Combining simulated annealing with local search heuristics

We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this meta-heuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon local search methods very significantly. For the traveling salesman problem with randomly distributed cities, in a square, the procedure improves on 3-opt by 1.6%, and on Lin-Kernighan local search by 1.3%. For the partitioning of sparse random graphs of average degree equal to 5, the improvement over Kernighan-Lin local search is 8.9%. For both CO problems, we obtain new best heuristics.     

Hybrid meta-heuristic algorithms for solving network design problem

Network design problem has been, and is, an important problem in transportation. Following an earlier effort in designing a meta-heuristic search technique by an ant system, this paper attempts to hybridize this concept with other meta-heuristic concepts such as genetic algorithm, simulated annealing, and tabu search. Seven hybrids have been devised and tested on the network of Sioux Falls. It has been observed that the hybrids are more effective to solve the network design problem than the base ant system. Application of the hybrid containing all four concepts on a real network of a city with over 2 million population has also proved to be more effective than the base network, in the sense of finding better solutions sooner.     

On a Local-Search Heuristic for a Class of Tracking Error Minimization Problems in Portfolio Management

In this paper we describe a 2-phase simulated annealing heuristic approach for a special class of portfolio management problems: the problem of optimizing a stock fund with respect to tracking error and transaction costs over time subject to a set of complex constraints with a linear factor return model “feeding” the objective function with data. Our results on managing two real-world funds of a major German capital investment company have shown that this meta-heuristic provides proposals for the fund manager which are feasible with respect to the investment guidelines and excellent in quality in acceptable time. Thus the approach is ideally suited to be used routinely and interactively within a decision support system to assist the fund manager in his complex task of portfolio control and optimization.     

Hub location–allocation in intermodal logistic networks

Within the context of intermodal logistics, the design of transportation networks becomes more complex than it is for single mode logistics. In an intermodal network, the respective modes are characterized by the transportation cost structure, modal connectivity, availability of transfer points and service time performance. These characteristics suggest the level of complexity involved in designing intermodal logistics networks. This research develops a mathematical model using the multiple-allocation p-hub median approach. The model encompasses the dynamics of individual modes of transportation through transportation costs, modal connectivity costs, and fixed location costs under service time requirements. A tabu search meta-heuristic is used to solve large size (100 node) problems. The solutions obtained using this meta-heuristic are compared with tight lower bounds developed using a Lagrangian relaxation approach. An experimental study evaluates the performance of the intermodal logistics networks and explores the effects and interactions of several factors on the design of intermodal hub networks subject to service time requirements.     

A robust parameter design for multi-response problems

Most real world search and optimization problems naturally involve multiple responses. In this paper we investigate a multiple response problem within desirability function framework and try to determine values of input variables that achieve a target value for each response through three meta-heuristic algorithms such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Each algorithm has some parameters that need to be accurately calibrated to ensure the best performance. For this purpose, a robust calibration is applied to the parameters by means of Taguchi method. The computational results of these three algorithms are compared against each others. The superior performance of SA over TS and TS over GA is inferred from the obtained results in various situations.     

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature.     

An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem

In this paper we consider the two-dimensional (2D) rectangular packing problem, where a fixed set of items have to be allocated on a single object. Two heuristics, which belong to the class of packing procedures that preserve bottom-left (BL) stability, are hybridised with three meta-heuristic algorithms (genetic algorithms (GA), simulated annealing (SA), naı̈ve evolution (NE)) and local search heuristic (hill-climbing). This study compares the hybrid algorithms in terms of solution quality and computation time on a number of packing problems of different size. In order to show the effectiveness of the design of the different algorithms, their performance is compared to random search (RS) and heuristic packing routines.     

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.     

A simulated annealing driven multi-start algorithm for bound constrained global optimization

A derivative-free simulated annealing driven multi-start algorithm for continuous global optimization is presented. We first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient-based trial point generation. We then suitably embed the multi-start procedure within the simulated annealing algorithm. We modify the derivative-free pattern search method and use it as the local search in the multi-start procedure. We study the convergence properties of the algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with a gradient-based simulated annealing algorithm and three population-based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms, specially for problems requiring ‘direct search’ type algorithm.     

