right decisions. Unlike a mathematical model, simulation can handle a variety of complex factors that are commonly found in real world. In addition, simulation is a cost-effective means for existing process redesign and new system design because alternative solutions can be studied and evaluated for correctness and feasibility before actual implementation. More importantly, the accuracy of the performance measures of the complex systems obtained from simulation models is normally higher than that of analytical methods because analytical methods in general involve making unrealistic assumptions for the systems or problems under investigation [1].

In real world, many problems no matter whether they are in the domain of engineering, finance, business, or science can be formulated into different forms of optimization problems. These problems are characterized by the requirement of finding the best possible solution that fulfills certain criteria under certain constraints. Most of the real-world optimization problems normally involve multiple objectives rather than one single objective, in which some objectives conflict with others. Solving this kind of problems is never an easy task because objectives of such problems are often found to be noncommensurable and conflicting. Very often, there is no single best solution to the multiobjectives optimization problems, but rather a set of optimal solutions that exists among the objectives. However, using simulation modeling alone cannot provide us with optimal solutions to these optimization problems. Therefore, an optimization algorithm is needed to guide the search process to the optimal solutions. Over the past decades, different algorithms have been developed for solving multiobjective optimization problems. However, some algorithms, such as Simulated Annealing (SA) [2] and Tabu Search (TS) [3–5], do not easily solve multiobjective optimization problems since they are initially developed for solving single objective optimization problems without having the ability to generate a set of optimal trade-off solutions. One of the possible approaches for them to solve the multiobjective optimization problems is to transform the multiple-objective problems into the single objective problems by emphasizing one particular optimal solution at each run [6]. Some other algorithms, such as Genetic Algorithm (GA) [7], Evolutionary Strategy (ES) [8], and Artificial Immune Systems (AIS) [9] which are inspired by natural processes, have been proved to be the effective algorithms in both single objective and multiobjective optimization contexts. Among these algorithms, AIS based on the concepts of biological immune system have received special attention among the research community because the biological immune system provides a rich source of stimulation and inspiration to the research community with their interesting characteristics: distributed nature, self-organization, memory, and learning capabilities. Motivated by its great potential for solving multiple-objective optimization problems, the study reported in this paper is to demonstrate how a real-life multiobjective simulation-based optimization problem in logistics industry where material handling system (MHS) is involved can be solved by a simulation-based optimization framework comprising a simulation tool together with an AIS-based algorithm.

This paper proceeds as follows: Section 2 starts by giving a brief overview of material handling and multiobjective optimization. Section 3 introduces the multiobjective optimization framework for simulation-based optimization. Section 4 evaluates the performance of the framework through a real-life case study on a MHS by benchmarking with some well-known optimization algorithms. Finally, concluding remarks are presented in Section 5.

#### 2. Background

##### 2.1. Importance of Material Handling in Distribution Industry

Material handling, which is the total management of material concerns in an operation, is a vital element of industrial processes. Material handling involves a variety of operations including the movement, storage, protection, and control of materials, products, and wastes throughout the processes of manufacturing, distribution, and disposal. Having efficient MHS is of great importance to various industries to maintain and facilitate a continuous flow of material through the workplace and guarantees that required materials are available when needed. It is especially important to logistics and manufacturing industries as it accounts for a large percentage of the operation in these industries. In the manufacturing sector, the time spent on different kinds of product handling and transportation can be as much as the time used on the value-added processes. Banks et al. [10] claimed that the time of material handling accounts for about 85% of the total manufacturing time. In addition to time, the money used on material handling activities is equally high because the material handling equipment and systems require large capital investment in terms of system design, installation, operations, maintenance, and so forth. A number of studies conducted in different industries show that the cost of material handling alone is about 20–25% of the total manufacturing cost [11].

There are different kinds of material handling equipment and systems available that range from simple hand truck and pallet rack to complex conveyor system and Automated Storage and Retrieval System (AS/RS). A typical MHS is composed of different smaller components closely working together, thus making business activities more efficient and cost-effective. Over the past decade, MHS and its function have undergone a big change because of new advances in technologies, such as the development and applications of automation techniques and robotics, by which a large number of manual handling jobs are replaced by machines. Since the entire production or distribution process is automated, MHS has to respond just-in-time to the requirements of different processing activities. These new technologies, today, increasingly become prevalent in different industries as they help ease drudgery for manual labors and some of the mechanized or automated handling jobs are physically impossible to be done by workers.

