Solving the circular open dimension problem by using separate beams and look-ahead strategies

In this paper, a constructive method is investigated for solving the circular open dimension problem (CODP), a problem of the Cutting and Packing family. CODP is a combinatorial optimization problem which is characterized by a set of circular pieces of known radii and a strip of fixed width W and unlimited length. The objective is to determine the smallest rectangle of dimensions (L, W), where L is the length of the rectangle, that will contain all the pieces such that there is no overlapping between the placed pieces and all the demand constraints are satisfied. The method combines the separate-beams search, look-ahead, and greedy procedures. A study concerning both restarting and look-ahead strategies is undertaken to determine the best tuning for the method. The performance of the method is computationally analyzed on a set of instances taken from the literature and for which optimal solutions are not known. Best-known solutions are obtained.     

Algorithms for the circular two‐dimensional open dimension problem

In this paper, we propose three heuristics for the circular two‐dimensional open dimension problem, also known as the circular strip cutting/packing problem. We first propose an open strip generation solution procedure that uses the best local position rule into the open strip. Second, we propose a simple augmented version of the first heuristic by introducing an exchange‐order strategy. Third, we propose a hybrid heuristic that combines beam search and a series of target values belonging to a predetermined interval search. We evaluate the performance of these heuristics on several instances varying from small to large ones. Encouraging results have been obtained.     

Adaptive beam search lookahead algorithms for the circular packing problem

This paper addresses the circular packing problem (CPP), which consists in packing n circles C_i, each of known radius r_i, i∈N={1, …, n}, into the smallest containing circle C. The objective is to determine the radius r of C as well as the coordinates (x_i, y_i) of the center of C_i, i∈N. CPP is solved using two adaptive algorithms that adopt a binary search to determine r, and a beam search to check the feasibility of packing n circles into C when the radius is fixed at r. A node of level ?, ?=1, …, n, of the beam search tree corresponds to a partial packing of ? circles of N into C. The potential of each node of the tree is assessed using a lookahead strategy that, starting with the partial packing of the current node, assigns each unpacked circle to its maximum hole degree position. The beam search stops either when the lookahead strategy identifies a feasible packing or when it has fathomed all nodes. The computational tests on a set of benchmark instances show the effectiveness of the proposed adaptive algorithms.     

Some experiments with a simple tabu search algorithm for the manufacturer's pallet loading problem

The manufacturer's pallet loading problem consists in arranging, orthogonally and without overlapping, the maximum number of boxes with dimensions (l,w) or (w,l) onto a rectangular pallet with dimensions (L,W). This problem has been successfully handled by block heuristics, which generate loading patterns composed by one or more blocks where the boxes have the same orientation. A common feature of such methods is that the solutions provided are limited to the so-called first order non-guillotine patterns. In this paper we propose an approach based on the incorporation of simple tabu search (without longer-term memory structures) in block heuristics. Starting from an initial loading pattern, the algorithm performs moves that increase the size of selected blocks in the current pattern; as a result, other blocks are decreased, eliminated or created. Computational results indicate that the approach is capable of generating superior order optimal patterns for difficult instances reported in the literature.     

An effective hybrid harmony search-based algorithm for solving multidimensional knapsack problems

This study presents an effective hybrid algorithm based on harmony search (HHS) for solving multidimensional knapsack problems (MKPs). In the proposed HHS algorithm, a novel harmony improvisation mechanism is developed with the modified memory consideration rule and the global-best pitch adjustment scheme to enhance the global exploration. A parallel updating strategy is employed to enrich the harmony memory diversity. To well balance the exploration and the exploitation, the fruit fly optimization (FFO) scheme is integrated as a local search strategy. For solving MKPs, binary strings are used to represent solutions and two repair operators are applied to guarantee the feasibility of the solutions. The HHS is calibrated based on the Taguchi method of design-of-experiment. Extensive numerical investigations based on well-known benchmark instances are conducted. The comparative evaluations indicate the HHS is much more effective than the existing HS and FFO variants in solving MKPs.     

