H012225053

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 12, Issue 2 Ver. II (Mar - Apr. 2015), PP 50-53
www.iosrjournals.org
DOI: 10.9790/1684-12225053 www.iosrjournals.org 50 | Page
A Review on Non-Traditional Optimization Algorithm for
Simultaneous Scheduling Problems
P. Sreenivas1
, S. Vijaya Kumar 2
1,2,
(Assistant Professor, Dept of Mechanical Engineering, K.S.R.M College of Engg, Kadapa,
Andhra Pradesh, India)
_________________________________________________________________________________________
Abstract- This paper focuses on the applications of non-traditional optimization method. Here several un
conventional optimization were available in literature are critically reviewed to solve this combinatorial
optimization problem. In this paper In this paper, authors seek to assess the work done in the simultaneous
scheduling domain by providing a review of many of the techniques used for the industrial and production
environment. It is established that Non- conventional optimization methods should be considered
complementary rather than competitive. In addition, this work suggests guide-lines on features that should
incorporated to create a good scheduling system. Finally, the possible direction for future work is highlighted
so that current barriers within applications of non traditional optimization method may be surmounted as
researchers approach in the 21st century.
Keywords - non conventional optimizations, simultaneous scheduling, Industrial production environment,
review
I. Introduction
The application of optimization algorithms to real world problems has gained momentum in the last
decade. Dating back to the early 1940s, diverse traditional mathematical methods such as linear programming
(LP), nonlinear programming (NLP) or dynamic programming (DP) were first employed for solving complex
optimization problems by resorting to different relaxation methods of the underlying formulation.
These techniques are capable of cost efficiently obtaining a global optimal solution in problem models
subject to certain particularities (e.g. optimal sub structure ability and sub problem overlap for dynamic
programming), but unfortunately their application range does not cover the whole class of NP complete
problems, where an exact solution cannot be found in polynomial time. In fact, the solution space (and hence,
the solving time) of the problem increases exponentially with the number of inputs, which makes them
unfeasible for practical applications.
II. Literature Survey
In the course of the most recent three epochs much exploration has been done in this part. Lots of Metaheuristic
algorithms have been advanced to create ideal schedule and part-releasing policies. Maximum of these algorithms comprise
enumerative procedures, mathematical programming and approximation techniques, i.e., linear programming, integer
programming, goal programming, dynamic programming, transportation and network analysis, branch and bound, priority-
rule-based heuristics, local search algorithms (ITS, TS, SA), evolutionary algorithm (GA), etc. Of these techniques, little is
specific to particular objectives, and few are precise to particular problem illustrations with respect to computational time
required. Shankar and Tzen [1] measured scheduling problems in a random FMS as composite independent tasks. Lee [2]
revealed a goal-programming model for multiple conflicting objectives in manufacturing. Toker et al. [3] proposed an
approximation algorithm for „n‟ job „m‟ machine problem. Steeke and Soldverg [4] investigated various operating strategies
on a caterpillar FMS by meansof deterministic simulation with the number of completed assemblies on a performance
criterion manufacturing problem related with parallel identical machines throughout simulation. Chan and Pak [5] suggested
two heuristic algorithms for solving the scheduling problem with the goal of minimizing total cost in a statictically loaded
FMS. Shaw and Winston [6] spoke anartificial intelligence approach to the scheduling of FMS Schultz and Merkens [7]
equated the performance of an ES, a GA and priority rules for production systems.
III. Objectives Of Simultaneous Scheduling
The scheduling is made to meet specific objectives. The objectives are decided upon the situation,
market demands, company demands and the customer‟s satisfaction. There are two types for the scheduling
Objectives :
[1] Minimizing the make span
[2] Due date based cost minimization
The objectives considered under the minimizing the make span are,
(a) Minimize machine idle time

A Review On Non-Traditional Optimization Algorithm For Simultaneous Scheduling Problems
(b) Minimize the in process inventory costs
(c) Finish each job as soon as possible
(d) Finish the last job as soon as possible
The objectives considered under the due date based cost minimization are,
(a) Minimize the cost due to not meeting the due dates
(b) Minimize the maximum lateness of any job
(c) Minimize the total tardiness
(d) Minimize the number of late jobs
IV. Scheduling Techniques
These techniques are mainly divided into two categories i.e. Traditional and Non Traditional. A brief
introduction of these techniques is given below.
