This work presents an advanced particle swarm optimization algorithm featuring two decoding schemes, namely PSODS-I and PSODS-II, for solving the Vehicle Routing Problem with Time Windows (VRPTW). Both schemes begin by generating a customer precedence list, followed by the formation of a vehicle precedence list and subsequent route construction. To further enhance solution quality and reduce transportation cost, an intelligent local search mechanism is developed based on a heuristic improvement strategy. The proposed schemes are evaluated on Solomon's benchmark instances with 25 and100 customers using key performance indicators, including total travelled distance and number of vehicles. In addition, the consistency and robustness of the solutions are assessed and compared with the best known solutions and several state-of-the-art methodologies. Comparative analysis demonstrates that the proposed approach, particularly PSODSII, is highly competitive in terms of both fleet size and total distance travelled for solving the VRPTW.

This study proposes an adaptive local search heuristic to solve a real-world large-scale parallel machine scheduling problem with release dates and setup times, aiming to minimize total tardiness. The complexity of the problem stems from the need to synchronize machine availability, job release dates, and setup durations, which are crucial for meeting production deadlines and ensuring operational efficiency. Traditional optimization approaches often struggle to deliver timely solutions for large-scale industrial applications. Our heuristic method effectively explores the search space to identify schedules that significantly reduce total tardiness while adhering to the constraints of the production system. The approach was tested using real production data, and the results indicate that the heuristic consistently generated high-quality solutions within short computational times. The approach proved viable and efficient, offering a practical tool for improving scheduling performance and minimizing total tardiness in industries with similar operational constraints.

As the simple assembly line balancing problem type 1 (SALBP1) has been proven to be NP-hard, heuristic and metaheuristic approaches are widely used for solving middle to large instances. Nevertheless, the characteristics (fitness landscape) of the problem’s search space have not been studied so far and no rigorous justification for implementing various metaheuristic methods has been presented. Aiming to fill this gap in the literature, this study presents the first comprehensive and in-depth Fitness Landscape Analysis (FLA) study for SALBP1. The FLA was performed by generating a population of 1000 random solutions and improving them to local optimal solution, and then measuring various statistical indices such as average distance, gap, entropy, amplitude, length of the walk, autocorrelation, and fitness-distance among all solutions, to understand the complexity, structure, and topology of the solution space. We solved 83 benchmark problems with various cycle times taken from Scholl’s dataset which required 83000 local searches from initial to optimal solutions. The analysis showed that locally optimal assembly line balances in SALBP1 are distributed nearly uniformly in the landscape of the problem, and the small average difference between the amplitudes of the initial and optimal solutions implies that the landscape was almost plain. In addition, the large average gap between local and global solutions showed that global optimum solutions in SALBP1 are difficult to find, but the problem can be effectively solved using a single-solution-based metaheuristic to near-optimality. In addition to the FLA, a new mathematical formulation for the entropy (diversity) of solutions in the search space for SALBP1 is also presented in this paper.

In the face of burgeoning data volumes, latency issues present a formidable challenge to cloud computing. This problem has been strategically tackled through the advent of fog computing, shifting computations from central cloud data centers to local fog devices. This process minimizes data transmission to distant servers, resulting in significant cost savings and instantaneous responses for users. Despite the urgency of many fog computing applications, existing research falls short in providing time-effective and tailored algorithms for fog computing task scheduling. To bridge this gap, we introduce a unique local search mechanism, Card Sorting Local Search (CSLS), that augments the non-dominated solutions found by the Bi-objective Simplified Swarm Optimization (BSSO). We further propose Fast Elite Selecting (FES), a ground-breaking one-front non-dominated sorting method that curtails the time complexity of non-dominated sorting processes. By integrating BSSO, CSLS, and FES, we are unveiling a novel algorithm, Elite Swarm Simplified Optimization (EliteSSO), specifically developed to conquer time-efficiency and non-dominated solution issues, predominantly in large-scale fog computing task scheduling conundrums. Computational evidence reveals that our proposed algorithm is both highly efficient in terms of time and exceedingly effective, outstripping other algorithms on a significant scale.

In recent years, the Vehicle Routing Problem (VRP) has become an important issue for distribution companies. Also, the rapid development of communication means and the appearance of reverse logistics have given rise to new variants of the VRP. This article deals with an important variant of the VRP which is Dynamic Vehicle Routing Problem with Simultaneous Delivery and Pickup (DVRPSDP), in which new customers appear during the working day and each customer requires simultaneous delivery and pickup. A Memetic Algorithm (MA) that combines Genetic Algorithm (GA) and local search procedure have been proposed to solve the problem. The performance of the algorithm is evaluated with the tests carried out on a set of benchmarks found in the literature. The proposed memetic algorithm is very efficient and gives many good solutions.

In this paper, we consider the multi depot heterogeneous vehicle routing problem with time windows in which vehicles may be replenished along their trips. Using the modeling technique in a new-generation solver, we construct a novel formulation considering a rich series of constraint conditions and objective functions. Computation results are tested on an example comes from the real-world application and some cases obtained from the benchmark problems. The results show the good performance of local search method in the efficiency of replenishment system and generalization ability. The variants can be used to almost all kinds of vehicle routing problems, without much modification, demonstrating its possibility of practical use.

Clustering is a critical data analysis and it is a popular data mining technique. This paper presents a rapid Ant based clustering-genetic algorithm (RAC-GA) with local search to solve clustering problem. GA and local search are used as a global and local search to obtain better results. The proposed algorithm is evaluated by testing on some of the well-known real-world datasets, and the results are compared with other popular heuristics in clustering, such as GA, SA, TS, ACO and RAC. The results show strong improvement both in quality solution and process time area, especially in process time which is much less than previous algorithms