Scatter Search for the Point-Matching Problem in 3D Image Registration

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in 1960s for combining decision rules and problem constraints such as the surrogate constraint method, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we develop a general purpose heuristic for a class of nonlinear optimization problems. The procedure is based on the scatter search methodology and treats the objective function evaluation as a black box, making the search algorithm context-independent. Most optimization problems in the chemical and bio-chemical industries are highly nonlinear in either the objective function or the constraints. Moreover, they usually present differential-algebraic systems of constraints. In this type of problem, the evaluation of a solution or even the feasibility test of a set of values for the decision variables is a time-consuming operation. In this context, the solution method is limited to a reduced number of solution examinations. We have implemented a scatter search procedure in Matlab (Mathworks, 2004) for this special class of difficult optimization problems. Our development goes beyond a simple exercise of applying scatter search to this class of problems, but presents innovative mechanisms to obtain a good balance between intensification and diversification in a short-term search horizon. Computational comparisons with other recent methods over a set of benchmark problems favor the proposed procedure.

It has recently been important to obtain optimal solutions to multidimensional nonlinear integer programming problems with multiple constraints. The surrogate constraint method is very effective in obtaining high-quality solutions of the original multidimensional problems. The surrogate constraint method translates a multidimensional problem into a one-dimensional problem by using a surrogate multiplier. But when there exists a surrogate duality gap between the translated one-dimensional problem and the original multidimensional problem, the optimal solution to the surrogate problem is not optimal with respect to the original problem. Nakagawa has recently proposed an improved surrogate constraint (ISC) method that can reduce the surrogate duality gap and provide an exact solution to the original problem. By using this method, we can obtain exact solutions to separable nonlinear integer programming problems with 1000 variables and 5 or 6 constraints. The ISC method requires an optimal surrogate multiplier. However, there are problems of calculation time and memory requirements in the algorithm for obtaining the optimal surrogate multiplier when the number of constraints is large. In this paper, the Dyer algorithm and Nakagawa's Cutting-Off Polyhedron (COP) algorithm for an algorithm that obtains the optimal surrogate multiplier in the ISC method are compared in computational experiments, and the advantages and disadvantages of these algorithms are investigated. In addition, an improved Dyer algorithm is proposed and computational experiments show that the improved algorithm is more effective than the original algorithm. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(8): 38–48, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20114

Hybrid scatter search and path relinking for the capacitated p-median problem

Reservoir simulation plays an important role in managerial decisions during the life of a reservoir. Thus, it is vital that the simulations present an accurate prospect of real reservoir performance. The main goal of the History Matching (HM) process is to improve the quality of numerical models by contrasting simulated with observed data. A typical HM process evaluates a chosen objective function (OF) comprised by non-linear functions on the uncertain reservoir properties that measure the current mismatch. Thus, the HM problem is a minimization problem where the decision variables are reservoir characterization properties and the goal is to find a set of values for the decision variables that minimize the OF. This paper focuses on the use of an optimization technique called Scatter Search (SS) to perform the HM. The main feature of SS is that it works on a set of solutions called the reference set. The goal is to improve the overall quality of the reference set after each new iteration. New solutions are generated by a non-convex combination of reference solutions. The proposed methodology was used in both automatic and assisted HM processes and the analyzed reservoir models presented increasing challenges to the algorithm. This paper describes how the HM problem was solved with the SS framework, the expected performance of the methodology in dealing with complex solution spaces and also points how it can be expanded to better scale to a growing number of optimization parameters. The application of the SS methodology to the HM problem is a recent trend. Unlike most metaheuristics, SS can be effective even when the simulation time of each instance of the problem is long. Most of the current HM methodologies do not perform well when the solution space is both large and complex.

The evolutionary, population based metaheuristic called Scatter Search has been successfully applied to many combinatorial optimization problems. Within the Scatter Search framework, however, there are numerous alternatives for how to implement the different components of the search. In this paper we explore a variety of these alternatives in a Scatter Search for solving the demand constrained multidimensional knapsack problem. Our best Scatter Search implementations produce good results, compared both to previous heuristic work as well as to exact solvers.

PurposeThe purpose of this paper is to tackle a satellite module layout design problem (SMLDP). As a complex engineering layout and combinatorial optimization problem, SMLDP cannot be solved effectively by traditional exact methods. Although evolutionary algorithms (EAs) have shown some promise of tackling SMLDP in previous work, the solution quality and computational efficiency still pose a challenge. This paper aims to address these two issues.Design/methodology/approachScatter search (SS) and a cooperative co‐evolutionary architecture are integrated to form a new approach called a cooperative co‐evolutionary scatter search (CCSS). The cooperative co‐evolutionary architecture is characterized by the decomposition and cooperation for dealing with complex engineering problems. SS is a flexible meta‐heuristic method that can effectively solve the combinatorial optimization problems. Designing the elements of SS is context‐dependent. Considering the characteristics of SMLDP, our work focuses on two folds: the diversification method, and the reference set update method. The diversification method is built on the method of coordinate transformation and the controlled randomness. The reference set is updated by the static method on the basis of two dissimilarities. Two test problems for circles packing illustrated the capacity of SS. However, when solving SMLDP, SS shows some limitations in the computational time and quality. This study adopts divide‐conquer‐coordination strategy to decompose SMLDP into several layout sub‐problems. Then CCSS is applied to cooperatively solve these sub‐problems. The experimental results illustrate the capability of the proposed approach in tackling the complex problem with less computational effort.FindingsApplying CCSS to SMLDP can obtain satisfying solutions in terms of quality and computational efficiency. This contrasts with the limiting experimental results of SMLDP with some approaches (including modified SS).Originality/valueA new CCSS is proposed to provide an effective and efficient way of solving SMLDP. Some elements of SS are improved to address the layout problem. SMLDP is decomposed into several sub‐problems that can be solved cooperatively by CCSS after its characteristics are taken into consideration.