A solution approach based on beam search algorithm for disassembly line balancing problem

The disassembly line balancing (DLB) problem is the process of allocating a set of disassembly tasks to an ordered sequence of workstations in such a way that optimizes some performance measures (e.g., cycle time, number of stations). Since DLB problems belong to the class of NP hard, many heuristic and meta-heuristic algorithms are applied to cope with the complexity of the DLB problems in order to obtain acceptable solutions in a reasonable amount of time. In this study, a beam search (BS) based approach for the DLB problem is proposed. Minimization of number of workstations is used as the performance measure. The proposed algorithm is compared with the optimal solutions of well-known real cases and generated test problems. The results indicate that the proposed approach based on BS is a very competitive and promising tool for further researches.     

A tabu search-based algorithm for the fuzzy clustering problem

The Fuzzy Clustering Problem (FCP) is a mathematical program which is difficult to solve since it is nonconvex, which implies possession of many local minima. The fuzzy C-means heuristic is the widely known approach to this problem, but it is guaranteed only to yield local minima. In this paper, we propose a new approach to this problem which is based on tabu search technique, and aims at finding a global solution of FCP. We compare the performance of the algorithm with the fuzzy C-means algorithm.     

Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts

This paper deals with the two-dimensional bin packing problem with conflicts (BPC-2D). Given a finite set of rectangular items, an unlimited number of rectangular bins and a conflict graph, the goal is to find a conflict-free packing of the items minimizing the number of bins used. In this paper, we propose a new framework based on a tree-decomposition for solving this problem. It proceeds by decomposing a BPC-2D instance into subproblems to be solved independently. Applying this decomposition method is not straightforward, since merging partial solutions is hard. Several heuristic strategies are proposed to make an effective use of the decomposition. Computational experiments show the practical effectiveness of our approach.     

A stochastic beam search for the berth allocation problem

In this paper, the optimization of the Berth Allocation Problem (BAP) is transformed into a multiple stage decision making procedure and a new multiple stage search method, namely stochastic beam search algorithm, is proposed to solve it. New techniques such as an improved beam search scheme, a two-phase node goodness estimation, and a stochastic node selection criteria are proposed. Real-life information provided by Singapore Port was collected as our test data. Experimental results show that the proposed stochastic beam search is more accurate and efficient than both the state-of-the-art meta-heuristic and the traditional determinist beam search.     

A new heuristic algorithm for the circular packing problem with equilibrium constraints

The circular packing problem with equilibrium constraints is an optimization problem about simplified satellite module layout design.A heuristic algorithm based on tabu search is put forward for solving this problem.The algorithm begins from a random initial configuration and applies the gradient method with an adaptive step length to search for the minimum energy configuration.To jump out of the local minima and avoid the search doing repeated work,the algorithm adopts the strategy of tabu search.In the pr...     

An improved algorithm for the longest common subsequence problem

The Longest Common Subsequence problem seeks a longest subsequence of every member of a given set of strings. It has applications, among others, in data compression, FPGA circuit minimization, and bioinformatics. The problem is NP-hard for more than two input strings, and the existing exact solutions are impractical for large input sizes. Therefore, several approximation and (meta) heuristic algorithms have been proposed which aim at finding good, but not necessarily optimal, solutions to the problem. In this paper, we propose a new algorithm based on the constructive beam search method. We have devised a novel heuristic, inspired by the probability theory, intended for domains where the input strings are assumed to be independent. Special data structures and dynamic programming methods are developed to reduce the time complexity of the algorithm. The proposed algorithm is compared with the state-of-the-art over several standard benchmarks including random and real biological sequences. Extensive experimental results show that the proposed algorithm outperforms the state-of-the-art by giving higher quality solutions with less computation time for most of the experimental cases.     

A two phase removing algorithm for minimum independent dominating set problem

The minimum independent dominating set (MIDS) problem is a famous combinatorial optimization problem and is widely used in real-world domains. In this paper, we design a novel local search algorithm with tabu method and two phase removing strategies including double-checked removing strategy and random diversity removing strategy to solve the MIDS problem. The first removing strategy checks and then removes the second-level neighbourhood of the just removal vertex to break the limitation of the independence property. When the quality of candidate solution has not been improved after some steps, the second removing strategy dynamically and greedily removes lots of vertices so that the current candidate solution can escape from suboptimal search space, and then we introduce the random walk into the repair process. Experiments are carried out on two classical benchmarks named DIMACS and BHOSLIB, and the results show that the proposed algorithm significantly outperforms the previous state-of-the-art MIDS heuristic algorithms.     

