Multi-start Local Search Research Articles

Tramp ship routing and scheduling with speed optimization

Tramp shipping companies are committed to transport a set of contracted cargoes and try to derive additional revenue from carrying optional spot cargoes. Traditionally, models for ship routing and scheduling problems are based on fixed speed and a given fuel consumption rate for each ship. However, in real life a ship’s speed is variable within an interval, and fuel consumption per time unit can be approximated by a cubic function of speed. Here we present the tramp ship routing and scheduling problem with speed optimization, where speed on each sailing leg is introduced as a decision variable. We present a multi-start local search heuristic to solve this problem. To evaluate each move in the local search we have to determine the optimal speed for each sailing leg of a given ship route. To do this we propose two different algorithms. Extensive computational results show that the solution method solves problems of realistic size and that taking speed into consideration in tramp ship routing and scheduling significantly improves the solutions.

Discovering Unique, Low-Energy Pure Water Isomers: Memetic Exploration, Optimization, and Landscape Analysis

The discovery of low-energy stable and meta-stable molecular structures remains an important and unsolved problem in search and optimization. In this paper, we contribute two stochastic algorithms, the archiving molecular memetic algorithm (AMMA) and the archiving basin hopping algorithm (ABHA) for sampling low-energy isomers on the landscapes of pure water clusters (H2O)n. We applied our methods to two sophisticated empirical water cluster models, TTM2.1-F and OSS2, and generated archives of low-energy water isomers (H2O)n n=3-15. Our algorithms not only reproduced previously-found best minima, but also discovered new global minima candidates for sizes 9-15 on OSS2. Further numerical results show that AMMA and ABHA outperformed a baseline stochastic multistart local search algorithm in terms of convergence and isomer archival. Noting a performance differential between TTM2.1-F and OSS2, we analyzed both model landscapes to reveal that the global and local correlation properties of the empirical models differ significantly. In particular, the OSS2 landscape was less correlated and hence, more difficult to explore and optimize. Guided by our landscape analyses, we proposed and demonstrated the effectiveness of a hybrid local search algorithm, which significantly improved the sampling performance of AMMA on the larger OSS2 landscapes. Although applied to pure water clusters in this paper, AMMA and ABHA can be easily modified for subsequent studies in computational chemistry and biology. Moreover, the landscape analyses conducted in this paper can be replicated for other molecular systems to uncover landscape properties and provide insights to both physical chemists and evolutionary algorithmists.

A tabu search heuristic for ship routing and scheduling

The purpose of this paper is to solve a planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. An efficient tabu search algorithm has been developed to ensure quick decision support for the planners. The solutions generated by the tabu search heuristic are compared with those produced by a previously published multi-start local search heuristic. Computational results show that the tabu search heuristic yields optimal or near-optimal solutions to real-life instances within reasonable time. For large and tigthly constrained cases, the tabu search heuristic provides much better solutions than the multi-start local search heuristic. A version of the tabu search heuristic will be integrated as an improved solver in a prototype decision support system used by several shipping companies.

Evaluating a local genetic algorithm as context-independent local search operator for metaheuristics

Local genetic algorithms have been designed with the aim of providing effective intensification. One of their most outstanding features is that they may help classical local search-based metaheuristics to improve their behavior. This paper focuses on experimentally investigating the role of a recent approach, the binary-coded local genetic algorithm (BLGA), as context-independent local search operator for three local search-based metaheuristics: random multi-start local search, iterated local search, and variable neighborhood search. These general-purpose models treat the objective function as a black box, allowing the search process to be context-independent. The results show that BLGA may provide an effective and efficient intensification, not only allowing these three metaheuristics to be enhanced, but also predicting successful applications in other local search-based algorithms. In addition, the empirical results reported here reveal relevant insights on the behavior of classical local search methods when they are performed as context-independent optimizers in these three well-known metaheuristics.

Fleet deployment in liner shipping: a case study

The fleet deployment problem is an important planning problem in liner shipping. It deals with optimally assigning voyages to available vessels in the fleet and determining vessel routes and schedules in a way that minimizes costs or maximizes profit. This paper presents a new model for a fleet deployment problem in liner shipping, and we also propose a multi-start local search heuristic to solve the problem. The heuristic has been embedded in a prototype decision support system (DSS) that has been implemented and tested at Höegh Autoliners, a major global provider of ro-ro (roll-on roll-off) vehicle transportation services. The heuristic was able to produce high-quality solutions within a few minutes to a real planning problem with more than 55 vessels and 150 voyages over a planning horizon of 4–6 months. Tests indicated that the solutions suggested by the DSS gave between 2 and 10% improvements compared with solutions from manual planning. What is almost equally important is that using the DSS can ease the planning process.

