Solution Of Combinatorial Optimization Problems Research Articles

Solving flexible job-shop scheduling problem using hybrid particle swarm optimisation algorithm and data mining

Flexible job-shop scheduling problem (FJSSP) is an extension of the classical job-shop scheduling problem that allows an operation to be processed by any machine from a given set along different routes. It is very important in both fields of production management and combinatorial optimisation. This paper presents a new approach based on a hybridisation of the particle swarm optimisation (PSO) algorithm with data mining (DM) technique to solve the multi-objective flexible job-shop scheduling problem. Three minimisation objectives – the maximum completion time, the total workload of machines and the workload of the critical machines are considered simultaneously. In this study, PSO is used to assign operations and to determine the processing order of jobs on machines. The objectives are optimised by data mining technique which extracts the knowledge from the solution sets to find the near optimal solution of combinatorial optimisation problems. The computational results have shown that the proposed method ...

Parallel Robot Scheduling to Minimize Mean Tardiness with Unequal Release Date and Precedence Constraints Using a Hybrid Intelligent System

This paper considers the problem of scheduling a given number of jobs on a specified number of identical parallel robots with unequal release dates and precedence constraints in order to minimize mean tardiness. This problem is strongly NP-hard. The author proposes a hybrid intelligent solution system, which uses Genetic Algorithms and Simulated Annealing (GA+SA). A genetic algorithm, as is well known, is an efficient tool for the solution of combinatorial optimization problems. Solutions for problems of different scales are found using genetic algorithms, simulated annealing and a Hybrid Intelligent Solution System (HISS). Computational results of empirical experiments show that the Hybrid Intelligent Solution System (HISS) is successful with regards to solution quality and computational time.

Sliced Neighborhood Search

The integration of tree search and metaheuristic techniques for the solution of combinatorial optimization problems is a research area widely explored in the last decade. We propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing constraint programming tree search (along with constraint propagation). SNS encloses concepts from metaheuristic techniques. SNS can be used both as a stand alone search strategy, and embedded in other strategies as intensification and diversification mechanism. We provide an extensive experimental evaluation of SNS on hard instances of the Asymmetric Traveling Salesman Problem with Time Windows. We show the effectiveness of SNS as a stand alone strategy when compared to Limited Discrepancy Search and of SNS when included in a heuristic framework such as the constraint programming based local branching.

Optimal Layout Design for Agricultural Facility Using Simulated Annealing

(Keywords) combinatorial optimization problem, rational construction, simulated annealing, agricultural facility, optimal layout design Abstract In this study, optimal layout design approach was used to solve problems related to site layout design of agricultural facilities such as refrigeration house, grading and packing house and warehouse. A basic program to support the rational construction of such facilities using Simulated Annealing (SA), one heuristic algorithm and one solution for combinatorial optimization problems, was coded in C language (Satake(1999)). Layout design simulations were carried out to obtain information for the development of a program for solving practical problems. And, to clarify the feasibility of applying SA to the optimal layout design problems, the layout design simulation using the hill climbing (HC), which is another heuristic algorithm, was carried out for comparison with SA. As a result of the comparison with the optimum solution by HC, the value of cost evaluation by SA using exponential annealing was lower than that of hill climbing. Furthermore, in addition to this simulation, preliminary layout design simulation was also carried out to determine the applicability of the optimal layout design simulator to practical design. In this study, the layout design for a new building and parking was carried out. In the layout design, the site is not rectangular. As a result, the optimal design satisfying our condition was obtained.

Obtaining industrial experimental designs using a heuristic technique

There are several methods of obtaining orthogonal fractions of symmetrical and asymmetrical factorials, including Hadamard matrices, collapsing and replacing, and orthogonal arrays. The objective is to find the right permutations of levels of each factor in order to obtain uncorrelated main effects with a minimum number of runs. This leads to a combinatorial optimization problem. Simulated annealing is an optimization technique that has been successfully used to find a good solution for combinatorial optimization problems. By applying the computational technique of simulated annealing to orthogonal fractional factorial designs, we provide a method to obtain uncorrelated main effects for symmetrical and asymmetrical factorials.

A parallel immune algorithm for traveling salesman problem and its application on cold rolling scheduling

Parallel computing provides efficient solutions for combinatorial optimization problem. However, since the communications among computing processes are rather cost-consuming, the actual parallel or distributed algorithm comes with substantial expenditures, such as, hardware, management, and maintenance. In this study, a parallel immune algorithm based on graphic processing unit (GPU) that originally comes to process the computer graphics in display adapter is proposed. Genetic operators and a structure of vaccine taboo list are designed, and the internal memory utility of GPU structure is optimized. To verify the effectiveness and efficiency of the proposed algorithm, various middle-scale traveling salesman problems (TSP) are employed to demonstrate the potential of the proposed techniques. The simulation examples demonstrate that the developed method can greatly improve the computing efficiency for solving the TSP, and the results are more remarkable when the scale of TSP becomes higher. Furthermore, the derived algorithm is verified by a practical application in steel industry that arranges the cold rolling scheduling of a batch of steel coils.

