Multi-objective Scatter Search Research Articles

Bi-level programming and multi-objective optimization for the distribution of resources in hierarchical organizations

The decision regarding the hierarchical distribution of resources is crucial for many organizations that want to allocate such resources efficiently. At the upper level of the hierarchy, a decision-maker may have an objective and a set of feasible solutions partially determined by the lower level. Nevertheless, the upper level can influence but not control the decision-maker at the lower level. Moreover, the objectives of the upper and lower levels are conflicting. Hence, the hierarchical distribution of resources can be formulated as a bi-level programming model. This paper reformulates the hierarchical allocation of resources. The Hooke-Jeeves (HJ) algorithm and the hybrid scatter search–Nelder-Mead (SSNM) method are proposed to solve the newly formulated problem. The problem is also analyzed from a multi-objective perspective to equally prioritize the upper and lower levels while subjecting each to an interdependent set of constraints; a multi-objective scatter search algorithm (MSSA) was developed for that purpose. Tailor-made instances were also designed for the implementation of the developed algorithms. The findings demonstrated that the HJ algorithm provides the best solution according to the upper-level objective function. However, it does not guarantee the best result for the lower level. In comparison, MSSA has a set of best possible solutions for both objectives. The hybrid SSNM method could not match the results provided by the former methods.

Energy-Aware Scheduling of Two-Stage Flexible Flow Shop Based on Group Technology: Consideration of the Inconsistency of Process Differences

The diversity of consumer demand makes the manufacturing industry shift from the production mode of small variety and large batch to the production mode of multi-variety and small batch, which leads to the increase of production cost and the decrease of production efficiency, especially the increase of energy consumption. In this paper, the energy-aware scheduling problem of two-stage flexible flow shop based on group technology is studied, in which the process differences of jobs in the two stages are inconsistent. To solve the problem of unbalanced load of machines caused by group technology, this paper uses a dynamic splitting strategy to balance the load of machines on the basis of increasing the setup energy consumption as little as possible. Considering that the research problem is a multi-objective optimization problem, this study develops an improved multi-objective scatter search algorithm. According to the characteristics of the problem, the coding scheme, decoding scheme, diversity generation method and combination method are designed. The experimental results show that the group technology can effectively reduce energy consumption, and the dynamic split strategy can balance the load of machines effectively. Moreover, the results show the proposed method is better than the existing methods in terms of obtaining better solutions.

Three Hybrid Scatter Search Algorithms for Multi-Objective Job Shop Scheduling Problem

The Job Shop Scheduling Problem (JSSP) consists of finding the best scheduling for a set of jobs that should be processed in a specific order using a set of machines. This problem belongs to the NP-hard class problems and has enormous industrial applicability. In the manufacturing area, decision-makers consider several criteria to elaborate their production schedules. These cases are studied in multi-objective optimization. However, few works are addressed from this multi-objective perspective. The literature shows that multi-objective evolutionary algorithms can solve these problems efficiently; nevertheless, multi-objective algorithms have slow convergence to the Pareto optimal front. This paper proposes three multi-objective Scatter Search hybrid algorithms that improve the convergence speed evolving on a reduced set of solutions. These algorithms are: Scatter Search/Local Search (SS/LS), Scatter Search/Chaotic Multi-Objective Threshold Accepting (SS/CMOTA), and Scatter Search/Chaotic Multi-Objective Simulated Annealing (SS/CMOSA). The proposed algorithms are compared with the state-of-the-art algorithms IMOEA/D, CMOSA, and CMOTA, using the MID, Spacing, HV, Spread, and IGD metrics; according to the experimental results, the proposed algorithms achieved the best performance. Notably, they obtained a 47% reduction in the convergence time to reach the optimal Pareto front.

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.

The Integrated Supply Chain of After-sales Services Model: A Multi-objective Scatter Search Optimization Approach

Abstract: In recent decades, high profits of extended warranty have caused that third-party firms consider it as a lucrative after-sales service. However, customers division in terms of risk aversion and effect of offering extended warranty on manufacturers’ basic warranty should be investigated through adjusting such services. Since risk-averse customers welcome extended warranty, while the customers without taking on risk may remain at the level of basic warranty. In this paper, a multi-objective integer nonlinear programming model is presented for integrating the supply chain of after-sales services. In the suggested model, firstly strategies used by the manufacturers in the basic warranty period and the third party’s policy during the extended warranty period, including the development of a new imperfect maintenance approach, are regulated. Then, the effects of these strategies on the desirability of customers with different levels of risk-taking are analyzed. To optimize the model, the scatter search based approach was introduced for extracting set of non-dominated solutions. The results indicated that increasing level of customers’ risk-taking convinces manufacturers to diminish the basic warranty period and the third party can apply less costly preventive maintenance. Key Words: Warranty, Extended warranty, After-sales services, Customers’ risk-taking, Pareto-set solutions, Multi-objective scatter search

Scatter search for the bi-criteria p-median p-dispersion problem

The bi-criteria p-median p-dispersion is a challenging optimization problem that belongs to the family of location problems. To our knowledge, no metaheuristic has been proposed to this problem, where a multi-objective approach has to be considered. In this paper, we propose a multi-objective Scatter Search implementation in which three different improvement methods have been analyzed. Our results have been compared with the state of the art obtaining better hypervolume values and promising results in terms of dominance of solutions.