Metaheuristics are solution methods which combine local improvement procedures and higher strategies for solving combinatorial and nonlinear optimization problems. In general, metaheuristics require an important amount of effort focused on parameter setting to improve its performance. In this work a 2-level metaheuristic approach is proposed so that Scatter Search and Ant Colony Optimization act as “low level metaheuristics, whose parameters are set by a “higher level Genetic Algorithm during execution, seeking to improve the performance and to reduce the maintenance. The Set Covering Problem is taken as reference since is one of the most important optimization problems, serving as basis for facility location problems, airline crew scheduling, nurse scheduling, and resource allocation.

This paper explores different crossover operators and how they affect the Scatter Search (SS) algorithm in unconstrained function optimization. It also explores how the size of the reference set affects convergence and robustness. An introduction to Scatter Search is given along with the typical template. It follows with a thorough explanation of the specific implementation that is used. Two types of tests are designed: (1) what is the best fitness value that it can reach within a maximum number of fitness evaluations and (2) how fast it can converge to goal fitness. These tests are performed using different crossover operators and reference set sizes. Results are also compared apples to apples with a basic implementation of Particle Swarm Optimization (PSO). The results show that although PSO is quicker at converging, SS shows more robustness with higher overall success rates.

A scatter search algorithm for stacking sequence optimisation of laminate composites

An empirical investigation on parallelization strategies for Scatter Search

Scatter search (SS) and path relinking (PR) are evolutionary methods that have been successfully applied to a wide range of hard optimization problems. The fundamental concepts and principles of the methods were first proposed in the 1970s and 1980s, and were based on formulations, dating back to the 1960s, for combining decision rules and problem constraints. The methods use strategies for search diversification and intensification that have proved effective in a variety of optimization problems and that have sometimes been embedded in other evolutionary methods to yield improved performance. This paper examines the scatter search and path relinking methodologies from both conceptual and practical points of view, and identifies certain connections between their strategies and those adopted more recently by particle swarm optimization. The authors describe key elements of the SS & PR approaches and apply them to a hard combinatorial optimization problem: the minimum linear arrangement problem, which has been used in applications of structural engineering, VLSI and software testing.

The effect of elite pool in hybrid population-based meta-heuristics for solving combinatorial optimization problems

The probabilistic travelling salesman problem (PTSP) is an extension of the well-known travelling salesman problem (TSP), which has been extensively studied in the field of combinatorial optimization. The goal of the TSP is to find the minimum length of a tour to all customers, given the distances between all pairs of customers whereas the objective of the PTSP is to minimize the expected length of the a priori tour where each customer requires a visit only with a given probability (Bertsimas, 1988; Bertsimas et al., 1990; Jaillet, 1985). The main difference between the PTSP and the TSP is that in the PTSP the probability of each node being visited is between 0.0 and 1.0 while in TSP the probability of each node being visited is 1.0. Due to the fact that the element of uncertainty not only exists, but also significantly affects the system performance in many real-world transportation and logistics applications, the results from the PTSP can provide insights into research in other probabilistic combinatorial optimization problems. Moreover, the PTSP can also be used to model many real-world applications in logistical and transportation planning, such as daily pickup-delivery services with stochastic demand, job sequencing involving changeover cost, design of retrieval sequences in a warehouse or in a cargo terminal operations, meals on wheels in senior citizen services, trip-chaining activities, vehicle routing problem with stochastic demand, and home delivery service under e-commerce (Bartholdi et al., 1983; Bertsimas et al., 1995; Campbell, 2006; Jaillet, 1988; Tang & Miller-Hooks, 2004). Early PTSP computational studies, dating from 1985, adopted heuristic approaches that were modified from the TSP (e.g., nearest neighbor, savings approach, spacefilling curve, radial sorting, 1-shift, and 2-opt exchanges) (Bartholdi & Platzman, 1988; Bertsimas, 1988; Bertsimas & Howell, 1993; Jaillet, 1985, 1987; Rossi & Gavioli, 1987). With its less than satisfactory performance in yielding solution quality, researchers in the recent years switch to metaheuristic methods, such as ant colony optimization (Bianchi, 2006; Branke & Guntsch, 2004), evolutionary algorithm (Liu et al., 2007), simulated annealing (Bowler et al., 2003), threshold accepting (Tang & Miller-Hooks, 2004) and scatter search (Liu, 2006, 2007, 2008). Because the genetic algorithm (GA), a conceptual framework of the population-based metaheuristic method, has been shown to yield promising outcomes for solving various complicated optimization problems in the past three decades (Back et al., 1997; Davis, 1991; O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Parallel image restoration using surrogate constraint methods

A Hybrid Heuristic in GPU-CPU Based on Scatter Search for the Generalized Assignment Problem