Ant colony optimization-based bio-inspired hardware: survey and prospect

Bio-inspired hardware (BHW) refers to hardware that can change its architecture and behaviour dynamically and autonomously by interacting with its environment, and ant colony optimization is a meta-heuristic algorithm for the approximate solution of combinatorial optimization problems that has been inspired by the foraging behaviour of real ant colonies. In this paper, we take a broad survey on the recent progresses of ant colony optimization-based BHW, which includes ant colony optimization-based fuzzy controller, ant colony optimization-based hardware for the Travelling Salesman Problem (TSP), digital circuits, digital infinite impulse-response (IIR) filters, hardware-oriented ant colony optimization with look-up table and hardware/software partition. Some important issues of the challenges of ant colony optimization-based BHW are also presented. Online realization, robustness, generalization, disaster problems, theoretical analysis, implementation, swarm robotics, applications and hybrid approaches are eight key challenging issues for the ant colony optimization-based BHW.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

GRASP: basic components and enhancements

GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This paper gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies.

Eight-phase sequence sets design for radar

In this paper a novel Modified Simulated Annealing Algorithm (MSAA) is used as global optimization technique to find the solution of combinatorial optimization problem which is usually difficult to tackle. MSAA combines good methodologies like global minimum converging property of Simulated Annealing algorithm and fast convergence rate of Hamming scan algorithm. Orthogonal Netted Radar System (ONRS) and spread spectrum communication system can fundamentally improve the system performance by using a group of specially designed orthogonal signals. MSAA is used to synthesize orthogonal eight-phase sequence sets with good autocorrelation and cross correlation properties. Some of the synthesized sequence sets are presented, and their properties are better than four-phase sequence sets known in the literature. The synthesized eight-phase sequence sets are promising for practical application to Netted Radar System and spread spectrum communication. The effect of Doppler shift on synthesized sequences set is also investigated using ambiguity function. The convergence rate of the algorithm is shown to be good.

Dynamic Programming Optimization over Random Data: The Scaling Exponent for Near-Optimal Solutions

A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over $A\subseteq\{1,2,\ldots,n\}$, the objective function $|A|-\sum_i\xi_i{\rm1\hspace{-0.90ex}1}(i\in A,i+1\in A)$ for given $\xi_i>0$. This problem, with random $(\xi_i)$, provides a test example for studying the relationship between optimal and near-optimal solutions of combinatorial optimization problems. We show that, amongst solutions differing from the optimal solution in a small proportion $\delta$ of places, we can find near-optimal solutions whose objective function value differs from the optimum by a factor of order $\delta^2$ but not of smaller order. We conjecture this relationship holds widely in the context of dynamic programming over random data, and Monte Carlo simulations for the Kauffman–Levin NK model are consistent with the conjecture. This work is a technical contribution to a broad program initiated in [D. J. Aldous and A. G. Percus, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 11211–11215] of relating such scaling exponents to the algorithmic difficulty of optimization problems.

Computational Ability of Cells based on Cell Dynamics and Adaptability

Learning how biological systems solve problems could help to design new methods of computation. Information processing in simple cellular organisms is interesting, as they have survived for almost 1 billion years using a simple system of information processing. Here we discuss a well-studied model system: the large amoeboid Physarum plasmodium. This amoeba can find approximate solutions for combinatorial optimization problems, such as solving a maze or a shortest network problem. In this report, we describe problem solving by the amoeba, and the computational methods that can be extracted from biological behaviors. The algorithm designed based on Physarum is both simple and useful.

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.

Genetic algorithms-baes solution approach to combinatorial optimisation problems

This paper presents various methods and algorithms used in the solution of combinatorial optimisation problems. A definition of a combinatorial optimisation problem is first given. The definition is followed by a discussion on the depth first branch-and-bound algorithm and the local search algorithm; two approaches used for solving these kinds of problems. An introduction to Genetic Algorithms (GAs) coupled with an explanation of their role in solving combinatorial optimisation problems such as the travelling salesman problem is then presented. The discussion on genetic algorithms focuses on the advantages and disadvantages of using this technique as a tool or solving combinatorial optimisation problems. A sample instance of the Travelling Salesman Problem (TSP) is then solved using a GA. Finally, some conclusions are presented to emphasise the implications, benefits and drawbacks of using genetic algorithms in the solution of various combinatorial optimisation problems.

