Scatter Search Algorithm Research Articles

Optimum contributions of hydropower reservoirs to the minimum flow of Vu Gia – Thu Bon river basin

Abstract Upstream hydropower development has a great impact on downstream flows. According to the Regulation of Multi-reservoir Operation in Vu Gia – Thu Bon River Basin (Regulation 15371), four large-scale upstream reservoirs must discharge certain flow during the dry season to increase water levels at downstream hydrological stations named Ai Nghia and Giao Thuy. These stations are used as the control points for the downstream water supply. An optimizing-simulation based model was developed that both maximizes total electricity production and ensures minimum flow downstream as required. A thousand combinations of the reservoir inflows were generated by Monte Carlo simulation, considering the correlation between tributaries. Then, the Scatter search algorithm available in the Optquest module of Crystal Ball was used to find the optimal release from the reservoirs. The results show that the current Regulation 1537 can be improved for more efficient water resources management.

Improved scatter search algorithm based on meerkat clan algorithm to solve NP-hard problems

A modified Scatter Search (SS) algorithm based on Meerkat Clan Algorithm (MCA) has been presented in this paper. SS is one of the important metaheuristic algorithms, while the MCA is one of the recent swarm intelligence algorithms. The modified SS algorithm, including the main steps of MCA, through it the diversity and exploration of SS-MCA's solutions, have improved. The proposed algorithm has been applied to two important NP-Hard problems (Travelling Salesman Problem (TSP) and Flexible Job Shop Scheduling Problem (FJSSP)) to verify the performance of SS-MCA. The experimental results show that the performance of SS-MCA is better than both SS and MCA, respectively.

Inverse Design of a Taper by Scatter Search Metaheuristic

This paper deals with the optimization of photonic structures, specifically waveguide couplers between a continuous waveguide (CWG) and a periodically segmented waveguide (PSW). For this purpose, a numerical technique called finite element method (FEM) is used in conjunction with an adapted optimization technique called Scatter Search (SS). In this work the possibilities of finding high coupling efficiencies are extended through the creation of adaptations to the Scatter Search algorithm and the enormous amount of solutions generated to be evaluated by such procedure. The results have showed that the adaptation of the technique is valid for optimization of tapers.

A multi-modal competitive hub location pricing problem with customer loyalty and elastic demand

This paper develops a multi-modal competitive hub location pricing problem whose target is the design of a transportation system for a company that plans to enter into a market with elastic demand, in which an existing transportation company operates its hub-and-spoke network. The entrant company aims to attract customers in the market by convenient locations for its hubs and proper pricing of its transportation services, while customer loyalty is different in the nodes. Hence, mixed-integer programming based on a multi-nominal logit model is proposed. Thereafter, to solve the single allocation hub-and-spoke model, it is decomposed into a bi-level model. In the new structure, the master problem is associated with hub location and assignment decisions, and the sub-problem is associated with pricing decisions. Moreover, upper and lower bounds are calculated to determine the price of transportation routes. Finally, based on a nested approach, a scatter search algorithm is used to search the solution space of the master problem, and a matheuristic method is designed to solve the pricing problem interactively. The proposed approach is employed to solve a case study in the postal service industry of Iran.