Heuristic,meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation

The allocation of fresh produce to shelf space represents a new decision support research area which is motivated by the desire of many retailers to improve their service due to the increasing demand for fresh food. However, automated decision making for fresh produce allocation is challenging because of the very short lifetime of fresh products. This paper considers a recently proposed practical model for the problem which is motivated by our collaboration with Tesco. Moreover, the paper investigates heuristic and meta-heuristic approaches as alternatives for the generalized reduced gradient algorithm, which becomes inefficient when the problem size becomes larger. A simpler single-item inventory problem is firstly studied and solved by a polynomial time bounded procedure. Several dynamic greedy heuristics are then developed for the multi-item problem based on the procedure for the single-item inventory problem. Experimental results show that these greedy heuristics are much more efficient and provide competitive results when compared to those of a multi-start generalized reduced gradient algorithm. In order to further improve the solution, we investigated simulated annealing, a greedy randomized adaptive search procedure and three types of hyper-heuristics. Their performance is tested and compared on a set of problem instances which are made publicly available for the research community.     

A controlled search simulated annealing method for the single machine weighted tardiness problem

In this paper, a new controlled search simulated annealing method is developed for addressing the single machine weighted tardiness problem. The proposed method is experimentally shown to solve optimally 99% of fifteen job problems with less than 0.2 CPU seconds, and to solve one hundred job problems as accurately as any existing methods, but with far less computational effort. This superior performance is achieved by using controlled search strategies that employ a good initial solution, a small neighborhood for local search, and acceptance probabilities of inferior solutions that are independent of the change in the objective function value.     

Parallelization of population-based multi-objective meta-heuristics: An empirical study

In single-objective optimization it is possible to find a global optimum, while in the multi-objective case no optimal solution is clearly defined, but several that simultaneously optimize all the objectives. However, the majority of this kind of problems cannot be solved exactly as they have very large and highly complex search spaces. Recently, meta-heuristic approaches have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. Most of these meta-heuristics use a population of solutions, and hence the runtime increases when the population size grows. An interesting way to overcome this problem is to apply parallel processing. This paper analyzes the performance of several parallel paradigms in the context of population-based multi-objective meta-heuristics. In particular, we evaluate four alternative parallelizations of the Pareto simulated annealing algorithm, in terms of quality of the solutions, and speedup.     

An evolutionary algorithm with the partial sequential forward floating search mutation for large-scale feature selection problems

Several meta-heuristic algorithms, such as evolutionary algorithms (EAs) and genetic algorithms (GAs), have been developed for solving feature selection problems due to their efficiency for searching feature subset spaces in feature selection problems. Recently, hybrid GAs have been proposed to improve the performance of conventional GAs by embedding a local search operation, or sequential forward floating search mutation, into the GA. Existing hybrid algorithms may damage individuals’ genetic information obtained from genetic operations during the local improvement procedure because of a sequential process of the mutation operation and the local improvement operation. Another issue with a local search operation used in the existing hybrid algorithms is its inappropriateness for large-scale problems. Therefore, we propose a novel approach for solving large-sized feature selection problems, namely, an EA with a partial sequential forward floating search mutation (EAwPS). The proposed approach integrates a local search technique, that is, the partial sequential forward floating search mutation into an EA method. Two algorithms, EAwPS-binary representation (EAwPS-BR) for medium-sized problems and EAwPS-integer representation (EAwPS-IR) for large-sized problems, have been developed. The adaptation of a local improvement method into the EA speeds up the search and directs the search into promising solution areas. We compare the performance of the proposed algorithms with other popular meta-heuristic algorithms using the medium- and large-sized data sets. Experimental results demonstrate that the proposed EAwPS extracts better features within reasonable computational times.     

Annealing-tabu PAES: a multi-objective hybrid meta-heuristic

Most real-life optimization problems require taking into account not one, but multiple objectives simultaneously. In most cases these objectives are in conflict, i.e. the improvement of some objectives implies the deterioration of others. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined, but rather a set of solutions. In the last decade most papers dealing with multi-objective optimization use the concept of Pareto-optimality. The goal of Pareto-based multi-objective strategies is to generate a front (set) of non-dominated solutions as an approximation to the true Pareto-optimal front. However, this front is unknown for problems with large and highly complex search spaces, which is why meta-heuristic methods have become important tools for solving this kind of problem. Hybridization in the multi-objective context is nowadays an open research area. This article presents a novel extension of the well-known Pareto archived evolution strategy (PAES) which combines simulated annealing and tabu search. Experiments on several mathematical problems show that this hybridization allows an improvement in the quality of the non-dominated solutions in comparison with PAES, and also with its extension M-PAES.     