A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

A heuristic recursive algorithm for the two-dimensional rectangular strip packing problem is presented. It is based on a recursive structure combined with branch-and-bound techniques. Several lengths are tried to determine the minimal plate length to hold all the items. Initially the plate is taken as a block. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. The dividing cut is vertical if the block width is equal to the plate width; otherwise it is horizontal. Both lower and upper bounds are used to prune unpromising branches. The computational results on a class of benchmark problems indicate that the algorithm performs better than several recently published algorithms.     

基于禁忌搜索的启发式算法求解带平衡约束的圆形装填问题

带平衡约束的圆形装填(Packing)问题是一类简化的卫星舱布局优化问题.现提出一个基于禁忌搜索的启发式(TSH)算法对该问题进行求解.算法从任一初始格局出发,应用基于自适应步长的梯度法进行能量极小化.为了使计算能有效地逃离局部极小点的陷阱且避免迂回搜索,算法采用了禁忌搜索的策略.在禁忌搜索的过程中,我们对传统的邻域解、禁忌对象以及当前解接受原则进行了有效的改进.对两组共11个有代表性的算例进行了实算.计算结果表明,TSH算法刷新了其中7个算例的当今国际上的最好纪录,对于其余4个算例,该算法均达到问题的最优解.     

On solving the assembly line worker assignment and balancing problem via beam search

Certain types of manufacturing processes can be modelled by assembly line balancing problems. In this work we deal with a specific assembly line balancing problem that is known as the assembly line worker assignment and balancing problem (ALWABP). This problem appears in settings where tasks must be assigned to workers, and workers to work stations. Task processing times are worker specific, and workers might even be incompatible with certain tasks. The ALWABP was introduced to model assembly lines typical for sheltered work centers for the Disabled.     

An algorithm based on ant colony optimization for the minimum connected dominating set problem

Ant colony optimization is a well established metaheuristic from the swarm intelligence field for solving difficult optimization problems. In this work we present an application of ant colony optimization to the minimum connected dominating set problem, which is an NP-hard combinatorial optimization problem. Given an input graph, valid solutions are connected subgraphs of the given input graph. Due to the involved connectivity constraints, out-of-the-box integer linear programming solvers do not perform well for this problem. The developed ant colony optimization algorithm uses reduced variable neighborhood search as a sub-routine. Moreover, it can be applied to the weighted and to the non-weighted problem variants. An extensive experimental evaluation presents the comparison of our algorithm with the respective state-of-the-art techniques from the literature. It is shown that the proposed algorithm outperforms the current state of the art for both problem variants. For comparison purposes we also develop a constraint programming approach based on graph variables. Even though its performance deteriorates with growing instance size, it performs surprisingly well, solving 315 out of 481 considered problem instances to optimality.     

A parallel hybrid local search algorithm for the container loading problem

In this contribution, a parallel hybrid local search algorithm for the three‐dimensional container loading problem (CLP) is proposed. First a simulated annealing method for the CLP is developed, which is then combined with an existing tabu search algorithm to form a hybrid metaheuristic. Finally, parallel versions are introduced for these algorithms. The emphasis is on CLP instances with a weakly heterogeneous load. Numerical tests based on the well‐known 700 test instances from Bischoff and Ratcliff are performed, and the outcome is compared with methods from other authors. The results show a high solution quality obtained with reasonable computing time.     

Multi-objective multi-population biased random-key genetic algorithm for the 3-D container loading problem

The container loading problem (CLP) has important industrial and commercial application for global logistics and supply chain. Many algorithms have been proposed for solving the 2D/3D container loading problem, yet most of them consider single objective optimization. In practice, container loading involves optimizing a number of objectives. This study aims to develop a multi-objective multi-population biased random-key genetic algorithm for the three-dimensional single container loading problem. In particular, the proposed genetic algorithm applied multi-population strategy and fuzzy logic controller (FLC) to improve efficiency and effectiveness. Indeed, the proposed approach maximizes the container space utilization and the value of total loaded boxes by employing Pareto approach and adaptive weights approach. Numerical experiments are designed to compare the results between the proposed approach and existing approaches in hard and weak heterogeneous cases to estimate the validity of this approach. The results have shown practical viability of this approach. This study concludes with discussions of contributions and future research directions.