Abstract: In this work, a novel Hybrid Quantum Genetic Algorithm (HQGA) for the 0-1 Knapsack Problem (KP) is presented. It is based on quantum computing principles, such as qubits, superposition, and entanglement of states. The HQGA was simulated in the Qiskit simulator. Qiskit simulator is a platform developed by IBM that allows working with quantum computers at the level of circuits, pulses, and algorithms. The performance of HQGA is evaluated in three strongly correlated KP data sets, and computational results are compared with a Quantum-Inspired Evolutionary Algorithm (QIEA), a modified version of a QIEA (QIEA-Q), and a modified version of the HQGA (HQGA-Q). Experimental results demonstrate that the proposed HQGA can obtain the best solutions in all the KP data sets, and performs well on robustness.

ABSTRACT The present research deals with the two-dimensional knapsack problem by considering the cutting of irregular items from a rectangular plate with defects. While the defects are only known at the time of cutting (in the future), we need first to select which items to produce from cutting the plate. The final items cannot have any defects and the goal is to maximize the profit from cutting the plate and producing the items. We propose a two-stage stochastic optimization model that makes use of a discrete set of scenarios with the realization of the plate defects. The first-stage decisions involve selecting items for cutting and possible production. The second-stage decisions consider the positioning of items in the plate given the scenarios with defects, and then the cancellation and non-production of some selected items, if any. We also extend this model to include a measure of risk, aiming at robust solutions. We perform computational tests on instances adapted from the literature that consider three types of defects, eight scenarios, and four cases for determining each scenario’s probability. The tests evaluate the impact of uncertainties on the problem by calculating the expected value of perfect information and the value of the stochastic solution. The results indicate a percentage reduction in the profit of up to 27.7%, on average, when considering a fully risk-averse decision-maker.

ABSTRACT The knapsack problem is basic in combinatorial optimization and possesses several variants and expansions. In this paper, we focus on the multi-objective stochastic quadratic knapsack problem with random weights. We propose a Multi-Objective Memetic Algorithm With Selection Neighborhood Pareto Local Search (MASNPL). At each iteration of this algorithm, crossover, mutation, and local search are applied to a population of solutions to generate new solutions that would constitute an offspring population. Then, we use a selection operator for the best solutions to the combined parent and offspring populations. The principle of the selection operation relies on the termination of the non-domination rank and the crowding distance obtained respectively by the Non-dominated Sort Algorithm and the Crowding-Distance Computation Algorithm. To evaluate the performance of our algorithm, we compare it with both an exact algorithm and the NSGA-II algorithm. Our experimental results show that the MASNPL algorithm leads to significant efficiency.

Resumen En este trabajo presentamos un enfoque de Búsqueda Tabú independiente del dominio para problemas con múltiples objetivos y variables mixtas (enteras y reales). En el mismo investigamos dos aspectos: la independencia del dominio y la aplicabilidad en la optimización práctica, para ello nos centramos en problemas que se encuentran frecuentemente en el mundo real, como son los problemas de redes logísticas (por ejemplo: problemas de redes de distribución con múltiples etapas, localización asignación, tablas de tiempo); también investigamos su desempeño sobre problemas clásicos como cubri-miento de conjuntos, particionamiento de conjunto, mochila multidimensional y camino más corto. Todos los problemas considerados son de la clase NP-duros, con gran número de variables, conteniendo un número de restricciones heterogéneas, presentando un reto para hallar soluciones factibles.

Abstract In this work we present a domain-independent Tabu Search approach for multiobjective optimization with mixed-integer variables. In this we investigate two aspects: domain-independence and applicability in optimization practice and focus our attention in problems that appear frequently in the real world, like logistic network (for example: multi-stage distribution networks problems, location-allocation problems, time-tabling problems); however, other classical problems were investigated, like: coverage set problem, partitioning set problem, multidimentional knapsack problem and shortest path problem. All these problems belong to the NP-hard class, with a great number of decision variables, containing a great number of heterogeneous constrains, presenting a challenge to find feasible solutions.