(a) Traditional techniques:
These techniques are slow and guarantee of global convergence as long as problems are small. Traditional
Techniques are also called as Optimization Techniques. They are
 Mathematical programming like Linear programming, Integer programming, Dynamic programming,
Transportation etc.
 Enumerate Procedure Decomposition like Lagrangian Relaxation.
(b) Non traditional techniques:
These methods are very fast but they do not guarantee for optimal solutions. Non Traditional
Techniques are also called as Approximation Methods. They involve
 Constructive Methods like Priority dispatch rules, composite dispatching rules.
 Insertion Algorithms like Bottleneck based heuristics, Shifting Bottleneck Procedure.
 Evolutionary Programs like Genetic Algorithm, Particle Swarm Optimization.
 Local Search Techniques like Ants Colony Optimization, Simulated Annealing, adaptive Search, Tabu
Search, Problem Space methods
 Iterative Methods like Artificial Intelligence Techniques, Artificial Neural Network, Heuristics Procedure,
Beam-Search, and Hybrid Techniques.
V. Some Non Traditional Techniques
5.1 Genetic Algorithm
In actual fact, a GA is a set of techniques which when common enable solutions to particular problems. To
accomplish the objectives, the GA produces consecutive population alternate solutions until a solution is obtained which
yields acceptable results. With in the generation of each successive population, improvements in the quality of the individual
solutions are increased. In this manner, a GA can rapidly transfer to a fruitful result without having to inspect all likely
solution to the problem. The procedure used is centered on the vital processes that regulate the growth of biological
organisms, namely, natural selection and reproduction. These two processes together improve an organism‟s capacity to
persist within its atmosphere in the following manner:
1. Usual selection governs which organisms will have the chance to reproduce and persist within a population.
2. Reproduction involves genes from two discrete individuals uniting to form offspring that take over the persistence features
of their parents. These algorithms pursue to start the manner in which are useful genes reproduce themselves from end to
end consecutive populations and in future subsidize to the steady ability of an organism to stay alive.
5.2 Simulated Annealing
The simulated annealing algorithm has its roots in statistical mechanics. The concern in simulated
annealing initiated with the work ofKirkpatrick [9], and Cemy [10]. They proposed a simulated annealing
algorithm, which is based on the comparison between the annealing process of solids and the problem of solving
optimization problems. Launch in 1983, simulated annealing was advertised as a global optimization procedure
that mimics the physical annealing process by which molten substances cool to crystalline lattices of minimal
energy. This marketing scheme had a polarizing effect, attracting those who enchanted in metaphor and
separating others who found metaphor inadequate at best and facile at worst. Actually, the emotional outbreaks
that supplement many negotiations of simulated annealing are an unfortunate disturbance. Whatever its pros and
cons, simulated annealing can be deal with in rigorous mathematics.
