Ant colony optimization and local search for bin packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.     

Applying Ant System for solving Unequal Area Facility Layout Problems

Ant Colony Optimization (ACO) is a young metaheuristic algorithm which has shown promising results in solving many optimization problems. To date, a formal ACO-based metaheuristic has not been applied for solving Unequal Area Facility Layout Problems (UA-FLPs). This paper proposes an Ant System (AS) (one of the ACO variants) to solve them. As a discrete optimization algorithm, the proposed algorithm uses slicing tree representation to easily represent the problems without too restricting the solution space. It uses several types of local search to improve its search performance. It is then tested using several case problems with different size and setting. Overall, the proposed algorithm shows encouraging results in solving UA-FLPs.     

A Hybrid Metaheuristic for the Quadratic Assignment Problem

The quadratic assignment problem (QAP) is known to be NP-hard. We propose a hybrid metaheuristic called ANGEL to solve QAP. ANGEL combines the ant colony optimization (ACO), the genetic algorithm (GA) and a local search method (LS). There are two major phases in ANGEL, namely ACO phase and GA phase. Instead of starting from a population that consists of randomly generated chromosomes, GA has an initial population constructed by ACO in order to provide a good start. Pheromone acts as a feedback mechanism from GA phase to ACO phase. When GA phase reaches the termination criterion, control is transferred back to ACO phase. Then ACO utilizes pheromone updated by GA phase to explore solution space and produces a promising population for the next run of GA phase. The local search method is applied to improve the solutions obtained by ACO and GA. We also propose a new concept called the eugenic strategy intended to guide the genetic algorithm to evolve toward a better direction. We report the results of a comprehensive testing of ANGEL in solving QAP. Over a hundred instances of QAP benchmarks were tested and the results show that ANGEL is able to obtain the optimal solution with a high success rate of 90%. This work was supported in part by the National Science Council, R.O.C., under Contract NSC 91-2213-E-005-017.     

One-Dimensional Cutting Stock Problem with a Given Number of Setups: A Hybrid Approach of Metaheuristics and Linear Programming

One-dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which arises in many industrial applications. Since the setup costs for switching different cutting patterns become more dominant in recent cutting industry, we consider a variant of 1D-CSP, called the pattern restricted problem (PRP), to minimize the number of stock rolls while constraining the number of different cutting patterns within a bound given by users. For this problem, we propose a local search algorithm that alternately uses two types of local search processes with the 1-add neighborhood and the shift neighborhood, respectively. To improve the performance of local search, we incorporate it with linear programming (LP) techniques, to reduce the number of solutions in each neighborhood. A sensitivity analysis technique is introduced to solve a large number of associated LP problems quickly. Through computational experiments, we observe that the new algorithm obtains solutions of better quality than those obtained by other existing approaches.     

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.     

Analytical and stochastic modelling techniques

In mining supply chains, large combinatorial optimization problems arise. These are NP-hard and typically require a large number of computing resources to solve them. In particular, the run-time overheads can become increasingly prohibitive with increasing problem sizes. Parallel methods provide a way to manage such run-time issues by utilising several processors in independent or shared memory architectures. However it is not obvious how to adapt serial optimisation algorithms to perform best in a parallel environment. Here, we consider a resource constrained scheduling problem which is motivated in mining supply chains and present two popular meta-heuristics, ant colony optimization (ACO) and simulated annealing and investigate how best to parallelize these methods on a shared memory architecture consisting of several cores. ACO’s solution construction framework is inherently parallel allowing a relatively straightforward parallel implementation. However, for best performance, ACO needs an element of local search. This significantly complicates the paralellization. Several alternative schemes for parallel ACO with elements of local search are considered and evaluated empirically. We find that ACO with local search is the most effective single-threaded algorithm. The best parallel implementation can obtain similar quality results to the serial method in significantly less elapsed time.     

