Heuristics for container loading of furniture

We consider a container loading problem that occurs at a typical furniture manufacturer. Each furniture item has an associated profit. Given container dimensions and a set of furniture items, the problem is to determine a subset of items with maximal profit sum that is loadable in the container. In the studied company, the problem arises hundreds of times daily during transport planning. Instances may contain more than one hundred different items with irregular shapes. To solve this complex problem we apply a set of heuristics successively that each solve one part of the problem. Large items are combined in specific structures to ensure proper protection of the items during transportation and to simplify the problem. The solutions generated by the heuristic has an average loading utilization of 91.3% for the most general instances with average running times around 100 seconds.     

Global Optimization by Multilevel Coordinate Search

Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.     

Heuristics and exact methods for number partitioning

Number partitioning is a classical NP-hard combinatorial optimization problem, whose solution is challenging for both exact and approximative methods. This work presents a new algorithm for number partitioning, based on ideas drawn from tree search, breadth first search, and beam search. A new set of benchmark instances for this problem is also proposed. The behavior of the new method on this and other testbeds is analyzed and compared to other well known heuristics and exact algorithms.     

A Parallel Grasp for the Steiner Tree Problem in Graphs Using a Hybrid Local Search Strategy

In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for the Steiner problem in graphs. GRASP is a two-phase metaheuristic. In the first phase, solutions are constructed using a greedy randomized procedure. Local search is applied in the second phase, leading to a local minimum with respect to a specified neighborhood. In the Steiner problem in graphs, feasible solutions can be characterized by their non-terminal nodes (Steiner nodes) or by their key-paths. According to this characterization, two GRASP procedures are described using different local search strategies. Both use an identical construction procedure. The first uses a node-based neighborhood for local search, while the second uses a path-based neighborhood. Computational results comparing the two procedures show that while the node-based variant produces better quality solutions, the path-based variant is about twice as fast. A hybrid GRASP procedure combining the two neighborhood search strategies is then proposed. Computational experiments with a parallel implementation of the hybrid procedure are reported, showing that the algorithm found optimal solutions for 45 out of 60 benchmark instances and was never off by more than 4% of the optimal solution value. The average speedup results observed for the test problems show that increasing the number of processors reduces elapsed times with increasing speedups. Moreover, the main contribution of the parallel algorithm concerns the fact that larger speedups of the same order of the number of processors are obtained exactly for the most difficult problems.     

一般约束极大极小优化问题一个强收敛的广义梯度投影算法

该文考虑求解带非线性不等式和等式约束的极大极小优化问题,借助半罚函数思想,提出了一个新的广义投影算法.该算法具有以下特点:由一个广义梯度投影显式公式产生的搜索方向是可行下降的;构造了一个新型的最优识别控制函数;在适当的假设条件下具有全局收敛性和强收敛性.最后,通过初步的数值试验验证了算法的有效性.     

Heuristics for workforce planning with worker differences

This study considers decisions in workforce management assuming individual workers are inherently different as measured by general cognitive ability (GCA). A mixed integer programming (MIP) model that determines different staffing decisions (i.e., hire, cross-train, and fire) in order to minimize workforce related costs over multiple periods is described. Solving the MIP for a large problem instance size is computationally burdensome. In this paper, two linear programming (LP) based heuristics and a solution space partition approach are presented to reduce the computational time. A genetic algorithm was also implemented as an alternative method to obtain better solutions and for comparison to the heuristics proposed. The heuristics were applied to realistic manufacturing systems with a large number of machine groups. Experimental results shows that performance of the LP based heuristics performance are surprisingly good and indicate that the heuristics can solve large problem instances effectively with reasonable computational effort.     

A sequential quadratically constrained quadratic programming method for unconstrained minimax problems

In this paper, a sequential quadratically constrained quadratic programming (SQCQP) method for unconstrained minimax problems is presented. At each iteration the SQCQP method solves a subproblem that involves convex quadratic inequality constraints and a convex quadratic objective function. The global convergence of the method is obtained under much weaker conditions without any constraint qualification. Under reasonable assumptions, we prove the strong convergence, superlinearly and quadratic convergence rate.     

基于非单调线搜索非拟牛顿法的全局收敛性

本文就非拟牛顿法在无约束最优化问题上，对采用非单调线搜索的情况下是否具有全局收敛性进行了研究，在目标函数满足一致凸的条件下，证明了非拟牛顿族是全局收敛的．     

Heuristics—the relational approach

A review of the literature on heuristics would suggest two approaches to their use in problem solving: mathematical and engineering. It is suggested however that there is a third approach for real world application, which the authors have called relational. Instead of investigating a problem through the medium of mathematical models and then deriving heuristics because direct optimising techniques are not available, it is advocated that a close relationship between problem owner and problem solver can be achieved by setting down together the decision rules that the owner employs. In this way, a heuristic model is developed directly, with the opportunity to introduce additional procedures as the situation allows. The result is a consistent control mechanism which is invaluable for both strategic and operational decision making. The model can be a predictor of the effects of policy decisions as well as a means by which those decisions can be implemented and monitored, dependent as much upon the balancing of sometimes conflicting objectives by management as upon the setting of bounds to achieve a guaranteed performance.     

Heuristics for the Stochastic Eulerian Tour Problem

The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. The SETP is NP-hard and in this paper, we develop three constructive heuristics for this problem. The first two are greedy tour construction heuristics while the third is a sub-tour concatenation heuristic. Our experimental results show that for grid networks, the sub-tour concatenation heuristic performs well when the probability of service of each edge is greater than 0.1. For Euclidean networks, as the number of edges increases, the second heuristic performs the best among the three. Also, the expected length of our overall best solution is lower than the expected length of a random tour by up to 10% on average for grid networks and up to 2% for Euclidean networks.     