Norman [12] claimed that equipment capacity, speed, and arrangement are the most critical considerations when modeling and optimizing MHS. Capacity under this context is the maximum quantity of products handled by the equipment. Speed is the average operating speed of the equipment, which may include acceleration, deceleration, and speeds of various equipment components. Configuration is the layout and structure of the MHS or its moving paths.

##### 2.2. Optimization of MHS via Simulation

In the literature, there are a number of studies that dedicatedly contribute to the optimization of MHS via simulation. For example, Ebbesen et al. [13] studied the baggage handling system at airports. They developed an approach to optimize the design of conveyor systems, that is, the design of tracks suited for baggage handling systems with the use of a time domain simulation model of the entire system. Sergueyevich et al. [14] proposed a simulation model of the overhead monorail conveyor system coupled with statistical methods for analyzing and solving the multiobjective optimization problem regarding the manufacturing process. The aim was to determine the optimum speed of conveyor, lengths of queues, time in system, capacity of machines, and so forth under certain limitations. Elahi et al. [15] studied the General Motors paint shop conveyor system by developing a simulation model. The model works firmly with a decision optimizer incorporating integer linear programming model and dynamic programming model at critical points such as the beginning and end of buffer conveyors in the system in order to regroup batches of different color cars. Leung and Lau [16] proposed a simulation-based optimization framework that combines the processes of optimization and simulation for solving typical linear optimization problems related to logistics and production operation. The framework integrates an AIS-based algorithm with a simulation tool for the evaluation of optimal system parameters and to reveal the performance of systems. Subulan and Cakmakci [17] made use of ARENA simulation program and Taguchi experimental design method to build a solution model for effectively designing material handling–transfer systems and optimizing the performance of automation technologies in automobile industry. Chang et al. [18] proposed a framework that integrates simulation optimization and data envelopment analysis techniques to find out the optimal vehicle fleet size for a multiobjective problem in automated materials handling systems. Lin and Huang [19] extended the optimal computing budget allocation by adding Genetic Algorithm together with the help of a simulation model for optimizing the vehicle allocation for the automated material handling system in semiconductor industry.

##### 2.3. Multiobjective Simulation-Based Optimization Approaches

In practice, optimization problems involve several objectives that often conflict with each other and must be simultaneously optimized so that a possibly uncountable set of trade-off solutions rather than a single optimal point is found with respect to the contradicting objectives. Therefore, the aim of these problems is to find out the global trade-off solutions that effectively spread over the Pareto front. No solution from the Pareto front is worse than any other solution because it is better in at least one objective. These problems are normally termed as multiobjective problems, which were first studied in an economic context and then extended to the fields of science and engineering [20]. Since multiobjective optimization problems involve several objectives, the view towards optimum has changed, hence changing the aim from finding a single solution to obtaining a set of compromised solutions. Today, the notion of optimum for a multiobjective optimization problem is frequently called Pareto optimum, which was first proposed by Edgeworth [21] and then generalized by Pareto [22, 23].

As is known, the notion of optimality for multiobjective optimization problems is different from that of single objective optimization problems because the aim of multiobjective optimization problems is to find a set of optimal trade-off solutions rather than a single optimal solution. Thus, in the absence of preference information on the objectives, the concept of Pareto optimality is adopted in this study for solving multiobjective optimization problems [24] and several definitions about Pareto optimality [20, 25, 26] are considered and stated below.

*Definition 1 (Pareto optimality). *A point in the search space is said to be Pareto optimal/nondominated with respect to Ω if and only if there are no other solutions for which dominates *. *In other words, is Pareto optimal with regard to the whole decision variable space if it cannot be improved in any one objective without resulting in a simultaneous degradation in other objectives.

*Definition 2 (Pareto dominance). *Consider, without loss of generality, two decision vectors and of a minimization problem. Then, a vector of decision variables is said to dominate another vector , which is denoted by , if and only if is partially less than . That is, the following two conditions must be satisfied:(1) is not worse than in all objectives(2) is better than in at least one objectivewhere is the number of objectives.

However, when any of these conditions are violated, the two solutions and are said to be indifferent to each other instead of dominating the other or being dominated by the other. Based on the above relations, Pareto optimal set, Pareto front, and nondominated set are defined below.