A parallel multi-objective scatter search for optimising incentive contract design in projects

We present a novel optimisation approach for incentive contract design within a project setting. the structure of the remuneration is one of the key challenges faced by the project owner when (s)he decides to hire a contractor. The proposed technique builds on the recently proposed contract design methodology by Kerkhove and Vanhoucke (Omega, 2015). Specifically, a novel multi-objective scatter search heuristic is proposed and implemented using parallelisation. Both single- and multi-population implementations of this heuristic are compared to the original full-factorial approach as well as commercial optimisation software. The results of the computational experiments indicate that the single-population parallel scatter search procedure significantly outperforms the other solution strategies in terms of both speed and solution quality.

A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron–steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.

Concurrent cell formation and layout design using scatter search

Two key decisions in designing cellular manufacturing systems are cell formation and layout design problems. In the cell formation problem, machine groups and part families are determined while in the facility layout problem the location of each machine in each cell (intra-cell layout) and the location of each cell (inter-cell layout) are decided. Owing to the fact that there are interactions between two problems, cell formation and layout design problem must be tackled concurrently to design a productive manufacturing system. In this research, two problems are investigated concurrently. Some important and realistic factors such as inter-cell layout, intra-cell layout, operations sequence, part demands, batch size, number of cells, cell size, and variable process routings are incorporated in the problem. The problem is formulated as a mathematical model. Three different methods are described to solve the problem: multi-objective scatter search (MOSS), non-dominated genetic algorithm (NSGA-II), and the e-constraint method. The methods are employed to solve nine problems generated and adopted from the literature. Sensitivity analysis is accomplished on the parameters of the problem to investigate the effects of them on objective function values. The results show that the proposed MOSS algorithm performs better than NSGA-II and produces better solutions in comparison to multi-stage approaches.

Multiobjective scatter search approach with new combination scheme applied to solve environmental/economic dispatch problem

The environmental/economic dispatch (EED) is an important daily optimization task in the operation of many power systems. It involves the simultaneous optimization of fuel cost and emission objectives which are conflicting ones. The EED problem can be formulated as a large-scale highly constrained nonlinear multiobjective optimization problem. In recent years, many metaheuristic optimization approaches have been reported in the literature to solve the multiobjective EED. In terms of metaheuristics, recently, scatter search approaches are receiving increasing attention, because of their potential to effectively explore a wide range of complex optimization problems. This paper proposes an improved scatter search (ISS) to deal with multiobjective EED problems based on concepts of Pareto dominance and crowding distance and a new scheme for the combination method. In this paper, we have considered the standard IEEE (Institute of Electrical and Electronics Engineers) 30-bus system with 6-generators and the results obtained by proposed ISS algorithm are compared with the other recently reported results in the literature. Simulation results demonstrate that the proposed ISS algorithm is a capable candidate in solving the multiobjective EED problems.

Cell formation and layout design with alternative routing: a multi-objective scatter search approach

Cellular manufacturing is a technology to improve the productivity and flexibility of manufacturing systems. Cell formation and layout design are two main problems in designing cellular manufacturing systems (CMSs). Due to the interaction between the two problems, these problems must be solved simultaneously to obtain the optimal solution. The problem is formulated as three different mathematical models which differ with respect to layout constraints and backward movements. A multi-objective scatter search is proposed to solve the integrated cell formation and layout design problem in CMSs. We introduce a new solution representation which is used in the algorithm. The performance of the algorithm is compared with the epsilon-constraint method and a well-known multi-objective evolutionary algorithm, non-dominated sorting genetic algorithm II (NSGA-II). The proposed algorithm not only obtained better solutions in comparison to the solutions proposed by past authors, but also it performs better than NSGA-II.

City-courier routing and scheduling problems

This research seeks to propose innovative routing and scheduling strategies to help city couriers reduce operating costs and enhance service level. The strategies are realized by constructing a new type of routing and scheduling problem. The problem directly takes into account the inherent physical and operating constraints associated with riding in city distribution networks, which makes the problem involve multiple objectives and visiting specified nodes and arcs. Through network transformations, this study first formulates the city-courier routing and scheduling problem as a multi-objective multiple traveling salesman problem with strict time windows (MOMTSPSTW) that is NP-hard and new to the literature, and then proposes a multi-objective Scatter Search framework that seeks to find the set of Pareto-optimal solutions to the problem. Various new and improved sub-procedures are embedded in the solution framework. This is followed by an empirical study that shows and analyzes the results of applying the proposed method to a real-life city-courier routing and scheduling problem.