At the heart of the method of simulated annealing is an correlation with thermodynamics, exactly with
the manner that liquids freeze and crystallize, or metals cool and anneal. At high temperatures, the molecules of
a liquid move freely with respect to one another. If the liquid is cooled gently, thermal mobility is gone. In
reality, if a liquid metal is cooled rapidly or “quenched,” it does not reach this state but rather ends up in a
polycrystalline or amorphous state having slightly higher energy. So the principle of the process is slow cooling,
allowing sufficient time for restructuring of the atoms as they drop mobility. This is the mechanical definition of

annealing, and it is vital for confirming that a low energy state will be attained. Even if the analogy is not
perfect, there is a logic in which all of the minimization algorithms correspond to rapid cooling or quenching. In
all cases, we have gone greedily for the fast, nearby solution: From the starting point, go immediately downward
as far as you can go. This leads to a local, but not necessarily a global, minimum. Nature‟s own minimization
algorithm is based on quite a different procedure. The so-called Boltzmann probability distribution,
Prob (E) = exp(−E/kT)
5.3 swarm intelligence
PSO is a robust stochastic optimization technique based on the movement and intelligence swarms. It was
developed in 1995 by James Kennedy (social psychologist) and Russell Eberhart (Electrical Engineer). PSO is a method for
optimizing hard numerical functions on metaphor of fish. Suppose the following scenario, a flock of birds is randomly
searching for food in an area, where there is only one piece of food available and none of them knows where it is, but they
can estimate how for it would be at each iteration. The problem here is what is the best strategy to find and get the food.
Obviously the simplest strategy is to follow the bird known as the nearest one to the food.
PSR inventors were inspired of such natural process based scenarios to solve the optimization problems. In PSO
each single solution, called a particle, is considered as a bird, the group becomes a swarm (population) and the search space
is the area to explore. Each particle has a fitness value calculated by a fitness function, and a velocity of flying towards the
optimum, the food. All particles fly across the problem space following the particle nearest to the optimum. PSO starts with
initial population of solutions, which is updated iteration by iteration. Therefore PSO can be counted as an evolutionary
algorithm besides being a meta heuristics method, which allows exploiting the searching experience of a single particle as
well as the best of the whole swarm.
In a PSO algorithm, [9] swarm is initiated randomly with finding the personal best (best value of each individual
so far) and global best (best particle in the whole swarm). Initially, each individual with its dimensions and fitness value is
assigned to its person best. The best individual among particle best swarm, with its dimension and fitness value is, on the
other hand, assigned to the global best. Then a loop starts to converge to an optimum solution. In the loop, particle and
global bests are determined to update the velocity first. Then the current position of each particle is updated with the current
velocity. Evaluation is again performed to complete the fitness of particles in the swarm. This loop is terminated with a
stopping criterion predetermined in advance. The application of the PSO requires that parameters are initialized and the
population to be generated randomly.
5.4 Artificial Immune System
Artificial Immune Systems have emerged during the last decade. They are incited by many researchers
to design and build immune-based models for a variety of application domains. Artificial immune systems can
be defined as a computational paradigm that is inspired by theoretical immunology, observed immune functions,
principles and mechanisms. The function of biological IS is to protect the body from the foreign matters, more
known as antigens. Antigens stimulate the antibodies that reside in the body. The key roles of antibodies are to
identify, bind and eliminate the antigens. Clonal selection explains the response of IS, when a non-self antigen
pattern is recognized by the B cells. It is selected to proliferate and produce antibodies in high volume by
cloning. The new clonal cells undergo hype rmutation for improving antibodies affinity that leads to antigenic
neutralization and elimination. The overall procedure of clonal selection is schematically shown in Fig. 1
Fig. 1

5.5 Differential Evolution (DE) Algorithm
Differential Evolution (DE) is the Stochastic, population-based optimization algorithm. It is one of the
Evolutionary Algorithms (EAs) for global optimization over continuous search space (Storn and Price [2], 1995). Its
theoretical framework is simple and requires inexpensive computation in term of CPU time (Bin et al., 2008). Due to its
advantage of relatively few control variables but performing well in convergence, DE has been widely applied and shown its
strengths in many application areas.
Working principle of DE
In DE algorithm, solutions are represented as chromosomes based on floating-point numbers. In the mutation
process of this algorithm, the weighted difference between two randomly selected population members is added to a third
member to generate a mutated solution followed by a crossover operator to combine the mutated solution with the target
solution so as to generate a trial solution. Then a selection operator is applied to compare the fitness function value of both
competing solutions, namely, target and trial solutions to determine who can survive for the next generation. The basic DE
algorithm consists of four steps, namely, initialization of population, mutation, crossover and selection.