A binary social spider algorithm for uncapacitated facility location problem

In order to find efficient solutions to real complex world problems, computer sciences and especially heuristic algorithms are often used. Heuristic algorithms can give optimal solutions for large scale optimization problems in an acceptable period. Social Spider Algorithm (SSA), which is a heuristic algorithm created on spider behaviors are studied. The original study of this algorithm was proposed to solve continuous problems. In this paper, the binary version of the Social Spider Algorithm called Binary Social Spider Algorithm (BinSSA) is proposed for binary optimization problems. BinSSA is obtained from SSA, by transforming constant search space to binary search space with four transfer functions. Thus, BinSSA variations are created as BinSSA1, BinSSA2, BinSSA3, and BinSSA4. The study steps of the original SSA are re-updated for BinSSA. A random walking schema in SSA is replaced by a candidate solution schema in BinSSA. Two new methods (similarity measure and logic gate) are used in candidate solution production schema for increasing the exploration and exploitation capacity of BinSSA. The performance of both techniques on BinSSA is examined. BinSSA is named as BinSSA(Sim&Logic). Local search and global search performance of BinSSA is increased by these two methods. Three different studies are performed with BinSSA. In the first study, the performance of BinSSA is tested on the classic eighteen unimodal and multimodal benchmark functions. Thus, the best variation of BinSSA and BinSSA(Sim&Logic) is determined as BinSSA4(Sim&Logic). BinSSA4(Sim&Logic) has been compared with other heuristic algorithms on CEC2005 and CEC2015 functions. In the second study, the uncapacitated facility location problems (UFLPs) are solved with BinSSA(Sim&Logic). UFL problems are one of the pure binary optimization problems. BinSSA is tested on low-scaled, middle-scaled, and large-scaled fifteen UFLP samples and obtained results are compared with eighteen state-of-art algorithms. In the third study, we solved UFL problems on a different dataset named M* with BinSSA(Sim&Logic). The results of BinSSA(Sim&Logic) are compared with the Local Search (LS), Tabu Search (TS), and Improved Scatter Search (ISS) algorithms. Obtained results have shown that BinSSA offers quality and stable solutions.

Wireless Sensor Networks Fault-Tolerance Based on Graph Domination with Parallel Scatter Search.

In wireless sensor/ad hoc networks, all wireless nodes frequently flood the network channel by transmitting control messages causing “broadcast storm problem”. Thus, inspired by the physical backbone in wired networks, a Virtual Backbone (VB) in wireless sensor/ad hoc networks can help achieve efficient broadcasting. A well-known and well-researched approach for constructing virtual backbone is solving the Connected Dominating Set (CDS) problem. Furthermore, minimizing the size of the CDS is a significant research issue. We propose a new parallel scatter search algorithm with elite and featured cores for constructing a wireless sensor/ad hoc network virtual backbones based on finding minimum connected dominating sets of wireless nodes. Also, we addressed the problem of VB node/nodes failure by either deploying a previously computed VBs provided by the main pSSEF algorithm that does not contain the failed node/nodes, or by using our proposed FT-pSSEF algorithm repairing the broken VBs. Finally, as nodes in a VB incur extra load of communication and computation, this leads to faster power consumption compared to other nodes in the network. Consequently, we propose the virtual backbone scheduling algorithm SC-pSSEF which aims to find multiple VBs using the VBs provided by the pSSEF algorithm and switch between them periodically to prolong the network life time.

On convergence of scatter search and star paths with directional rounding for 0–1 mixed integer programs

Scatter Search is an evolutionary metaheuristic introduced by Glover (1977) as a heuristic for integer programming and was joined with a directional rounding strategy for 0–1 Mixed Integer Programming (MIP) problems based on Star Paths in Glover (1995). In this paper, we address directional rounding both independently and together with these other algorithmic components, studying its properties as a mapping from continuous to discrete (binary) space. We establish several useful properties of directional rounding and show that it provides an extension of classical rounding and complementing operators. Moreover, we observe that directional rounding of a line, as embodied in a Star Path, contains a finite number of distinct 0–1 points. This property, together with those of the solution space of 0–1 MIP, enables us to organize the search for an optimal solution of 0–1 MIP problems using Scatter Search in association with both cutting plane and extreme point solution approaches. Building on this, we provide a Convergent Scatter Search algorithm for 0–1 Mixed Integer Programs with proof of its finite convergence, along with two variants of its implementation and examples that illustrate the running of the approach.

Bi-objective optimization of basic and extended warranty policies regarding preventive maintenance and burn-in policies: Weibull bathtub-shaped failure rate

Today's after-sales services play an important role in the competitive market for product manufacturing and supply. The manufacturer, as the provider of basic warranty and third-party companies specializing in maintenance as extended warranty provider, seeks to minimize their costs, as well as improve product quality and customer attraction. In this regard, the application of burn-in policies can help the producer and the third-parties to achieve this. In this paper a nonlinear programming model is developed to (1) minimizing the total maintenance costs during the basic warranty and burn-in periods and (2) minimizing the total maintenance costs during the extended warranty period. Due to the complexity of the model, the multi-objective meta-heuristic solution approach is proposed based on a scatter search algorithm and variable neighborhood search algorithm. The optimization results showed that the application of burn-in policies by the manufacturer reduces the cost of preventive and corrective maintenance for the manufacturer and the third party. Also, the lack of a computational gap between the proposed solution approach and the exact solution method indicates the high efficiency of the proposed solution procedure through optimization of the research problem.