Multiobjective scatter search for a commercial territory design problem

In this paper, a multiobjective scatter search procedure for a bi-objective territory design problem is proposed. A territory design problem consists of partitioning a set of basic units into larger groups that are suitable with respect to some specific planning criteria. These groups must be compact, connected, and balanced with respect to the number of customers and sales volume. The bi-objective commercial territory design problem belongs to the class of NP-hard problems. Previous work showed that large instances of the problem addressed in this work are practically intractable even for the single-objective version. Therefore, the use of heuristic methods is the best alternative for obtaining approximate efficient solutions for relatively large instances. The proposed scatter search-based framework contains a diversification generation module based on a greedy randomized adaptive search procedure, an improvement module based on a relinked local search strategy, and a combination module based on a solution to an assignment problem.

A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm

The location of manufacturing facilities is one of the most important strategic decisions considered in the design of logistic systems. Another important strategic decision is the structure and management of the fleets. Most often, even if two types of problem (i.e., location of facilities and vehicle routing) have occurred in a given scenario, they have been studied and solved separately. This paper presents a new integrated mathematical model for a bi-objective multi-depot location-routing problem where the total demand served is to be maximized and the total cost, consisting of start-up of the facility, fixed and variable depots and variable delivery cost, is to be minimized. Since this type of the problem is NP-hard, a new multi-objective scatter search (MOSS) algorithm is proposed to obtain the Pareto frontier for the given problem. To validate the performance of the proposed MOSS algorithm in terms of the solution quality and diversity level, various test problems are carried out and the efficiency of this algorithm based on some comparison metrics is compared with the elite tabu search (ETS). The computational results show that the proposed MOSS outperforms the ETS, especially in large-sized problems.

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.

A multi-objective scatter search for a dynamic cell formation problem

Cellular manufacturing system—an important application of group technology (GT)—has been recognized as an effective way to enhance the productivity in a factory. Consequently, a multi-objective dynamic cell formation problem is presented in this paper, where the total cell load variation and sum of the miscellaneous costs (machine cost, inter-cell material handling cost, and machine relocation cost) are to be minimized simultaneously. Since this type of problem is NP-hard, a new multi-objective scatter search (MOSS) is designed for finding locally Pareto-optimal frontier. To demonstrate the efficiency of the proposed algorithm, MOSS is compared with two salient multi-objective genetic algorithms, i.e. SPEA-II and NSGA-II based on some comparison metrics and statistical approach. The computational results indicate the superiority of the proposed MOSS compared to these two genetic algorithms.

A multi-objective scatter search for a mixed-model assembly line sequencing problem

A mixed-model assembly line (MMAL) is a type of production line where a variety of product models similar to product characteristics are assembled. There is a set of criteria on which to judge sequences of product models in terms of the effective utilization of this line. In this paper, we consider three objectives, simultaneously: minimizing total utility work, total production rate variation, and total setup cost. A multi-objective sequencing problem and its mathematical formulation are described. Since this type of problem is NP-hard, a new multi-objective scatter search (MOSS) is designed for searching locally Pareto-optimal frontier for the problem. To validate the performance of the proposed algorithm, in terms of solution quality and diversity level, various test problems are made and the reliability of the proposed algorithm, based on some comparison metrics, is compared with three prominent multi-objective genetic algorithms, i.e. PS-NC GA, NSGA-II, and SPEA-II. The computational results show that the proposed MOSS outperforms the existing genetic algorithms, especially for the large-sized problems.

Scatter search techniques applied to electromagnetic problems

This paper presents a new multiobjective scatter search algorithm. First, one demonstrates the standard scatter search performance by applying it to solve a single-objective inverse electromagnetic scattering problem. Then, the changes necessary to solve multiobjective optimization problems that should be implemented in a single-objective algorithm are discussed. As a result of this discussion, one proposes the use of a nondominated sorting technique and a niched-type penalty method in order to extend the scatter search technique to multiobjective problems. The results obtained by the new algorithm show its performance and helpfulness in solving multiobjective electromagnetic problems.

Quadratic loss functions and signal-to-noise ratios for a bivariate response

We present a novel optimisation approach for incentive contract design within a project setting. the structure of the remuneration is one of the key challenges faced by the project owner when (s)he decides to hire a contractor. The proposed technique builds on the recently proposed contract design methodology by Kerkhove and Vanhoucke (Omega, 2015). Specifically, a novel multi-objective scatter search heuristic is proposed and implemented using parallelisation. Both single- and multi-population implementations of this heuristic are compared to the original full-factorial approach as well as commercial optimisation software. The results of the computational experiments indicate that the single-population parallel scatter search procedure significantly outperforms the other solution strategies in terms of both speed and solution quality.