混合启发式算法求解多配送人员车辆路径问题

为解决带时间窗和多配送人员的车辆路径问题,本文采用混合启发式算法对其进行求解。该算法主要由整数规划重组、局部搜索算法和模拟退火算法三部分组成。在算法中,整数规划重组有效提高了解的质量,局部搜索算法和模拟退火算法保证了算法搜索的深入性和广泛性。通过与CPLEX和禁忌搜索算法进行对比,证实了混合启发式算法实用价值更高,求解效果更好。     

A hybrid genetic local search algorithm for the permutation flowshop scheduling problem

Traditionally, the permutation flowshop scheduling problem (PFSP) was with the criterion of minimizing makespan. The permutation flowshop scheduling problem to minimize the total flowtime has attracted more attention from researchers in recent years. In this paper, a hybrid genetic local search algorithm is proposed to solve this problem with each of both criteria. The proposed algorithm hybridizes the genetic algorithm and a novel local search scheme that combines two local search methods: the Insertion Search (IS) and the Insertion Search with Cut-and-Repair (ISCR). It employs the genetic algorithm to do the global search and two local search methods to do the local search. Two local search methods play different roles in the search process. The Insertion Search is responsible for searching a small neighborhood while the Insertion Search with Cut-and-Repair is responsible for searching a large neighborhood. Furthermore, the orthogonal-array-based crossover operator is designed to enhance the GA’s capability of intensification. The experimental results show the advantage of combining the two local search methods. The performance of the proposed hybrid genetic algorithm is very competitive. For the PFSP with the total flowtime criterion, it improved 66 out of the 90 current best solutions reported in the literature in short-term search and it also improved all the 20 current best solutions reported in the literature in long-term search. For the PFSP with the makespan criterion, the proposed algorithm also outperforms the other three methods recently reported in the literature.     

A reactive tabu search for the vehicle routing problem

The classical vehicle routing problem (VRP) involves determining a fleet of homogeneous size vehicles and designing an associated set of routes that minimizes the total cost. Our tabu search (TS) algorithm to solve the VRP is based on reactive tabu search (RTS) with a new escape mechanism, which manipulates different neighbourhood schemes in a very sophisticated way in order to get a balanced intensification and diversification continuously during the search process. We compare our algorithm with the best methods in the literature using different data sets and report results including new best known solutions for several well-known benchmark problems.     

An efficient grouping genetic algorithm for U-shaped assembly line balancing problems with maximizing production rate

U-type assembly line is one of the important tools that may increase companies’ production efficiency. In this study, two different modeling approaches proposed for the assembly line balancing problems have been used in modeling type-II U-line balancing problems, and the performances of these models have been compared with each other. It has been shown that using mathematical formulations to solve medium and large size problem instances is impractical since the problem is NP-hard. Therefore, a grouping genetic and simulated annealing algorithms have been developed, and a particle swarm optimization algorithm is adapted to compare with the proposed methods. A special crossover operator that always obtains feasible offspring has been suggested for the proposed grouping genetic algorithm. Furthermore, a local search procedure based on problem-specific knowledge was applied to increase the intensification of the algorithm. A set of well-known benchmark instances was solved to evaluate the effectiveness of the proposed and existing methods. Results showed that while the mathematical formulations can only be used to solve small size instances, metaheuristics can obtain high quality solutions for all size problem instances within acceptable CPU times. Moreover, grouping genetic algorithm has been found to be superior to the other methods according to the number of optimal solutions, or deviations from the lower bound values.     

Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times

We compare several heuristics for solving a single machine scheduling problem. In the operating situation modelled, setup times are sequence-dependent and the objective is to minimize total tardiness. We describe an Ant Colony Optimization (ACO) algorithm having a new feature using look-ahead information in the transition rule. This feature shows an improvement in performance. A comparison with a genetic algorithm, a simulated annealing approach, a local search method and a branch-and-bound algorithm indicates that the ACO that we describe is competitive and has a certain advantage for larger problems.     

Solving the short-term electrical generation scheduling problem by an adaptive evolutionary approach

In this paper, we introduce an adaptive evolutionary approach to solve the short-term electrical generation scheduling problem (STEGS). The STEGS is a hard constraint satisfaction optimization problem. The algorithm includes various strategies proposed in the literature to tackle hard problems with constraints such as: the representation used a non-binary coding scheme that drastically reduces the search space compared with the traditional evolutionary approaches. Specialized operators are especially designed for this problem and for this kind of representation, which also includes a local search procedure. Furthermore, the algorithm is guided by an adaptive parameter control strategy. We used some very well known benchmarks for STEGS to evaluate our approach. The results are very encouraging and we have obtained new better values for all the systems tested. Our aim here is to show that evolutionary approaches can be considered as good techniques to be used to solve real-world highly constrained problems.     