Hybrid Scatter Search Algorithm for Optimal and Energy-Efficient Steelmaking-Continuous Casting

This article studies a steelmaking-continuous casting (SCC) scheduling problem by considering ladle allocation. It takes technological rules in steel manufacturing and ladle-related constraints into account. A scheduling problem is formulated to determine allocation equipment for jobs, production sequence for jobs processed by the same equipment, and modification operations for empty ladles after their service for jobs. To ensure the fastest production and least energy consumption, we present a mixed integer mathematical programming model with the objectives to minimize the maximum completion time, idle time penalties, and energy consumption penalties related to waiting time. To solve it, we develop a two-stage approach based on a combination of scatter search (SS) and mixed integer programming (MIP). The first stage applies an SS algorithm to determine the assignment and sequence variables for charges. For the obtained solution, we construct a temporal constraint network and establish an MIP model at the second stage. We apply ILOG.CPLEX to solve the model and find the final solution. We analyze and compare the performance of the proposed approach with a hybrid method that combines a genetic algorithm with MIP on instances constructed from a real iron-steel plant. To further verify the effectiveness of the proposed algorithm, we compare its results with optimal solutions of the constraint-relaxed original problem. The experimental results show the effectiveness of the proposed approach in solving the SCC-scheduling problem.

Adaptive Scatter Search to Solve the Minimum Connected Dominating Set Problem for Efficient Management of Wireless Networks

An efficient routing using a virtual backbone (VB) network is one of the most significant improvements in the wireless sensor network (WSN). One promising method for selecting this subset of network nodes is by finding the minimum connected dominating set (MCDS), where the searching space for finding a route is restricted to nodes in this MCDS. Thus, finding MCDS in a WSN provides a flexible low-cost solution for the problem of event monitoring, particularly in places with limited or dangerous access to humans as is the case for most WSN deployments. In this paper, we proposed an adaptive scatter search (ASS-MCDS) algorithm that finds the near-optimal solution to this problem. The proposed method invokes a composite fitness function that aims to maximize the solution coverness and connectivity and minimize its cardinality. Moreover, the ASS-MCDS methods modified the scatter search framework through new local search and solution update procedures that maintain the search objectives. We tested the performance of our proposed algorithm using different benchmark-test-graph sets available in the literature. Experiments results show that our proposed algorithm gave good results in terms of solution quality.

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

A scatter search algorithm to configure service function chaining

Network functions virtualisation (NFV) emerges to deal with the challenges of reducing both the capital expenses (CAPEX) and operational expenses (OPEX) of cloud providers. The NFV is done by implementing network functions and providing them as software commodities. Network services are provided by chaining a set of network functions together. The key problem will be how and where network functions should be placed in the network and how traffic is routed through them. This is the well-known service function chaining problem and it is known to be NP-hard so exhaustive search algorithms have no significant benefit in large-scale context. This paper proposes a scatter search-based solution to configure service function chain. The aim is to produce the optimal number and placement of the required virtual network functions with the dynamic traffic steering over them. This is done while respecting computing and network resources constraints.

A scatter search algorithm to configure service function chaining

Network functions virtualisation (NFV) emerges to deal with the challenges of reducing both the capital expenses (CAPEX) and operational expenses (OPEX) of cloud providers. The NFV is done by implementing network functions and providing them as software commodities. Network services are provided by chaining a set of network functions together. The key problem will be how and where network functions should be placed in the network and how traffic is routed through them. This is the well-known service function chaining problem and it is known to be NP-hard so exhaustive search algorithms have no significant benefit in large-scale context. This paper proposes a scatter search-based solution to configure service function chain. The aim is to produce the optimal number and placement of the required virtual network functions with the dynamic traffic steering over them. This is done while respecting computing and network resources constraints.