Attraction probabilities in variable neighborhood search

Empirical evidence demonstrates that when the same local search operator is used, variable neighborhood search consistently outperforms random multistart local search on all types of combinatorial and global optimization problems tested. In this paper we suggest that this superiority in performance may be explained by the distribution of the attraction basins around a current solution as a function of the distance from the solution. We illustrate with a well-known instance of the multisource Weber problem that the “attraction probabilities” for finding better solutions can be orders of magnitude larger in neighborhoods that are close to the current solution. The paper also discusses the global convergence properties of both general methods in the context of attraction probabilities.

Solving the Multiple Competitive Facilities Location and Design Problem on the Plane

A continuous location problem in which a firm wants to set up two or more new facilities in a competitive environment is considered. Other facilities offering the same product or service already exist in the area. Both the locations and the qualities of the new facilities are to be found so as to maximize the profit obtained by the firm. This is a global optimization problem, with many local optima. In this paper we analyze several approaches to solve it, namely, three multistart local search heuristics, a multistart simulated annealing algorithm, and two variants of an evolutionary algorithm. Through a comprehensive computational study it is shown that the evolutionary algorithms are the heuristics that provide the best solutions. Furthermore, using a set of problems for which the optimal solutions are known, only the evolutionary algorithms were able to find the optimal solutions for all the instances. The evolutionary strategies presented in this paper can be easily adapted to handle other continuous location problems.

多スタート局所探索法を用いた多数人物追跡のための複数能動カメラの同時視線プランニング

多スタート局所探索法を用いた多数人物追跡のための複数能動カメラの同時視線プランニング

On the effectiveness of incorporating randomness and memory into a multi-start metaheuristic with application to the Set Covering Problem

The construction of good starting solutions for multi-start local search heuristics is an important, yet not well-studied problem. In these heuristics, randomization methods are usually applied to explore new promising areas and memory mechanisms are incorporated with the main purpose of reinforcing good solutions. Under the template of a typical multi-start metaheuristic, Meta-RaPS (Meta-heuristic for Randomized Priority Search), this paper presents several randomization methods and memory mechanisms with a focus on comparing their effectiveness and analyzing their interaction effects. With the Set Covering Problem (SCP) as the application problem, it is found that these randomization methods work well for Meta-RaPS with an improvement phase while the memory mechanisms better the solution quality of the construction phase. The quality and efficiency of Meta-RaPS can be improved through the use of both memory mechanisms and randomization methods. This paper also discovers several efficient algorithms that maintain a good balance between randomness and memory and finds the optimal or best-known solutions for the 65 SCP test instances from the OR-library.

2A1-C17 複数人物の追跡のための複数カメラの視線プランニング

This paper describes a view planning of multiple cameras for tracking multiple persons. View planning of cameras is a very important problem in watching multiple persons in a large room by using a few cameras. We select the focuses of attention (FOAs) of cameras efficiently by predicting persons' future positions with their uncertainty. First, we propose an exhaustive search-based planning method and a multi-start local search-based method for tracking persons continuously and compare them. In these methods, we set the FOAs of cameras on the positions so that cameras can catch as many persons as possible. Next, we propose a multi-start local search method for tracking persons intermittently and compare this view planning with others based on a differnt evaluation criterion which allows frequent shifts of the FOAs of cameras. This view planning outperforms the others and is considered to be appropriate for wide area surveillance systems.

A multi-start local search heuristic for ship scheduling—a computational study

We present a multi-start local search heuristic for a typical ship scheduling problem. A large number of initial solutions are generated by an insertion heuristic with random elements. The best initial solutions are improved by a local search heuristic that is split into a quick and an extended version. The quick local search is used to improve a given number of the best initial solutions. The extended local search heuristic is then used to further improve some of the best solutions found. The multi-start local search heuristic is compared with an optimization-based solution approach with respect to computation time and solution quality. The computational study shows that the multi-start local search method consistently returns optimal or near-optimal solutions to real-life instances of the ship scheduling problem within a reasonable amount of computation time.

A multi-start dynasearch algorithm for the time dependent single-machine total weighted tardiness scheduling problem

We extend the dynasearch technique, recently proposed by Congram et al., in the context of time-dependent combinatorial optimization problems. As an application we consider a general time-dependent (idleness) version of the well known single-machine total weighted tardiness scheduling problem, in which the processing time of a job depends on its starting time of execution. We develop a multi-start local search algorithm and present experimental results on several types of instances showing the superiority of the dynasearch neighborhood over the traditional one.

