This article presents a framework for generating optimisation models using a pre-trained generative transformer. The framework involves specifying the features that the optimisation model should have and using a language model to generate an initial version of the model. The model is then tested and validated, and if it contains build errors, an automatic edition process is triggered. An experiment was performed using MiniZinc as the target language and two GPT-3.5 language models for generation and debugging. The results show that the use of language models for the generation of optimisation models is feasible, with some models satisfying the requested specifications, while others require further refinement. The study provides promising evidence for the use of language models in the modelling of optimisation problems and suggests avenues for future research.

Machine learning research has been able to solve problems in multiple domains. Machine learning represents an open area of research for solving optimisation problems. The optimisation problems can be solved using a metaheuristic algorithm, which can find a solution in a reasonable amount of time. However, the time required to find an appropriate metaheuristic algorithm, that would have the convenient configurations to solve a set of optimisation problems properly presents a problem. The proposal described in this article contemplates an approach that automatically creates metaheuristic algorithms given a set of optimisation problems. These metaheuristic algorithms are created by modifying their logical structure via the execution of an evolutionary process. This process employs an extension of the reinforcement learning approach that considers multi-agents in their environment, and a learning agent composed of an analysis process and a process of modification of the algorithms. The approach succeeded in creating a metaheuristic algorithm that managed to solve different continuous domain optimisation problems from the experiments performed. The implications of this work are immediate because they describe a basis for the generation of metaheuristic algorithms in an online-evolution.

The paper addresses the NP-Hard cell formation problem, which involves organizing machines and parts into manufacturing cells to minimize piece movement. The research used a dataset with three manufacturing cells and conducted a global search experiment to find optimal solutions using constraint programming techniques.

In this article a preliminary experiment is carried out in which a set of elements and procedures are described to be able to solve problems of continuous domains integrated in the Andean Condor Algorithm. The Andean Condor Algorithm is a metaheuristic algorithm of swarm intelligence inspired by the movement pattern of the Andean condor when searching for its food. An experiment focused on solving the problem of the function 1st De Jong's \(f(x_1 \cdots x_n) = \sum_{i=1}^n x_i^2,~ -100 \leq x_i \leq 100\). According to the results obtained, solutions have been obtained close to the overall optimum value of the problem.

This research focused on the resolution of a dynamic prey–predator spatial model. This model has six life cycles and simulates a theoretical population of prey and predators. Cellular automata represent a set of prey and predators. The cellular automata move in a discrete space in a 2d lattice that has the shape of a torus. African buffaloes represent the predators, and the grasslands represent the prey in the African savanna. Each buffalo moves in the discrete space using the proper motion equation of the African buffalo optimization metaheuristic. Two types of approaches were made with five experiments each. The first approach was the development of a dynamic prey–predator spatial model using the movement of the African buffalo optimization metaheuristic. The second approach added the characteristic of regulating the population of buffaloes using autonomous multi-agents that interact with the model dynamic prey–predator spatial model. According to the obtained results, it was possible to adjust and maintain a balance of prey and predators during a determined period using multi-agents, therefore preventing predators from destroying an entire population of prey in the coexistence space.

Conservation organizations worldwide face the agonizing challenge of choosing which areas to protect when they can't save everything. This research teaches computers to think like migrating animal herds, creating virtual ecosystems that help us choose which wild spaces to protect forever. Using four different particle swarm optimization transfer functions, the study successfully solved optimal natural reserve selection problems, with some configurations achieving perfect results—protecting 100% of target species within budget constraints.

The reserves or protected areas have a fundamental role in the biodiversity of the planet. The main objective of the reserves is to protect areas where a large number of animal and plant species coexist, considering also, a set of abiotic factors such as water, soil and sunlight. This research solves the budget-constrained maximal covering location (BCMCL) problem. The aim of BCMCL problem is to maximise the number of species to be protected by the constraints of a limited budget and the costs that have to protect each area. The BCMCL problem is an NP-hard optimisation problem with a binary domain. For the resolution of BCMCL problem, the authors propose a binary version of African buffalo optimisation (ABO). The tests performed to solve the BCMCL problem have used a set of 12 test instances that have been solved by the algorithm binary ABO. Moreover, eight transfer functions have been applied and experienced in the binary version of ABO. The algorithms migrating birds optimisation, random descent and steepest descent are used to compare the best results obtained by ABO. Finally, the results show that the binary version of ABO has competitive results compared with other algorithms.

The cell formation problem is a classic optimization problem devoted to the manufacturing industry. Such a problem proposes to divide a manufacturing plant in a set of cells, where each cell is composed of machines which in turn process product parts. The goal is to design a plant division in such a way the need for part interchange among cells is minimized. The idea is to reduce cost and increase productivity. In this paper, we propose different variations of the original migrating birds optimization algorithm for solving this problem. In particular, we propose two different leader exchange procedures and three different neighboring solution generations. We illustrate interesting results by solving well-known instances considering the group efficiency as optimization criterion in contrast to previous work done on this metaheuristic.

The Manufacturing Cell Design Problem (MCDP) is a complex combinatorial optimization problem that involves the formation of manufacturing cells by grouping machines and parts into families. This paper presents a novel approach using Artificial Bee Colony (ABC) algorithm enhanced with adaptive population mechanisms to solve the MCDP. The adaptive population strategy dynamically adjusts the colony size based on the search progress, improving both exploration and exploitation capabilities. Experimental results demonstrate the effectiveness of the proposed approach in finding high-quality solutions for various MCDP instances.