A novel hybrid whale–Nelder–Mead algorithm for optimization of design and manufacturing problems

This paper introduces a new hybrid optimization algorithm (HWOANM) based on the Nelder–Mead local search algorithm (NM) and whale optimization algorithm (WOA). The aim of hybridization is to accelerate global convergence speed of the whale algorithm for solving manufacturing optimization problems. The main objective of our study on hybridization is to accelerate the global convergence rate of the whale algorithm to solve production optimization problems. This paper is the first research study of both the whale algorithm and HWOANM for the optimization of processing parameters in manufacturing processes. The HWOANM is evaluated using the well-known benchmark problems such as cantilever beam problem, welded beam problem, and three-bar truss problem. Finally, a grinding manufacturing optimization problem is solved to investigate the performance of the HWOANM. The results of the HWOANM for both the design and manufacturing problems solved in this paper are compared with other optimization algorithms presented in the literature such as the ant colony algorithm, genetic algorithm, scatter search algorithm, differential evolution algorithm, particle swarm optimization algorithm, simulated annealing algorithm, artificial bee colony algorithm, improved differential evolution algorithm, harmony search algorithm, hybrid particle swarm algorithm, teaching-learning–based optimization algorithm, cuckoo search algorithm, grasshopper optimization algorithm, salp swarm optimization algorithm, mine blast algorithm, gravitational search algorithm, ant lion optimizer, multi-verse optimizer, whale optimization algorithm, and the Harris hawks optimization algorithm. The results show that the HWOANM provides better exploration and exploitation properties, and can be considered as a promising new algorithm for optimizing both design and manufacturing optimization problems.

Enriched metaheuristics for the resource constrained unrelated parallel machine scheduling problem

A Scatter Search algorithm together with an enriched Scatter Search and an enriched Iterated Greedy for the unrelated parallel machine problem with one additional resource are proposed in this paper. The optimisation objective is to minimise the maximum completion of the jobs on the machines, that is, the makespan. All the proposed methods start from the best known heuristic for the same problem. Non-feasible solutions are allowed in all the methods and a Repairing Mechanism is applied to obtain a feasible solution from a resource constraint point of view. All the proposed algorithms apply different local search procedures based on insertion, swap and restricted neighbourhoods. Computational experiments are carried out using an exhaustive benchmark of instances. After analysing the results, we can conclude that the enriched methods obtain superior results, outperforming the best known solutions for the same problem.

An improved scatter search algorithm for the uncapacitated facility location problem

The uncapacitated facility location (UFL) problem is a NP-hard and pure binary optimization problem. The main goal of UFL is that try to find an undetermined number of facilities to minimize the sum of constant setup and serving costs of customers. Nowadays, in solving many NP problems, optimization techniques are preferred instead of conventional ones due to their simple structure, ease of application and acceptable results in reasonable time. In this study, the scatter search algorithm (SS) was improved to solve the UFL problems. The SS method can be applied directly to problems with binary search space and supports random search mechanism with good solutions obtained from previous problem solving efforts as opposed to other evolutionary algorithms. In order to compromise between exploitation and exploration in the improved scatter search (ISS), the global search ability of the basic SS algorithm is enhanced by using different crossover techniques like an ensemble, while the local search ability is improved by mutation operations on the best solutions. To investigate effects of the improvements and to show its performance, the ISS is compared with the twelve different methods found in the literature for solving the 15 UFL problems in the OR-Lib dataset. The experimental results show that the proposed method obtained the optimum value for 13 of the 15 problems and had a superior performance compared to other techniques considering the solution quality and robustness. The ISS is also compared with a technique using the local search method on the OR-Lib and a different dataset named M*. When all experimental results are evaluated, it is seen that the proposed method is an effective, robust and successful tool for solving the UFL problems.

Lexicographic Multiobjective Scatter Search for the Optimization of Sequence-Dependent Selective Disassembly Subject to Multiresource Constraints.