Abstract Paper aims We propose a modified Sequential Heuristic Procedure (MSHP) to reduce the cutting waste and number of setups for the One-Dimensional Cutting Stock Problem with Setup Cost. Originality This heuristic modifies Haessler’s sequential heuristic procedure (1975) by adapting the Integer Bounded Knapsack Problem to generate cutting patterns, instead of the original lexicographic search employed. The solution strategy is to generate different cutting plans using MSHP, and then to use an integer programming model to seek even better results. Research method It is a axiomatic research, ordinary in studies of Operational Research. Main findings In the computational experiments, we demonstrate the effectiveness of the algorithm with two sets of benchmark instances by comparing it with other approaches, and obtaining better solutions for some scenarios. Implications for theory and practice The approach is suitable for practitioners from different industrial settings due to its easily coding and possible adaptation for problem extensions.

ABSTRACT In this paper, we study the stochastic knapsack problem with expectation constraint. We solve the relaxed version of this problem using a stochastic gradient algorithm in order to provide upper bounds for a branch-and-bound framework. Two approaches to estimate the needed gradients are studied, one based on Integration by Parts and one using Finite Differences. The Finite Differences method is a robust and simple approach with efficient results despite the fact that estimated gradients are biased, meanwhile Integration by Parts is based upon more theoretical analysis and permits to enlarge the field of applications. Numerical results on a dataset from the literature as well as a set of randomly generated instances are given.

An order picking system in a distribution centre consisting of parallel unidirectional picking lines is considered. The objectives are to minimise the walking distance of the pickers, the largest volume of stock on a picking line over all picking lines, the number of small packages, and the total penalty incurred for late distributions. The problem is formulated as a multi-objective multiple knapsack problem that is not solvable in a realistic time. Population-based algorithms, including the artificial bee colony algorithm and the genetic algorithm, are also implemented. The results obtained from all algorithms indicate a substantial improvement on all objectives relative to historical assignments. The genetic algorithm delivers the best performance.

'n Stelsel vir die opmaak van bestellings bestaande uit parallelle eenrigting uitsoeklyne in 'n distribusiesentrum word beskou. Die doelwitte is om die loopafstand van die werkers, die grootste volume van voorraad op 'n uitsoeklyn oor alle uitsoeklyne, die aantal klein pakkette, en die totale koste van laat distribusies te minimeer. Die probleem word geformuleer as 'n meerdoelige veelvuldige rugsakprobleem, maar kan nie in 'n realistiese tyd opgelos word nie. Bevolking-gebaseerde algoritmes, insluitend die kunsmatige by-kolonie-algoritme en genetiese algoritme, is ook geïmplementeer. Al die algoritmes verkry 'n beduidende verbetering op historiese toewysings vir al die doelwitte. Die genetiese algoritme vaar die beste.

In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (ABDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The ABDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (AGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (AIGA). The results show that ABDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.

The 0-1 exact k-item quadratic knapsack problem (E - kQKP) consists of maximizing a quadratic function subject to two linear constraints: the first one is the classical linear capacity constraint; the second one is an equality cardinality constraint on the number of items in the knapsack. Most instances of this NP-hard problem with more than forty variables cannot be solved within one hour by a commercial software such as CPLEX 12.1. We propose therefore a fast and efficient heuristic method which produces both good lower and upper bounds on the value of the problem in reasonable time. Specifically, it integrates a primal heuristic and a semidefinite programming reduction phase within a surrogate dual heuristic. A large computational experiments over randomly generated instances with up to 200 variables validates the relevance of the bounds produced by our hybrid dual heuristic, which yields known optima (and prove optimality) in 90% (resp. 76%) within 100 seconds on the average.