The manufacturing cell design problem (MCDP) aims to minimise the movements of parts between the production cells. The MCDP is an NP-Hard optimisation problem with a binary domain. For the resolution of the MCDP, the authors employ the firefly algorithm (FA) metaheuristic. FA is a metaheuristic with a real domain; therefore, an efficient method for transfer and discretisation from the real domain to the binary domain has been used. The second metaheuristic used is Egyptian vulture optimisation algorithm (EVOA). EVOA is a recent metaheuristic inspired by the behaviour of the Egyptian vulture bird. EVOA uses a set of operators which must be adapted to the MCDP optimisation problem. Two types of experiments have been performed. The first experiment consists of solving the MCDP with a set of 90 homogeneous incidence matrices. In the tests, FA and EVOA have been used obtaining good results. Subsequently, the obtained results have been compared versus other eight metaheuristics. The second experiment consists in a set of 35 inhomogeneous incidence matrices. The global optimum value for 13 problems has been obtained using constraint programming. Finally, for the other 22 problems, the authors have reported the best values found using FA and EVOA.

The Manufacturing Cell Design Problem consists in the division of a manufacturing plant into cells, each one of them containing machines processing a group of parts. The goal is to increase the productivity by minimizing the exchange of material between cells. In this paper, we solve this problem by using Cuckoo Search, which is an easy-to-implement and fast-convergence metaheuristic inspired on the interesting reproduction strategy of cuckoo birds. We perform different experiments on a set of 90 well-known problem instances where our approach is able to reach the global optimum for all of them.

The machine-part cell formation (MPCF) problem is to organize an assembly as a set of cells, where each cell contains certain machines that process a sub-set of parts. In recent years, different types of metaheuristics have been used to solve the problem of MPCF. This publication focuses on solving the MPCF problem using a metaheuristic inspired on birds, called Migrating Birds Optimization (MBO) algorithm. Experiments have been conducted to 180 test instances using 2 types of leader exchange in the flock of birds. The results obtained using MBO are equal to or better than other algorithms reported in the literature.

This research focuses on modeling and solving the Manufacturing Cell Design Problem (MCDP) through a Firefly Algorithm (FA). The MCDP consists in creating an optimal design of production plants, through the creation of cells that group machines and parts. The goal of the problem is to minimize movements and exchange of material between the cells. The FA is a metaheuristic based on the mating behavior or flash of fireflies, in order to communicate with each other or attract potential prey. Fireflies move through the search space by means of attraction that they feel toward other fireflies until the stop criteria established is complied. Finally, to test the efficiency of FA, the results obtained have been compared with previous research illustrating encouraging results.

Manufacturing Cell Design is a problem that is aimed at distributing the different machines of a center of production in cells, so that the parts of the final product to be manufactured with the least amount of travel in its manufacturing process. Bat Algorithm is an algorithm inspired by the behavior of echolocation in bats. Using a balance sheet of the frequency and automatic tuning of exploration and exploitation by controlling the rate of volume and emission pulses. The following work shows the resolution of the Manufacturing Cell Design, by means of Bat Algorithm, an algorithm that proved to be effective for this problem because it has reached the optimum in all problems with which the tests were conducted.

The Machine-Part Cell Formation Problem (MPCFP) is a NP-Hard optimization problem that consists in grouping machines and parts in a set of cells, so that each cell can operate independently and the intercell movements are minimized. This problem has largely been tackled in the literature by using different techniques ranging from classic methods such as linear programming to more modern nature-inspired metaheuristics. In this paper, we present an efficient parallel version of the Migrating Birds Optimization metaheuristic for solving the MPCFP. Migrating Birds Optimization is a population metaheuristic based on the V-Flight formation of the migrating birds, which is proven to be an effective formation in energy saving. This approach is enhanced by the smart incorporation of parallel procedures that notably improve performance of the several sorting processes performed by the metaheuristic. We perform computational experiments on 1080 benchmarks resulting from the combination of 90 well-known MPCFP instances with 12 sorting configurations with and without threads. We illustrate promising results where the proposal is able to reach the global optimum in all instances, while the solving time with respect to a nonparallel approach is notably reduced.

Machine-Part Cell Formation consists on organizing a plant as a set of cells, each one of them processing machines containing different part types. In recent years, different techniques have been used to solve this problem ranging from exact to approximate methods. This paper focuses on solving new instances of this problem for which no optimal value exists by using the classic Boctor's mathematical model. We employ constraint programming as the underlying solving technique illustrating that global optimums are achieved for the whole set of tested instances.

Open pit mining problems aims at correctly identifying the set of blocks to be mined in order to maximize the net present value of the extracted ore. Different constraints can be involved and may vary the difficulty of the problem. In particular, the Open-Pit Long-Term Production Planning Problem is one of the variants that better models the real mining operation. It considers, among others, limited processing plant and mining capacity as well as slope and grade blending constraints. During the last thirty years, different techniques have been proposed to solve the multiple variants of the open pit mining problem; however, the resolution via constraint programming has not been reported yet. In this paper, we present a performance evaluation of seven constraint programming solvers for the open pit mining long-term scheduling problem. We illustrate interesting and comparative results on a set of varied open pit mining instances.

Open pit mining problems aims at correctly identifying the set of blocks to be mined in order to maximize the net present value of the extracted ore. Different constraints can be involved and may vary the difficulty of the problem. In particular, the Open-Pit Long-Term Production Planning Problem is one of the variants that better models the real mining operation. It considers, among others, limited processing plant and mining capacity as well as slope and grade blending constraints. During the last thirty years, different techniques have been proposed to solve the multiple variants of the open pit mining problem; however, the resolution via constraint programming has not been reported yet. In this paper, we present a performance evaluation of seven constraint programming solvers for the open pit mining long-term scheduling problem. We illustrate interesting and comparative results on a set of varied open pit mining instances.