Industrial products' reuse, recovery, and recycling are very important because of their environmental and economic benefits. Effective product disassembly planning methods can improve their recovery efficiency and reduce their bad environmental impact. However, the existing approaches pay little attention to sequence-dependent disassembly with resource constraints, such as limited disassembly operators and tools, which makes the current planning methods ineffective in practice. This paper considers a multiobjective resource-constrained and sequence-dependent disassembly optimization problem with disassembly precedence constraints. Energy consumption is adopted to evaluate the disassembly efficiency. Its use with traditional optimization criterion leads to a novel multiobjective optimization model such that the energy consumption and disassembly time are minimized while disassembly profit is maximized. Since the problem complexity increases with the number of components in a product, a lexicographic multiobjective scatter search (SS) method is proposed to solve the proposed multiobjective optimization problem. Its effectiveness is verified by comparing the results of linear weight SS and genetic algorithms. The results show that it is able to provide a better solution in a short execution time and fulfills the precedence requirement in a product structure and resource constraints.

An improved scatter search algorithm for the corridor allocation problem considering corridor width

In the existing literature on the corridor allocation problem (CAP), the corridor width is not taken into consideration. But in the actual production, the corridor width plays a very important role in logistics transportation inside factories. To study the effect of the corridor width in a CAP problem, the corridor width is considered by a mixed-integer programming model proposed in this paper. Subsequently, an improved scatter search (ISS) algorithm is proposed to handle the CAP. Several improvement mechanisms have been applied to the ISS according to the special characteristics of the problem, such as the adoption of a simulated annealing operation, a dynamic reference set update method, and an improved subset generation method. The proposed ISS is evaluated on test instances of various sizes ranging from 9 to 49 facilities. Computational results demonstrate the validity of the ISS. Specifically, for small-sized instances, the acquired best solutions by the ISS are identical to the optimal solutions obtained by the exact solution given by GUROBI, while for moderate and large-sized instances, the objective values by the ISS are better than those solved by the method in GUROBI. Furthermore, the proposed algorithm shows better performance in solution quality and stability by comparing to the simulated annealing algorithm and the scatter search algorithm.

A mathematical model for location of temporary relief centers and dynamic routing of aerial rescue vehicles

This paper presents a new mathematical model for location of temporary relief centers and dynamic routing of aerial rescue vehicles distributing basic supplies in relief operations. The objective function of the proposed model minimizes the arrival time at the last designated temporary relief center. The proposed model seeks to locate the temporary relief centers in a way that all affected areas get covered by at least one temporary relief center. Considering the importance of quick action amid a post-disaster environment with characteristics such as uncertain demand for relief supplies, inaccurate information regarding victims, aftershocks, and extensively damaged road networks, in the proposed model, location and level of demand are considered to be dynamic, and relief supplies are assumed to be distributed by aerial transport vehicles. According to NP-Hardness of proposed problem, in this paper an improved hybrid metaheuristic algorithm based on scatter search combined with variable neighborhood search is presented. To evaluate the performance of the proposed algorithm, it is tested and compared with an exact method, basic scatter search and genetic algorithm. Results show the good performance of the proposed algorithm.

Intelligent Energy Management Algorithms for EV-charging Scheduling with Consideration of Multiple EV Charging Modes

Electric vehicles (EVs) are now attracting increasing interest from both industries and countries as an environmentally friendly and energy efficient mode of travel. Therefore, the EV charging and/or discharging issue has become an important challenge and research topic in power systems in recent years. An advanced and economic EV charging process, however, should employ smart scheduling, which depends on effective and robust algorithms. To that end, a comprehensive intelligent scatter search (ISS) algorithm within the frame of a basic scatter search has been designed with both unidirectional and bidirectional charging considered. The ISS structure also supports both a flexible and constant charging power rate by respectively employing filter-SQP (sequential quadratic programming) and mixed-integer SQP as local solvers with module control. The detailed design of ISS is presented and the objectives of smoothing the daily load profile and minimizing the charging cost have been tested. Compared with methods based on GS (global search), GA (genetic algorithm), and PSO (particle swarm optimization), the outcome-verified ISS can produce attractive results with a significantly short computational time. Moreover, to handle a large scale EV charging scenario, a hybrid method comprised of a GA and ISS approach has been further developed. Simulation results also verified its prominent performance, plus superbly low computational time.