A multi-start local search algorithm for the vehicle routing problem with time windows

In this paper a multi-start local search (MSLS) heuristic is proposed for the vehicle routing problem with time windows (VRPTW). In VRPTW the objective is to design least cost routes for a fleet of identical capacitated vehicles to service geographically scattered customers within pre-specified service time windows. The suggested approach is based on a MSLS framework and several new improvement heuristics. A new speedup technique is introduced for the construction heuristics, and the results of the MSLS are post-optimized by a threshold accepting post-processor. Experimental results on 358 benchmark problems from the literature show that the suggested method is highly efficient and competitive.

共通バッファ制限付きジョブショップスケジューリング問題の解法

A new jobshop scheduling problem with limited common buffers is dealt with in this paper. The standard genetic algorithm is not applicable to the present problem for deadlocks led by buffer constraints. A new algorithm is proposed by combining the genetic algorithm (GA) with a semi-active decoding which avoids deadlocks and satisfies the buffer constraints. Some benchmark problems appending with buffer constraints are tested by both the proposed GA and the multi-start local search method (MLS). Computation results show that the proposed GA outperforms MLS well. Computation is also made by varying the number of common buffers. These results are compared among the available results of the no-buffer jobshop problem and the normal jobshop problem. Consequently the results of the proposed GA are satisfactory.

Performance of a genetic algorithm for the graph partitioning problem

The performance of the genetic algorithm (GA) for the graph partitioning problem (GPP) is investigated by comparison with standard heuristics on well-known benchmark graphs. In general, there is a case where a practical performance of a conventional genetic approach, which performs only simple operations without a local search strategy, is not sufficient. However, it is known that a combination of GA and local search can produce better solutions. From this practice, we incorporate a simple local search algorithm into the GA. In particular, the search ability of the GA is compared with standard heuristics such as multistart local search and simulated annealing, which use the same neighborhood structure of the simple local search, for solving the GPP. Experimental results show that the GA performs better than its competitors.

A Fast Evolutionary Metaheuristic for the Vehicle Routing Problem with Time Windows

This paper presents a new evolutionary metaheuristic for the vehicle routing problem with time windows. Ideas on multi-start local search, ejection chains, simulated annealing and evolutionary computation are combined in a heuristic that is both robust and efficient. The proposed method produces results that are on par with the current best solutions, at a fraction of the computation time needed by previous best approaches. Given the significantly lower time consumption over methods proposed previously in the literature, we consider our approach especially useful in dynamic routing problems, where decisions must be made in real-time.

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

The unconstrained binary quadratic programming problem (BQP) is known to be NP-hard and has many practical applications. This paper presents a simulated annealing (SA)-based heuristic for the BQP. The new SA heuristic for the BQP is based on a simple (1-opt) local search heuristic and designed with a simple cooling schedule, but the multiple annealing processes are adopted. To show practical performances of the SA, we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi-start local search, the previous SA, tabu search, and genetic algorithm incorporating the 1-opt local search. Computational results indicate that our SA leads to high-quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set. Furthermore, the values of new best-known solutions found by the SA for several large instances are also reported.

Local search with perturbations for the prize‐collecting Steiner tree problem in graphs

AbstractGiven an undirected graph with prizes associated with its nodes and weights associated with its edges, the prize‐collecting Steiner tree problem consists of finding a subtree of this graph which minimizes the sum of the weights of its edges plus the prizes of the nodes not spanned. In this paper, we describe a multistart local search algorithm for the prize‐collecting Steiner tree problem, based on the generation of initial solutions by a primal‐dual algorithm using perturbed node prizes. Path‐relinking is used to improve the solutions found by local search and variable neighborhood search is used as a post‐optimization procedure. Computational experiments involving different algorithm variants are reported. Our results show that the local search with perturbations approach found optimal solutions on nearly all of the instances tested. © 2001 John Wiley & Sons, Inc.

Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning.

The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced. In particular, the local structure and the regularity of the dependency graph seems to be important for the performance of an algorithm, and in fact, algorithms that exploit these properties perform significantly better than others which do not. It will be shown that a simple hybrid multi-start local search exploiting locality in the structure of the graphs is able to find optimum or near optimum solutions very quickly. However, if the problem size increases or the graphs become unstructured, a memetic algorithm (a genetic algorithm incorporating local search) is shown to be much more effective.

Sequential Stopping Rules for Random Optimization Methods with Applications to Multistart Local Search

Sequential stopping rules are described for several stochastic algorithms that estimate the global minimum of a function. Stopping rules are described for pure random search and stratified random search. These stopping rules use an estimate of the probability measure of the $\epsilon$-close points to terminate these algorithms when a specified confidence has been achieved. Numerical results indicate that these stopping rules require fewer samples and are more reliable than the previous stopping rules for these algorithms. These stopping rules can also be applied to multistart local search and stratified multistart local search. Numerical results on a standard test set show that these stopping rules can perform as well as Bayesian stopping rules for multistart local search.