*Definition 3 (Pareto optimal set). *Pareto optimal set of solutions is a collection of all Pareto optimal solutions, which is defined asPareto optimal solutions are those solutions in the decision variable space whose corresponding objective vector elements cannot be all simultaneously improved [27]. The solutions inside the Pareto optimal set may have no apparent relationship except their membership in the set. Pareto optimal solutions are classified as such based on their values being evaluated through whatever means.

*Definition 4 (Pareto front). *A surface or line containing all nondominated solutions is called Pareto front, which is represented byAccording to the literature, finding an analytical expression of the Pareto front is a very difficult task. Therefore, a common approach for Pareto front generation is to find out the points within Ω and their corresponding value , . When this procedure is repeated a sufficient number of times, the nondominated points and hence the Pareto front are most likely to be found in the objective space [20].

*Definition 5 (nondominated set). *Of a solution set , a nondominated set of solutions comprises solutions that are not dominated by other solutions in the set . It is worth mentioning that while Pareto optimal solutions are always nondominated solutions, nondominated solutions may include both non-Pareto optimal solutions and Pareto optimal solutions, thus revealing that the true Pareto optimal solutions could hardly be represented by the nondominated solutions obtained from running an optimizer. Thus, the idea, stated by van Veldhuizen and Lamont [28], about the true Pareto front distinguishing it from the final set of nondominated solutions found by an algorithm is called known Pareto front .

Modern optimization approaches are very often population-based and evolutionary in nature. In such methods, the search for the global optima essentially comprises an iterative process that replaces the candidate solutions in the population by newly generated ones with an aim of achieving continuous improvement in the performance of the best candidate solutions through the help of mechanisms that guide the search to find a set of nondominated solutions. The use of the modern optimization approaches, especially population-based evolutionary algorithms, to solving the complex multiobjective optimization problems has been motivated mainly because of the following critical reasons. First, population-based evolutionary algorithms can recognize the specificity of multiobjective optimization problems by working simultaneously on all objectives and finally generating a group of optimal trade-off solutions, thus forming a uniformly distributed Pareto front. Second, as the name implies, the population-based approaches can deal with a population of candidate solutions simultaneously, allowing the generation of several elements of the Pareto optimal set in a single run of an optimizer instead of performing many separate runs when using classical mathematical programming methods [29]. This allows the decision-makers to simply pick the one that best fits the problem at hand, thus preventing the need to reconfigure and to rerun the optimization tool for finding other alternative Pareto optimal solutions. Third, their capability of maintaining diversity among the candidate solutions in the population is important to prevent the search from premature convergence to a specific region of the solution space, thus allowing a better exploration of the solution space and minimizing the susceptibility of the search to the presence of poor local optima in the optimization problems [30]. The final reason is that the population-based approaches are less susceptible to the continuity or shape of the Pareto front as they can deal with concave and discontinuous Pareto fronts without difficulty [27, 31]. Nevertheless, on the other hand, the weaknesses of these population-based methods are that they do not guarantee the identification of optimal trade-off solutions and the solutions obtained are likely to be stuck at some “good” approximations [32].

During the past few decades, a large number of publications have been done in population-based evolutionary algorithms and proved to be effective for solving multiobjective optimization problems since the first multiobjective evolutionary algorithm has been developed by Schaffer [33]. These algorithms include PAES [34], NSGA-II [35], PESA [36], SPEA2 [37], PESA-II [38], micro-GA [39], micro-GA2 [40], omni-aiNet [41], NNIA [42], omni-AIOS [43], MTLBO [44], and SCMIA [45].

#### 3. A Multiobjective Simulation-Based Optimization Framework

##### 3.1. Mechanisms of the Multiobjective Simulation-Based Optimization Framework

The optimization framework adopted in this study is developed by taking advantage of the idea of separation between the optimization method and the simulation model. For this reason, the optimization framework can remain the same or require only minor modifications such as changing range of parameters, data type of decision variables, and number of decision variables, to optimize the simulation model that incorporates new requirements. This framework in fact is a modified version of Leung and Lau’s work [16], which incorporates a multiobjective optimization algorithm instead of a single objective algorithm (Figure 1). The multiobjective algorithm adopted in the framework is Suppression-controlled Multiobjective Immune Algorithm (SCMIA) proposed by Leung and Lau [45]. Concepts of the algorithm are briefly discussed in the next section.