Enhancing Stochastic Search Performance by Value-Biased Randomization of Heuristics

This paper investigates the utility of introducing randomization as a means of boosting the performance of search heuristics. We introduce a particular approach to randomization, called Value-biased stochastic sampling (VBSS), which emphasizes the use of heuristic value in determining stochastic bias. We offer an empirical study of the performance of value-biased and rank-biased approaches to randomizing search heuristics. We also consider the use of these stochastic sampling techniques in conjunction with local hill-climbing. Finally, we contrast the performance of stochastic sampling search with more systematic search procedures as a means of amplifying the performance of search heuristics.     

Search Heuristics for Resource Constrained Project Scheduling

We develop a search procedure for project scheduling problems with multiple resource constraints as well as precedence constraints. The procedure is applied to three popular search heuristics, simulated annealing, tabu search and genetic algorithms. In the heuristics, a solution is represented with a string of numbers each of which denotes priority of each activity. The priorities are used to select an activity for scheduling among competing ones. The search heuristics with this encoding method can always generate feasible neighbourhood solutions for a given solution. Moreover, this encoding method is very flexible in that problems with objective functions of a general functional form (such as a nonlinear function) and complex constraints can be considered without much difficulty. Results of computational tests on the performance of the search heuristics showed that the search heuristics, especially the simulated annealing and tabu search algorithms worked better than existing heuristics.     

Global Optimization using Dynamic Search Trajectories

Two global optimization algorithms are presented. Both algorithms attempt to minimize an unconstrained objective function through the modeling of dynamic search trajectories. The first, namely the Snyman–Fatti algorithm, originated in the 1980's and still appears an effective global optimization algorithm. The second algorithm is currently under development, and is denoted the modified bouncing ball algorithm. For both algorithms, the search trajectories are modified to increase the likelihood of convergence to a low local minimum. Numerical results illustrate the effectiveness of both algorithms.     

Tabu Search for Frequency Assignment in Mobile Radio Networks

The main goal of the Frequency Assignment Problem in mobile radio networks consists of assigning a limited number of frequencies to each radio cell in a cellular network while minimizing electromagnetic interference due to the reuse of frequencies. This problem, known to be NP-hard, is of great importance in practice since better solutions will allow a telecommunications operator to manage larger cellular networks. This paper presents a new Tabu Search algorithm for this application. The algorithm is tested on realistic and large problem instances and compared with other methods based on simulated annealing, constraint programming and graph coloring algorithms. Empirical evidence shows that the Tabu algorithm is very competitive by giving the best solutions to the tested instances.     

多产品单层能力受限批量问题的前向启发式算法的可行性过程

本文讨论多产品、单层、能力受限批量问题的前向启发式算法,指出了这类算法中现有算法的一些不足之处。为了克服这些不足,我们给出了可行解存在的充分必要条件,并在此基础上提出一个可行化算法。     

Stochastic Methods for Practical Global Optimization

Engineering design problems often involve global optimization of functions that are supplied as black box functions. These functions may be nonconvex, nondifferentiable and even discontinuous. In addition, the decision variables may be a combination of discrete and continuous variables. The functions are usually computationally expensive, and may involve finite element methods. An engineering example of this type of problem is to minimize the weight of a structure, while limiting strain to be below a certain threshold. This type of global optimization problem is very difficult to solve, yet design engineers must find some solution to their problem – even if it is a suboptimal one. Sometimes the most difficult part of the problem is finding any feasible solution. Stochastic methods, including sequential random search and simulated annealing, are finding many applications to this type of practical global optimization problem. Improving Hit-and-Run (IHR) is a sequential random search method that has been successfully used in several engineering design applications, such as the optimal design of composite structures. A motivation to IHR is discussed as well as several enhancements. The enhancements include allowing both continuous and discrete variables in the problem formulation. This has many practical advantages, because design variables often involve a mixture of continuous and discrete values. IHR and several variations have been applied to the composites design problem. Some of this practical experience is discussed.     

A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs

In this paper we present an algorithm for solving nonconvex quadratically constrained quadratic programs (all-quadratic programs). The method is based on a simplicial branch-and-bound scheme involving mainly linear programming subproblems. Under the assumption that a feasible point of the all-quadratic program is known, the algorithm guarantees an -approximate optimal solution in a finite number of iterations. Computational experiments with an implementation of the procedure are reported on randomly generated test problems. The presented algorithm often outperforms a comparable rectangular branch-and-bound method.     

Using modifications to Grover’s Search algorithm for quantum global optimization

We study the problem of finding a global optimal solution to discrete optimization problems using a heuristic based on quantum computing methods. (Knowledge of quantum computing ideas is not necessary to read this paper.) We focus on a successful quantum computing method introduced by Baritompa, Bulger, and Wood, that we refer to as the BBW algorithm, and develop two modifications. First, we modify the BBW algorithm to achieve a dramatic speedup that lets us extend the known BBW static schedule from 33 to 43 points, thereby increasing its applicability. We further modify it by converting it from a static method to a dynamic one. Experimental results show the value of this latter modification.     

Heuristics for the fixed cost median problem

We describe in this paper polynomial heuristics for three important hard problems—the discrete fixed cost median problem (the plant location problem), the continuous fixed cost median problem in a Euclidean space, and the network fixed cost median problem with convex costs. The heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points. The derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem.