D e v e lo p m e n t o f M u lt io b je c t iv e G e n e t ic A lg o r it h m s f o r A g r i- F o o d S u p p ly C h a in
D e s ig n b y C o n s id e r in g G lo b a l C li m a t e C h a n g e
Yandra Arkeman
Artificial Intelligence Research Group Division of Business and Industrial Application, Department of Agroindustrial Technology (TIN) Bogor Agricultural University (IPB), Indonesia
Email: yandra@ipb.ac.id
Kenneth De Jong
Department of Computer Science ‘s Evolutionary Computation Laboratory
and Krasnow Institute for Advanced Study’s Adaptive Systems Laboratory
George Mason University, USA
A b s tra c t
Global climate change is becoming challenging for us. It has a severe impact in almost every domain of our lives, especially in agriculture and agro-industry. The impact of global climate change in agriculture will affect the food supply in the world. Thus, there is a need to study agri-food supply chain with respect to global climate change for today’s and tomorrow’s agricultural and agro-industrial systems.
Agri-food chains are complex systems involving multiple multifaceted firms usually working together within specific agro-industry to satisfy an increasingly globalized market demand for high value food products. In so doing, the groupings of companies involved in an agri-food chain undertake activities that require multidimensional, inter-organizational and cross inter-organizational decision making in the process of adding value to a raw commodity product through the production, manufacturing and distribution stages of the chain. Additional complexity is added by climate variability
which impacts randomly and unpredictably on decision making in every component of the chain.
The work proposed in this paper is aimed to develop genetic algorithms for designing an agri-food supply chain by considering the effect of global climate change.
Although, there were many research works on or related to agri-food supply chains, most of them used conventional techniques, such as linear programming (Apaiah and Hendrix, 2004), dynamic programming (Gigler, et.al 2002), mixed integer linear programming (Gunnarson et.al, 2004) or standard single/multi objective genetic algorithms (Stewart et.al, 2004; Mardle and Pascoe, 2000; global climate change as an important factor in every stage of the chains.
1 .2 . O b je c tiv
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chain by using simulation modeling and risk assessment. Despite the advantage of their research, their proposed approach needs to be enhanced so it can deal not only with microbiological food safety but also with other aspects of agri-food supply chain.
Another recent study by Sarker and Ray (2009) reported the development of an improved evolutionary algorithm for solving crop planning model. They formulated a crop-planning model as a multiobjective optimization model and solved it using -constrained method, NSGA-II and their proposed algorithm namely MCA (Multiobjective Constrained Algorithm). The first objective of their model is to maximize the total gross margin (from cultivated plus imported crops) and the second objective is to minimize total working capital required. Both objectives subject to some constraints such as demand, land, capital, contingent, area and import bound. Before that, Matthews et.al (2006) used a combination of deliberative and computer-based methods for multi-objective land-use planning. Two conflicting goals were stated in their paper: to maximize financial return and land-use diversity. The metric for financial goal was the farm gross margin expressed as a NPV over 60 years. The land-use diversity was measured using Shannon-Wiener (SW) index that is maximized when all potential land uses are present in equal proportions. Despite the success of Sarker et.al (2009) and Matthews et. al (2006) to use multiobjective model and apply (new) evolutionary algorithms, they only dealt with two objectives and did not consider the global climate change factors.
In addition, Zhang et.al. (2009) developed a fuzzy multiobjective model on paddy circular economy system. They used lexicographic method and genetic algorithm to optimize a three-objective model for arrangement of paddy planting pattern. This study tackled three objectives instead of two and also considered global climate change factor, but the optimization method used is still conventional. Instead, a multiobjective evolutionary algorithm can be used to tackle the problem. Before that, there were some works that used various methods such as agent based model (ABM) and Bayesian Belief Network (BBN) such as reported by Bryceson and Smith (2008), van der Vorst et.al (2007) and da Silva and Filho (2007). Although they have given a significant contribution to the optimization field, they did not consider global climate change as an important factor in every stage of the chains.
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Multi-objective optimization has been defined as finding a vector of decision variables satisfying constraints to give acceptable values to all objective functions. In general, it can be mathematically defined as: find the vector X* = [x1*, x2*, …,xn*]
T
to optimize
F(X) = [f1(X), f2(X), …fk(X)] T
(2.1) subject to m inequality constraints
gi(X) ≤ 0, i = 1, …, m (2.2)
and p equality constraints
hj(X) = 0, j=1, …,p (2.3)
where X* n is the vector of decision or design variables, and F(X) k is the vector of objective functions, which must each be either minimized or maximized. A set of solution of a multi-objective optimization problem (MOOP) is known as Pareto optimal solutions or Pareto front.
Evolutionary algorithms have been widely used for multi-objective optimization because of their natural properties suited for these types of problems. This is mostly because of their parallel or population-based search approach. Therefore, most of the difficulties and deficiencies within the classical methods in solving multi-objective optimization problems are eliminated. For example, there is no need for either several runs to find all individuals of the Pareto front or quantification of the importance of each objective using numerical weights. In this way, the original non-dominated sorting procedure given by Goldberg (1989) was the catalyst for several different versions of multi-objective optimization algorithms. However, it is very important that the genetic diversity within the population be preserved sufficiently. This main issue in multi-objective optimization problems has been addressed by many related research works. Consequently, the premature convergence of MOEAs is prevented and the solutions are directed and distributed along the Pareto front if such genetic diversity is well provided. The Pareto-based approach of NSGA-II (Deb, 2001) has been used recently in a wide area of engineering multi-objective problems because of its yet efficient non-dominance ranking and crowding distance procedure in yielding different level and diversity of Pareto frontiers. The algorithm for NSGA-II is as follow:
Pseudo Code of NSGA-II:
Create a random population Po
Sort the population into different non-dominated levels. Each solution is assigned a fitness equal to its non-domination level (1 is the best level). Thus, minimization of the fitness is assumed.
Create an offspring population Qo of size N by
using binary tournament selection (using ranking and crowding distance as criteria for winning the tournament), recombination and mutation.
Combine parent and offspring populations and create Rt = Pt Qt. Perform a non-dominated
sorting to Rt and identify different fronts: Fi, i =
1,2, …, etc.
Set new population Pt+1 = 0. Set a counter i = 1.
Until |Pt+1|+|Fi| < N, perform Pt+1 = Pt+1 Fi and i
= i + 1.
Perform the Crowding-sort (Fi, <c) procedure
(Deb, 2001) and include the most widely spread (N-|Pt+1|) solutions by using crowding distance value in the sorted Fi to Pt+1.
Create offspring population Qt+1 from Pt+1 by
using the crowded tournament selection, crossover and mutation. If termination condition is not met go to Step 4.
NSGA-II has been enhanced by some researchers to improve its performance using parallelism approach. An example of recent work in improving NSGA-II is MOCell reported by Nebro et. al (2009).
Nebro et.al. (2009) used cellular (also known as fine-grained or spatial) model, but the implementation is still on single processor machine. They also investigated the use of hyper-threading technology to speed-up the computation process. In fact, Nebro’s work can be enhanced by using distributed processing system or true parallel machine, instead of simulating parallelism using single processor machine.
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This research aims to develop two models, the first one is for agricultural part and the second one is for processing industry part. The typical and representative models for each part are discussed below.
First Part Model: Farming
The model for farming sector is based on multi-objective model for paddy circular economy system proposed by Zhang et.al (2009), called in this research as model Z-9, that take into consideration three objectives, i.e. production value maximization, grain crops yield maximization and ecological benefit of straw maximization. Mathematically the first objective function of Z-9 model is formulized as below:
Max E[f1(
x
)] = E[ ri]xi (2.4)
where xi(i=1,2, …,6) is the area that covered by the i -th planting pattern; x
=(x1,x2,…,x6) T
; ri is the income
of i-th pattern. Six planting pattern in model Z-9 are: (1) wheat-rice, (2) rape-rice, (3) wheat-rice-vegetable, (4) vegetable-rice-vegetable, (5) rape/potato-rice, and (6) potato-rice-potato. Price and yield are the key elements to determine the income of these planting patterns. They may change year by year, so the incomes are also not fixed and also fuzzy and need to be solved using expected value model. The second objective function is:
Max E[f2(
x
)] = E[ cij]xi (2.5)
where cij is the output per a unit of area of the j-th (j=1,2,..5) crops in the i-th planting pattern. The crops types include rice, wheat and rape. The weather influences grain crops yield, so the outputs of rice, wheat and rape are fuzzy variable and need to be solved by using expected value model. The third objective function is:
Max E[f3(
x
)] = sixi, (2.6)
where si is the ecological benefit of the i-th pattern. Although model Z-9 is developed for China, we found that Z-9 model is representative for many countries’ supply chain optimization problems. In fact, model Z-9 can be used for Indonesian case by adjusting the coefficients of the equations and changing the planting patterns. For these reasons, we use Z-9 model as a typical model in this research.
original model of Z-9 that is presented in Zhang et.al (2009).
