Improvement of scatter search using Bees Algorithm

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

This paper studies a kind of hybrid flow shop problem with transportation delays (HFSTD) between consecutive production stages. A scatter search (SS) algorithm is proposed to solve the scheduling problem. A two-point order combination operator is designed for the SS. The authors randomly generate 12 instances to test the performance of the proposed algorithm. Experimental results show that the SS algorithm is efficient and effective for solving the HFSTD scheduling problem.

Multistage hybrid flow shop scheduling problems are considered in this paper. Each stage consists of several identical machines. The jobs are to be processed on any one of the machines at each stage. In most of the scheduling research works it is assumed that all jobs are to be processed at all stages. But in real-life industries some of the jobs may not be processed at some stages. Hence hybrid flow shop scheduling problems with missing operations are considered in this paper with the objective of determining a schedule that minimises makespan. The hybrid flow shop scheduling problems are non-deterministic polynomial time hard (NP-hard) problems. We propose a hybrid meta-heuristic algorithm, namely improved hybrid genetic scatter search (IHGSS) algorithm, based on genetic algorithm and scatter search algorithms. A case study problem of a leading steel furniture manufacturing company in India is presented to illustrate the proposed algorithm. Computational experiments show that the proposed IHGSS algorithm outperforms other heuristic and meta-heuristic algorithms.

This paper presents a new approach based on the Scatter Search (SS) algorithm applied to the Location Management problem using the Location Area (LA) scheme. The LA scheme is used to achieve the best configuration of the network partitioning, into groups of cells (location areas), that minimizes the costs involved. In this work we execute five distinct experiments with the aim of setting the best values for the Scatter Search parameters, using test networks generated with realistic data [1]. We also want to compare the results obtained by this new approach with those achieved through classical strategies, other algorithms from our previous work and also by other authors. The simulation results show that this SS based approach is very encouraging.

A scatter search algorithm for stacking sequence optimisation of laminate composites

Material Recovery Facilities (MRFs) location and waste flow assignment decision problem were investigated. In a three stages network consisted of production factory, landfills and transfer stations, material recovery facilities, the decision problem is to choose a best set of material recovery facilities with capacity constraints and decide the optimal flow on the network to minimize the total operational cost. The problem is firstly formulated a mathematic model. Then, a scatter search algorithm with update strategy of reference set according to the level of the diversity and quality of solutions is developed to solve effectively the model. The computational experiments show that the scatter search algorithm can obtain the valid solution of the location problem and is better than the general scatter search without the special update strategy on solution quality.

Truck scheduling is an important optimization problem for successful crossdocking operations. Current efforts less focus on the problem considering the constraints of product unloading and loading sequences in trucks, which makes scheduling optimization more difficult and easily aggravates inefficiency of unsuitable scheduling. This paper proposes an integer programming model for such problem in a multi-door crossdocking system. The objective is to find an optimal door assignment and sequencing of inbound and outbound trucks that minimizes the makespan and satisfies the constraints. For solving it, a scatter search (SS) algorithm is developed. Computational experiments are conducted to evaluate the performance of the proposed SS approach in comparison with genetic algorithm (GA). The computational results show that SS produces better solutions in shorter CPU times for problem instances with different scales.

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

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

The unique foraging behaviour of bees via waggle dance has been computationally realised as an algorithm named bee colony optimisation (BCO) to solve different types of combinatorial optimisation problems such as travelling salesman problem (TSP). In order to enhance the performance of BCO, local optimisation can be integrated. However, local optimisation incurs high processing overhead especially when all solutions are allowed to undergo the local optimisation. This paper proposes a pruning strategy based on the top-k sequential patterns (TKS) mining algorithm. Specifically, TKS is employed to identify the frequent building blocks along the optimisation process. A total of 19 TSP benchmark problem instances ranging from 318 cities to 1,291 cities were used as the test bed. The proposed pruning strategy shows a significant reduction in terms of the computational time to yield TSP solutions with similar tour length as compared with two state-of-the-art approaches.

The evolutionary metaheuristic called scatter search has been applied successfully to optimization problems for several years. In this paper, we apply the scatter search technique to the well-known 0–1 multidimensional knapsack problem. We propose a new relaxation-based diversification generator, which produces an initial population with elite solutions. The computational results obtained for a set of classic and correlated instances clearly show that (1) this generator can also be used as a heuristic for solving the multidimensional knapsack problem; (2) using the population produced by our generator as a starting point for the scatter search algorithm leads to better performance. We also enhance the scatter search algorithm by integrating memory and by using adapted intensification phases. Overall, the results are interesting and competitive compared to other population-based algorithms, such as genetic algorithms.

In this paper we study two different meta-heuristics to solve a real-word frequency assignment problem (FAP) in GSM networks. We have used a precise mathematical formulation in which the frequency plans are evaluated using accurate interference information coming from a real GSM network. We have developed an improved version of the scatter search (SS) algorithm in order to solve this problem. After accurately tuning this algorithm, it has been compared with a version fixed for the FAP problem of the population-based incremental learning (PBIL) algorithm. The results show that SS obtains better frequency plannings than PBIL for all the experiments performed.

A binary social spider algorithm for uncapacitated facility location problem

New Formulations for the Orienteering Problem

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.