1. Population initialization:
2. Mutation
3. Crossover
4. Selection operat
5.6 Ant Colony Algorithm
ACO algorithms are inspired by the foraging behaviour of natural ant colonies in which individual ants deposit a
substance called pheromone on the path while moving from the nest to the food sources and vice versa. Other ants smell this
pheromone to find the food sources. The more is the pheromone in a path, the higher would be the probability of selecting
that path. Consequently, after some time all the ants would select the shortest path from the nest to the food source. For more
information in this regard, the interested reader is referred to[11]
Any ant algorithm must specify the following elements:
(1) construction of solutions,
(2) heuristic information,
(3) pheromone updating rule,
(4) selection probability,
(5) local search algorithm, and
(6) stopping criterion.
VI. Conclusions
Since Simultaneous scheduling problems fall into the class of NP-complete problems, they are among the most
difficult to formulate and solve. Some optimization problems (including various combinatorial optimization problems) are
sufficiently complex that it may not be possible to solve for an optimal solution with the kinds of exact algorithms. In such
cases, heuristic methods are commonly used to search for a good (but not necessarily optimal) feasible solution. Several
metaheuristics are available that provide a general structure and strategy guidelines for designing a specific heuristic method
to fit a particular problem.
A key feature of these metaheuristics procedures is their ability to escape from local optima and perform a robust
search of a feasible region. This paper introduces the most prominent types of non-conventional type algorithms or
meteheuristics. In addition, it may employ intensification and diversification strategies based on long-term memory to focus
the search on promising continuous. The following are the advantages of non-traditional techniques over the traditional
techniques:
 The non-traditional techniques yield a global optimal solution.
 The techniques use a population of points during search.
 Initial populations are generated randomly which enable to explore the search space.
 The techniques efficiently explore the new combinations with available knowledge to find a new generation.
 The objective functions are used rather than their derivatives
References
[1]. Shankar K,Tzen Y.J. A loading and dispatching problem in a random flexible manufacturing system. Int J Prod Res 23: 579- 595. 1985.
[2]. Lee, S.M., Jung H.J. A multi objective production planning model in flexible manufacturing environment. Int J Prod Res 27 (11): 1981-1992
[3]. Toker, A., Kondacki, S., Erkip, N., Job shop scheduling under a non-renewable resource constraint. J Oper Res Soc 45(8): 942-947, 1994.
[4]. Steeke, K.E., Soldberg, J.J., Loading and control policies for a flexible manufacturing system. Int J Prod Res 19(5):481 -490, 1982.
[5]. Chan, T.S., Pak, H.A., Heuristic job allocation in a flexible manufacturing system. Int J AdvManufTechnol 1(2):69-90, 1986.
[6]. Shaw, M.J., Whinston, A.B., An artificial intelligence approach to the scheduling of flexible manufacturing systems.IEEE Trans 21:170-
182,1989.
[7]. Schulz, J., Mertens P., A comparison between an expert system, a GA and priority for production scheduling. In: Proceedings of the 1st
international conference on operations and quantitative management, Jaipur, India, 2.506-513, 1997.
[8]. Richard W. Conway, William L. Maxwell, Louis W. Millep “Theory of Scheduling”. Addison – Wesley Publishing Company (1967).
[9]. Kirkpatrick, S; Gelatt, D.D and Vecchi, M.P. (1983).Optimization by Simulated Annealing. Science, Vol.220,pp 671-680.
[10]. Cemy, V. (1985). Thermodynamic approaches to the travelling salesman problems. J Optim. TheoryAppl. Vol.45,pp 41-51
[11]. Solimanpur and prem virat, An ant algorithm for the single row layout problem in Fexible manufacturing systems, Computers & Operations
Research 32 (2005) 583-598.

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