Dynamic tabu search strategies for the traveling purchaser problem

Tabu search is a metastrategy for guiding known heuristics to overcome local optimality with a large number of successful applications reported in the literature. In this paper we investigate two dynamic strategies, the reverse elimination method and the cancellation sequence method. The incorporation of strategic oscillation as well as a combination of these methods are developed. The impact of the different methods is shown with respect to the traveling purchaser problem, a generalization of the classical traveling salesman problem. The traveling purchaser problem is the problem of determining a tour of a purchaser buying several items in different shops by minimizing the total amount of travel and purchase costs. A comparison of the tabu search strategies with a simulated annealing approach is presented, too.     

Solution approaches for the capacitated single allocation hub location problem using ant colony optimisation

Hub and spoke type networks are often designed to solve problems that require the transfer of large quantities of commodities. This can be an extremely difficult problem to solve for constructive approaches such as ant colony optimisation due to the multiple optimisation components and the fact that the quadratic nature of the objective function makes it difficult to determine the effect of adding a particular solution component. Additionally, the amount of traffic that can be routed through each hub is constrained and the number of hubs is not known a-priori. Four variations of the ant colony optimisation meta-heuristic that explore different construction modelling choices are developed. The effects of solution component assignment order and the form of local search heuristics are also investigated. The results reveal that each of the approaches can return optimal solution costs in a reasonable amount of computational time. This may be largely attributed to the combination of integer linear preprocessing, powerful multiple neighbourhood local search heuristic and the good starting solutions provided by the ant colonies.     

Crane scheduling with non-crossing constraint

In this paper, we examine crane scheduling for ports. This important component of port operations management is studied when the non-crossing spatial constraint, which is common to crane operations, is considered. We assume that ships can be divided into holds and that cranes can move from hold to hold but jobs are not pre-emptive, so that only one crane can work on one hold or job to complete it. Our objective is to minimize the latest completion time for all jobs. We formulate this problem as an integer programming problem. We provide the proof that this problem is NP-complete and design a branch-and-bound algorithm to obtain optimal solutions. A simulated annealing meta-heuristic with effective neighbourhood search is designed to find good solutions in larger size instances. The elaborate experimental results show that the branch-and-bound algorithm runs much faster than CPLEX and the simulated annealing approach can obtain near optimal solutions for instances of various sizes.     

基于模拟退火的CRS算法

本文是对非线性规划问题提出的一种算法,该算法把模拟退火算法应用到CRS算法中,根据模拟退火算法每一次迭代都体现集中和扩散两个策略的平衡的特点,使CRS算法更能够搜索到全局最优解,而不会陷入局部最优解。最后把提出的算法应用到两个典型的函数优化问题中,结果表明,算法是可行的、有效的     

Analyzing the Performance of Generalized Hill Climbing Algorithms

Generalized hill climbing algorithms provide a framework to describe and analyze metaheuristics for addressing intractable discrete optimization problems. The performance of such algorithms can be assessed asymptotically, either through convergence results or by comparison to other algorithms. This paper presents necessary and sufficient convergence conditions for generalized hill climbing algorithms. These conditions are shown to be equivalent to necessary and sufficient convergence conditions for simulated annealing when the generalized hill climbing algorithm is restricted to simulated annealing. Performance measures are also introduced that permit generalized hill climbing algorithms to be compared using random restart local search. These results identify a solution landscape parameter based on the basins of attraction for local optima that determines whether simulated annealing or random restart local search is more effective in visiting a global optimum. The implications and limitations of these results are discussed.     

A Controlled Random Search Technique Incorporating the Simulated Annealing Concept for Solving Integer and Mixed Integer Global Optimization Problems

In this paper, a computational algorithm, named RST2ANU algorithm, has been developed for solving integer and mixed integer global optimization problems. This algorithm, which primarily is based on the original controlled random search approach of Price [22i], incorporates a simulated annealing type acceptance criterion in its working so that not only downhill moves but also occasional uphill moves can be accepted. In its working it employs a special truncation procedure which not only ensures that the integer restrictions imposed on the decision variables are satisfied, but also creates greater possibilities for the search leading to a global optimal solution. The reliability and efficiency of the proposed RST2ANU algorithm has been demonstrated on thirty integer and mixed integer optimization problems taken from the literature. The performance of the algorithm has been compared with the performance of the corresponding purely controlled random search based algorithm as well as the standard simulated annealing algorithm. The performance of the method on mathematical models of three realistic problems has also been demonstrated.