Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

Solving multifacility Huff location models on networks using metaheuristic and exact approaches

In this paper we consider multifacility Huff facility location problem on networks. First, we introduce a slight modification of the existing mixed integer nonlinear mathematical model and confirm its validity by using the solver for nonlinear optimization, KNITRO. Second, since the problem is NP-hard, we develop three methods that are based on three metaheuristic principles: Variable Neighborhood Search, Simulated Annealing, and Multi-Start Local Search. Based on extensive computational experiments on large size instances (up to 800 customers and 100 potential facilities), it appears that VNS based heuristic outperforms the other two proposed methods.     

Construct,Merge, Solve & Adapt A new general algorithm for combinatorial optimization

This paper describes a general hybrid metaheuristic for combinatorial optimization labelled Construct, Merge, Solve & Adapt. The proposed algorithm is a specific instantiation of a framework known from the literature as Generate-And-Solve, which is based on the following general idea. First, generate a reduced sub-instance of the original problem instance, in a way such that a solution to the sub-instance is also a solution to the original problem instance. Second, apply an exact solver to the reduced sub-instance in order to obtain a (possibly) high quality solution to the original problem instance. And third, make use of the results of the exact solver as feedback for the next algorithm iteration. The minimum common string partition problem and the minimum covering arborescence problem are chosen as test cases in order to demonstrate the application of the proposed algorithm. The obtained results show that the algorithm is competitive with the exact solver for small to medium size problem instances, while it significantly outperforms the exact solver for larger problem instances.     

Two metaheuristic approaches for solving multidimensional two-way number partitioning problem

In this paper, we address two metaheuristic approaches, a Variable Neighborhood Search (VNS) and an Electromagnetism-like metaheuristic (EM), on an NP-hard optimization problem: Multi-dimensional Two-way Number Partitioning Problem (MDTWNPP). MDTWNPP is a generalization of a Two-way Number Partitioning Problem (TWNPP), where a set of vectors is partitioned rather than a set of numbers. The simple k-swap neighborhoods allow an effective shaking procedure in the VNS search. The attraction–repulsion mechanism of EM is extended with a scaling procedure, which additionally moves EM points closer to local optima. Both VNS and EM use the same local search procedure based on 1-swap improvements. Computational results were obtained on 210 standard instances. Direct comparison with results from the literature confirm the significance of applying these methods to MDTWNPP.     

Multi-objective metaheuristic algorithms for the resource-constrained project scheduling problem with precedence relations

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multi-objective Variable Neighborhood Search (MOVNS) and Pareto Iterated Local Search (PILS) methods. The proposed algorithms use strategies based on the concept of Pareto Dominance to search for solutions and determine the set of non-dominated solutions. The solutions obtained by the algorithms, from a set of instances adapted from the literature, are compared using four multi-objective performance measures: distance metrics, hypervolume indicator, epsilon metric and error ratio. The computational tests have indicated an algorithm based on MOVNS as the most efficient one, compared to the distance metrics; also, a combined feature of MOG and MOVNS appears to be superior compared to the hypervolume and epsilon metrics and one based on PILS compared to the error ratio. Statistical experiments have shown a significant difference between some proposed algorithms compared to the distance metrics, epsilon metric and error ratio. However, significant difference between the proposed algorithms with respect to hypervolume indicator was not observed.     

MaxMinMin p-dispersion problem: A variable neighborhood search approach

In this work we have developed a Variable Neighborhood Search (VNS) method in order to solve the MaxMinMin p-dispersion problem, which adds a new type of plateau search mechanism to the classical VNS metaheuristic framework. Besides, several other contributions have been made to the basic VNS heuristic in terms of the ascent and perturbation functions. To the best of our knowledge this is the first application of the VNS to the MaxMinMin problem and our approach, compared to previous methods, finds or improves the results for all of the large-sized benchmarks with low computational efforts. Finding most of the proven optimal solutions in a fraction of a second, the robustness and quality of the solutions and the low complexity of the methods demonstrate the strength of the proposed heuristic solution procedures.     

Grey Wolf Optimizer

This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves (Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known test functions, and the results are verified by a comparative study with Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolution Strategy (ES). The results show that the GWO algorithm is able to provide very competitive results compared to these well-known meta-heuristics. The paper also considers solving three classical engineering design problems (tension/compression spring, welded beam, and pressure vessel designs) and presents a real application of the proposed method in the field of optical engineering. The results of the classical engineering design problems and real application prove that the proposed algorithm is applicable to challenging problems with unknown search spaces.     

Emergent nature inspired algorithms for multi-objective optimization

Many real-world decision-making situations possess both a discrete and combinatorial structure and involve the simultaneous consideration of conflicting objectives. Problems of this kind are in general of large size and contains several objectives to be “optimized”. Although Multiple Objective Optimization is a well-established field of research, one branch, namely nature inspired metaheuristics is currently experienced a tremendous growth. Over the last few years, developments of new methodologies, methods, and techniques to deal with multi-objective large size problems in particular those with a combinatorial structure and the strong improvement on computing technologies (during and after the 80s) made possible to solve very hard problems with the help of inspired nature based metaheuristics.     

On the configuration of supply chains for assemble-to-order products: Case studies from the automotive and the CNC machine building sectors

The product customisation trend has an unprecedented impact on manufacturing companies, as the ever-increasing number of product variants and the enlarged pool of cooperating partners vastly increase the feasible alternative supply chain configurations. In terms of decision theory, this is translated to enormous search spaces. For tackling these NP-hard problems, metaheuristic optimisation methods are utilised, which provide a trade-off between the quality of solutions and the computation time. This research work describes the modelling and solving of two supply chain configuration problems using the Simulated Annealing and Tabu Search methods. The performance of the identified solutions in terms of optimisation of multiple conflicting criteria, is compared against the results obtained from a custom Intelligent Search Algorithm and an Exhaustive enumerative method. The algorithms are developed into a web-based software platform. The approach is validated through real life applications to case studies from the automotive and CNC laser welding machine building industries.     

An iterated local search heuristic for the split delivery vehicle routing problem

This paper concerns the Split Delivery Vehicle Routing Problem (SDVRP). This problem is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) since the customers׳ demands are allowed to be split. We deal with the cases where the fleet is unlimited (SDVRP-UF) and limited (SDVRP-LF). In order to solve them, we implemented a multi-start Iterated Local Search (ILS) based heuristic that includes a novel perturbation mechanism. Extensive computational experiments were carried out on benchmark instances available in the literature. The results obtained are highly competitive, more precisely, 55 best known solutions were equaled and new improved solutions were found for 243 out of 324 instances, with an average and maximum improvement of 1.15% and 2.81%, respectively.