Este trabajo presenta la solución mono-objetivo y multi-objetivo del problema de la distribución de planta en celdas de manufactura a través de dos nuevos algoritmos híbridos discretos basados en quimiotaxis de bacterias y en algoritmos genéticos. Los modelos propuestos resuelven simultáneamente los dos inconvenientes que constituyen el problema de la distribución de planta en celdas de manufactura: la formación de las celdas y la distribución de planta intra e inter celdas, considerando el agrupamiento de las celdas y el costo de transporte y manipulación de materiales. El desempeño de las propuestas se evaluó con problemas de prueba de distribución de planta de celdas de manufactura, agente viajero (TSP) y el caso multi-objetivo del problema de las mochilas. Los resultados mono-objetivo se compararon con AG, BFOA y Bacterial-GA, mientras que los resultados multi-objetivo se compararon con los reconocidos algoritmos NSGA2 y SPEA2 en los que se obtuvo un mejor desempeño en los dos casos.

This paper presents the mono-objective and multi-objective solution to the cell manufacturing layout problem using two new discrete hybrid algorithms based on bacterial chemotaxis and genetic algorithms. The proposed models simultaneously solve the issues that constitute the problem of the layout of manufacturing cells: the formation of the cells and the inter- and intra-cell layout, considering the clustering of cells, and the cost of transportation and material handling. The performance of the proposals was evaluated with benchmark problems of manufacturing cells, traveling salesman problem and a multi-objective version of knapsack problem. The mono-objective results were compared with GA, BFOA and Bacterial-GA, while the multi-objective results were compared with well-known algorithms NSGA2 and SPEA2, obtaining better performances in both cases.

In real optimization problems it is generally desirable to optimize more than one performance criterion (or objective) at the same time. The goal of the multiobjective combinatorial optimization (MOCO) is to optimize simultaneously r > 1 objectives. As in the single-objective case, the use of heuristic/metaheuristic techniques seems to be the most promising approach to MOCO problems because of their efficiency, generality and relative simplicity of implementation. In this work, we develop algorithms based on Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Local Search (ILS) metaheuristics for the multiobjective knapsack problem. Computational experiments on benchmark instances show that the proposed algorithms are very robust and outperform other heuristics in terms of solution quality and running times.

A new machine system has been designed, developed and evaluated for extensive circle spraying of oil palms (Elaeis guineensis Jacq.) in an effort to overcome the inefficient spraying problem with the conventional spraying system. The machine system consists of a four-wheeled drive 4WD prime mover with front mounted machine attachments for the circle spraying operation. The configuration of the circle spraying attachment consists of a hexagonal curved spray boom, lifting arm, opening-tilting mechanism unit, storage tank, spray pump, solid cone nozzles, and associate hydraulic system. Field performance tests on the machine system showed an average effective field capacity of 7.89 ha per man per day and when compared to the earlier reported effective field capacity of the walking spray-operated equipment using Serena LT16 knapsack sprayer; a difference of 1.97 time for circle spraying of mature palms grove. Reduction in the human energy expenditure of 101.28 kJ man-1 h-1 or 10.68 % but an increase in the spraying cost of 1.53 USD ha-1 or 24.9 % were obtained with the machine system against the walking spraying-operated equipment using Serena LT16 knapsack sprayer. Justification for machine system to be cost effective could be satisfied if the present effective field capacity is increased to 1.263 time with good skilled operator or if the current R&D cost is reduced to 0.41 time. This is because the improved field capacity of new machine system could not rationalize its current R&D cost. Admittedly, the machine system has great potential to overcome the limitations with the current employed machine/equipment in the circle spraying operation of oil palms in the plantation.

Los problemas de empaquetamiento y corte óptimo son considerados clásicos dentro de la investigación de operaciones, debido a su gran espectro de aplicación en la industria y su alta complejidad tanto matemática como computacional. En este trabajo se presenta el problema de empaquetamiento óptimo bidimensional irrestricto de piezas rectangulares en una sola placa, con pesos asociados a las piezas y sin estos, al tiempo que se considera la posibilidad de rotar 90° las piezas y con restricciones de corte tipo guillotina (problema de la mochila bidimensional irrestricta guillotinada). Se describe el modelo matemático aplicado por diferentes grupos de investigación que estudian esta temática. Se propone, además, un tipo de codificación para aplicarla en este problema y se resuelve mediante un algoritmo de optimización que combina las principales características de cúmulo de partículas, recocido simulado y algoritmos genéticos. Para comprobar la eficiencia de la metodología presentada se tomaron casos de prueba de la literatura especializada, se analizan y comparan los métodos de solución presentados con los últimos avances del problema y se obtienen resultados de excelente calidad y nunca antes reportados en la literatura especializada.

