A Modified Simulated Annealing (MSA) Algorithm to Solve the Supplier Selection and Order Quantity Allocation Problem with Non-Linear Freight Rates

Abstract

Economic Order Quantity (EOQ) is an important optimization problem for inventory management with an impact on various industries; however, their mathematical models may be complex with non-convex, non-linear, and non-differentiable objective functions. Metaheuristic algorithms have emerged as powerful tools for solving complex optimization problems (including EOQ). They are iterative search techniques that can efficiently explore large solution spaces and obtain near-optimal solutions. Simulated Annealing (SA) is a widely used metaheuristic method able to avoid local suboptimal solutions. The traditional SA algorithm is based on a single agent, which may result in a low convergence rate for complex problems. This article proposes a modified multiple-agent (population-based) adaptive SA algorithm; the adaptive algorithm imposes a slight attraction of all agents to the current best solution. As a proof of concept, the proposed algorithm was tested on a particular EOQ problem (recently studied in the literature and interesting by itself) in which the objective function is non-linear, non-convex, and non-differentiable. With these new mechanisms, the algorithm allows for the exploration of different regions of the solution space and determines the global optimum in a faster manner. The analysis showed that the proposed algorithm performed well in finding good solutions in a reasonably short amount of time.

Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate

“…The improved method strictly outperformed the original SA in several baseline functions, such as Ackley, Dixon Price, and Rosenbrock. Similar to the previous study, a modified SA was found in a study of the supplier selection and order quantity allocation problem with nonlinear freight rates by Gonzalez-Ayala et al [22]. In comparison to Suarez et al [21], only sigmoid function was used to calculate the acceptance probability.…”

Multi-Strategy Improved Particle Swarm Optimization Algorithm and Gazelle Optimization Algorithm and Application

“…Heuristic algorithms, which draw inspiration from natural laws, can be broadly classified into the following categories: physical methods based on principles such as gravity, temperature, and inertia, which randomly search for the optimal solution to optimization problems, for instance, methods like gravitational search [1]; simulated annealing [2]; and black hole algorithms [3]. Evolutionary algorithms, grounded in Darwin's theory, facilitate the gradual discovery of optimal solutions as the individuals within a population evolve through iterations during the search process.…”