Second Part Model: Factory or Processing Industry The second model represents an adaptive production system for processing agricultural products into food. In this context adaptive means, ability to response well to the changes of the external factors of the industry such as customer demand, global climate and other economic factors. This adaptive agroindustry model (AAM) developed in this research is based on the previous models proposed by Shapiro (2001), Zhang (2009), Bryceson and Smith (2008), Chopra and Meindl (2007) to mention only a few. There are three objectives to be handled, i.e. minimizing total production cost, maximizing customer satisfaction (in term of product quality and delivery time), and maximizing production process flexibility (meaning minimizing the risk of mismatch in supply and demand). Mathematically these equations are formulized as below: expensive. In addition, determination of coefficients and parameter values for this factory model also requires advanced techniques such as fuzzy logic and expected value which is beyond the scope of this research. For these reasons, for the sake of application demonstration we determine those values hypothetically. As a consequence, no result comparison will be presented.
III. METHODOLOGY scientific method to solving complex decision making problems. The steps of scientific approach according to Taylor (2007) and adopted for this research are:
This step is intended to investigate real world problems in agri-food systems, (2)
optimum solution(s) for the model developed. New techniques such as Genetic Algorithms (GA) will be maker, the next step is implementing that solution in the real world. An appropriate implementation plan should be presented to the decision maker.
It should be noted that the solution to the optimization model (step 4) is to be done genetic algorithm. The logical steps to develop such a genetic algorithm are: (a) Conduct deep literature survey on GA , (b) Develop the most appropriate architectures based on several important criteria such as its suitability, robustness, effectiveness and efficiency, (c) Observe in details the characteristics of developed algorithms. Some further improvements and advancement will be needed to increase the algorithm performance, (d) Implementation (e) Test the system performance, and (f) Apply these techniques to solve the previously constructed optimization model that resulted from step 3.
IV. RESULTS AND DISCUSSIONS
In this section we present the results of our experiment of using multi-objective genetic algorithms to solve typical optimization models of agri-food supply chain. In the first section the future research directions are then presented.
4 .1 . S
The model used in the first experiment is model Z-9 originally proposed by Zhang et.al (2009). This model consists of three objectives to be maximized with regards to some constraints. The mathematical models have been discussed in Section 2.
Zhang et.al (2009) then performed a fuzzy mathematical model and an expected value model to determine the coefficient of the equations. After considering a large amount of data as well as performing a non-trivial fuzzy and expected value model they came up with a complete model as presented in their paper (Zhang et.al., 2009)
Then, they solved this mode combination of single objective genet and lexicographic method. The resu experiment are presented in Table 1 and
Tabel 1. The results when k1=0.9 an model Z-9
Tabel 2. The comparison results w transform indices
The aim of the experiment in this r optimize agri-food supply chain mod considering all three objectives using N plot of the Pareto front resulted experiment is presented in Figure 1.
Figure 1. Plot of Pareto Front for F1,
It should be noted that NSGA-II can Pareto optimum solutions in one run only one solution per run obt combination of genetic algorithm and
odel using a
his research is to model (Z-9) by that a multi-objective genetic algor term of producing Pareto front co lexicographic method. parallel multi-objective genetic algo NSGA-II. The models that will master-slave, island and diffusion will be tested using various test literature. The performance will using some metrics proposed in speed-up, efficiency, entropy, hyper-volume (Alba 2005 and Neb will be used to solve real world chain management optimization consists of two models: (1) Three model, and (2) Three-objective f should be noted here that at the t paper all of the experiments with progress. However, the prelimina the pMoGA developed in this resea tool for future application in agroindustrial systems, enginee computer science. use of multi-objective genetic a agri-food supply chain manageme focus our work to the developmen multi-objective genetic algorithm expand our work to see the fea some experiments on parallel mult algorithm. The experimental r multi-objective genetic algorithm research, i.e. NSGA-II, outperfo method such as genetic-lexicograp The performance of multi algorithm developed in this rese enhanced by parallelizing the com Our hypothesis is that parallelizat the computation as well as can im optimum solutions’ quality, as references. Although some of this research are still in progres results (either from references o experiments) support our hypothe
2 above). It is clear lgorithm is superior in t compare to genetic-orld agri-food supply ation problems that ree-objective farming ive factory model. It he time of writing this ith pMoGA are still in inary results showed esearch is a promising n in the area of gineering design and
IONS
e have presented the ic algorithm to solve gement problems. We ment of the sequential hm first and then we
lization can speed-up n improve the Pareto as also indicated in f the experiments in gress, the preliminary ces or from our own
A c k n o
This research is sponsored by Directorate General of Higher Education (Dikti), Ministry of National Education (Diknas) of Republic of Indonesia under Program of Academic Recharge Type-C (PAR-C) 2009. The research is conducted at Department of Computer Science’s Evolutionary Computation Laboratory and Krasnow Institute for Advanced Study’s Adaptive System Laboratory, George Mason University, USA, as host institution.
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