Cutting and packing problems are common in operations research, due to their big spectrum of application in the industry and its highly mathematical and computational complexity for the academy. In this study we present the unconstrained twodimensional cutting stock problem of rectangular items, with and without weights associated to the items, bearing in mind the possibility to rotate items at 90°, and with guillotine cuts (also known as unconstrained two-dimensional guillotineable single knapsack problem). For this problem, we describe the mathematical model recognized by the academic community. We develop an appropriate encoding of the problem so it is possible to work on it using metaheuristic hybrid algorithm particle swarm optimization and simulated annealing. To check the efficiency of this methodology, case studies were taken from specialized literature, where the presented solution method could be analyzed and compared with current problems. The results obtained had an excellent quality and had never been reported.

Os problemas de empacotamento e corte ótimo são considerados clássicos dentro da pesquisa de operações, devido a seu grande espectro de aplicação na indústria e sua alta complexidade tanto matemática como computacional. Neste trabalho apresenta-se o problema de empacotamento ótimo bidimensional irrestrito de peças retangulares em uma só placa, com pesos associados às peças e sem estes, ao mesmo tempo em que se considera a possibilidade de rotar 90° as peças e com restrições de corte tipo guilhotina (problema da mochila bidimensional irrestrita guilhotinada). Descreve-se o modelo matemático aplicado por diferentes grupos de pesquisa que estudam esta temática. Além disso, propõe-se também um tipo de codificação para aplicá-la neste problema e se resolve mediante um algoritmo de otimização que combina as principais características de cúmulo de partículas, recozimento simulado e algoritmos genéticos. Para comprovar a eficiência da metodologia apresentada se tomaram casos de prova da literatura especializada, analisam-se e comparam-se os métodos de solução apresentados com os últimos avanços do problema e se obtêm resultados de excelente qualidade e nunca antes relatados na literatura especializada.

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional small items inside a bi-dimensional large object. This problem is approached with an heuristic based on simulated annealing. Traditional " external penalization" techniques are avoided through the application of the no-fit polygon, that determinates the collision-free region for each small item before its placement. The simulated annealing controls: the rotation applied and the placement of the small item. For each non-placed small item, a limited depth binary search is performed to find a scale factor that when applied to the small item, would allow it to be fitted in the large object. Three possibilities to define the sequence on which the small items are placed are studied: larger-first, random permutation and weight sorted. The proposed algorithm is suited for non-convex small items and large objects.

Neste artigo apresentaremos a aplicação do Problema da Mochila Compartimentada (PMC) no Problema de Corte de Bobinas de Aço (PCBA), que é um problema de corte em duas etapas com restrições especiais de agrupamento dos itens. O PMC consiste em construir compartimentos de capacidades desconhecidas em uma mochila de capacidade conhecida, tendo em vista que os itens de interesse estão agrupados em subconjuntos, de modo que, itens de um agrupamento não podem ser combinados com itens de outro. Para entender melhor o PMC admita que a mochila de um alpinista deve ser composta por um número ideal de compartimentos com itens de quatro categorias (remédios, alimentos, ferramentas, roupas), porém, itens de categorias distintas não podem ser combinados para formar um mesmo compartimento, além do mais, são desconhecidas as capacidades ideais de cada compartimento da mochila.

In this paper we will present the application of the Compartmented Knapsack Problem (CKP) in the Cut Problem of Steel Rolls (CPSR), that it is a problem of cut in two stages with restrictions special of grouping of items. The CKP consists of constructing compartments of unknown capacities in a knapsack of known capacity, in view of that items of interest is grouped in subgroups, in mode that, items of a grouping cannot be matched with items of another one. To understand the CKP more good it admits that the knapsack of a alpinist must be composite for an ideal number of compartments with items of four categories (remedies, foods, tools, clothes), however, items of distinct categories cannot be matched to form one same compartment, in addition, is unknown the ideal capacities of each compartment of the knapsack.