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.     

An Ant Colony Optimization Algorithm for the Minimum Weight Vertex Cover Problem

Given an undirected graph and a weighting function defined on the vertex set, the minimum weight vertex cover problem is to find a vertex subset whose total weight is minimum subject to the premise that the selected vertices cover all edges in the graph. In this paper, we introduce a meta-heuristic based upon the Ant Colony Optimization (ACO) approach, to find approximate solutions to the minimum weight vertex cover problem. In the literature, the ACO approach has been successfully applied to several well-known combinatorial optimization problems whose solutions might be in the form of paths on the associated graphs. A solution to the minimum weight vertex cover problem however needs not to constitute a path. The ACO algorithm proposed in this paper incorporates several new features so as to select vertices out of the vertex set whereas the total weight can be minimized as much as possible. Computational experiments are designed and conducted to study the performance of our proposed approach. Numerical results evince that the ACO algorithm demonstrates significant effectiveness and robustness in solving the minimum weight vertex cover problem.     

Creating very large scale neighborhoods out of smaller ones by compounding moves

This paper discusses neighborhood search algorithms where the size of the neighborhood is “very large” with respect to the size of the input data. We concentrate on such a very large scale neighborhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts, swaps, and insertions. We present a systematic way of creating and searching CIM neighborhoods for routing problems with side constraints. For such problems, the exact search of the CIM neighborhood becomes NP-hard. We introduce a multi-label shortest path algorithm for searching these neighborhoods heuristically. Results of a computational study on the vehicle routing problem with capacity and distance restrictions shows that CIM algorithms are very competitive approaches for solving vehicle routing problems. Overall, the solutions generated by the CIM algorithm have the best performance among the current solution methodologies in terms of percentage deviation from the best-known solutions for large-scale capacitated VRP instances.     

Ant Colony Optimisation for Machine Layout Problems

Flexible machine layout problems describe the dynamic arrangement of machines to optimise the trade-off between material handling and rearrangement costs under changing and uncertain production environments. A previous study used integer-programming techniques to solve heuristically reduced versions of the problem. As an alternative, this paper introduces an ant colony optimisation (ACO) algorithm to generate good solutions. Experimental results are presented, with ACO obtaining better solutions than the reduction heuristic.     

An exact method with variable fixing for solving the generalized assignment problem

We propose a simple exact algorithm for solving the generalized assignment problem. Our contribution is twofold: we reformulate the optimization problem into a sequence of decision problems, and we apply variable-fixing rules to solve these effectively. The decision problems are solved by a simple depth-first lagrangian branch-and-bound method, improved by our variable-fixing rules to prune the search tree. These rules rely on lagrangian reduced costs which we compute using an existing but little-known dynamic programming algorithm.     

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.     

A memetic algorithm approach for solving the multidimensional multi-way number partitioning problem

In this paper, we describe a generalization of the multidimensional two-way number partitioning problem (MDTWNPP) where a set of vectors has to be partitioned into p sets (parts) such that the sums per every coordinate should be exactly or approximately equal. We will call this generalization the multidimensional multi-way number partitioning problem (MDMWNPP). Also, an efficient memetic algorithm (MA) heuristic is developed to solve the multidimensional multi-way number partitioning problem obtained by combining a genetic algorithm (GA) with a powerful local search (LS) procedure. The performances of our memetic algorithm have been compared with the existing numerical results obtained by CPLEX based on an integer linear programming formulation of the problem. The solution reveals that our proposed methodology performs very well in terms of both quality of the solutions obtained and the computational time compared with the previous method of solving the multidimensional two-way number partitioning problem.     

A scatter search algorithm for the single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, with the objective of minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard and research has focused on heuristics to solve large instances of the problem. In this paper we present a scatter search algorithm to solve large size SRFLP instances. Our computational experiments show that the scatter search algorithm is an algorithm of choice when solving large size SRFLP instances within limited time.