Tuning dynamic vibration absorbers by using ant colony optimization

The present contribution deals with the optimal tuning of two different types of dynamic vibration absorbers (DVA) by using ant colony optimization, namely the vibrating blade DVA and the multi-mode DVA. Dynamic vibration absorbers are mechanical appendages constituted by mass, spring and damping elements, which are coupled to a mechanical system to provide vibration attenuation. The tuning of the dynamic vibration absorber is the procedure that sets the anti-resonance frequency to a given value by adjusting the parameters of the dynamic vibration absorber. Based on this methodology, the optimization problem is defined as the minimization of the objective function that describes the vibration amplitude of the primary structure. To solve the optimization problem, ant colony optimization was used. In the early nineties, when the Ant Colony algorithm was first proposed, it was used as an alternative approach for the solution of combinatorial optimization problems, such as the traveling salesman problem. However, the extension for operating with continuous variables is recent and this feature is still under development. In the present formulation, the optimization technique was extended to handle continuous design variables. Numerical results are reported, aiming at illustrating the success of using the proposed methodology, as applied to mechanical system design.

Parallel robot scheduling to minimize mean tardiness with precedence constraints using a genetic algorithm

Identical parallel robot scheduling problem for minimizing mean tardiness with precedence constraints is a very important scheduling problem. But, the solution of this problem becomes much difficult when there are a number of robots, jobs and precedence constraints. Genetic algorithm is an efficient tool in the solution of combinatorial optimization problems, as it is well known. In this study, a genetic algorithm is used to schedule jobs that have precedence constraints minimizing the mean tardiness on identical parallel robots. The solutions of problems, which have been taken in different scales, have been done using simulated annealing and genetic algorithm. In particular, genetic algorithm is found noteworthy successful in large-scale problems.

An ant colony algorithm for scheduling in flowshops with sequence-dependent setup times of jobs

The problem of scheduling in flowshops with sequence-dependent setup times of jobs is considered and solved by making use of ant colony optimization (ACO) algorithms. ACO is an algorithmic approach, inspired by the foraging behavior of real ants, that can be applied to the solution of combinatorial optimization problems. A new ant colony algorithm has been developed in this paper to solve the flowshop scheduling problem with the consideration of sequence-dependent setup times of jobs. The objective is to minimize the makespan. Artificial ants are used to construct solutions for flowshop scheduling problems, and the solutions are subsequently improved by a local search procedure. An existing ant colony algorithm and the proposed ant colony algorithm were compared with two existing heuristics. It was found after extensive computational investigation that the proposed ant colony algorithm gives promising and better results, as compared to those solutions given by the existing ant colony algorithm and the existing heuristics, for the flowshop scheduling problem under study.

A Hybrid Genetic—GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem

Hybridization techniques are very effective for the solution of combinatorial optimization problems. This paper presents a genetic algorithm based on Expanding Neighborhood Search technique (Marinakis, Migdalas, and Pardalos, Computational Optimization and Applications, 2004) for the solution of the traveling salesman problem: The initial population of the algorithm is created not entirely at random but rather using a modified version of the Greedy Randomized Adaptive Search Procedure. Farther more a stopping criterion based on Lagrangean Relaxation is proposed. The combination of these different techniques produces high quality solutions. The proposed algorithm was tested on numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the algorithms of the DIMACS Implementation Challenge are also presented.

Weld sequence optimization: The use of surrogate models for solving sequential combinatorial problems

The solution of combinatorial optimization problems usually involves the consideration of many possible design configurations. This often makes such approaches computationally expensive, especially when dealing with complex finite element models. Here a surrogate model is proposed that can be used to reduce substantially the computational expense of sequential combinatorial finite element problems. The model is illustrated by application to a weld path planning problem.

Evaluating solution sets of a posteriori solution techniques for bi-criteria combinatorial optimization problems

The quality of an approximate solution for combinatorial optimization problems with a single objective can be evaluated relatively easily. However, this becomes more difficult when there are multiple objectives. One potential approach to solving multiple criteria combinatorial optimization problems when at least one of the single objective problems is NP-complete, is to use an a posteriori method that approximates the efficient frontier. A common difficulty in this type of approach, however, is evaluating the quality of approximate solutions, since sets of multiple solutions should be evaluated and compared. This necessitates the use of a comparison measure that is robust and accurate. Furthermore, a robust measure plays an important role in metaheuristic optimization for ?tuning? various parameters for evolutionary algorithms, simulated annealing, etc., which are frequently employed for multiple criteria combinatorial optimization problems. In this paper, the performance of a new measure, which we call Integrated Convex Preference (ICP) is compared to that of other measures appearing in the literature through numerical experiments?specifically, we use two a posteriori solution techniques based on genetic algorithms for a bi-criteria parallel machine scheduling problem and evaluate their performance (in terms of solution quality) using different measures. Experimental results show that the ICP measure evaluates the solution quality of approximations robustly (i.e., similar to visual comparison results) while other alternative measures can misjudge the solution quality. We note that the ICP measure can be applied to other non-scheduling multiple objective combinatorial optimization problems, as well.