Project scheduling using a competitive genetic algorithm

- The resource constrained project scheduling problem (RCPSP) is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. During the last couple of years many heuristic procedures have been developed for this problem, but still these procedures often fail in finding near-optimal solutions. This paper proposes a genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities and delay times of the activities are defined by the genetic algorithm. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm

Tensile behaviour of single and double-strap repairs on aluminium structures

In this work, an experimental study was performed on the influence of plug filling, loading rate and temperature on the tensile strength of single-strap (SS) and double-strap (DS) repairs on aluminium structures. The experimental programme includes repairs with different values of overlap length (LO=10, 20 and 30 mm), and with and without plug filling. The influence of the testing speed on the repairs strength is also addressed (considering 0.5, 5 and 25 mm/min). Accounting for the temperature effects, tests were carried out at room temperature, 50ºC and 80ºC. This will permit a comparative evaluation of the adhesive tested below and above the Glass Transition Temperature (Tg), established by the manufacturer at 67ºC. The global tendencies of the test results concerning the plug filling and overlap length analyses are interpreted from the fracture modes and typical stress distributions for bonded repairs. According to the results obtained from this work, design guidelines for repairing aluminium structures were recommended.

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Effect of hole drilling at the overlap on the strength of single-lap joints

Bonded unions are gaining importance in many fields of manufacturing owing to a significant number of advantages to the traditional fastening, riveting, bolting and welding techniques. Between the available bonding configurations, the single-lap joint is the most commonly used and studied by the scientific community due to its simplicity, although it endures significant bending due to the non-collinear load path, which negatively affects its load bearing capabilities. The use of material or geometric changes in single-lap joints is widely documented in the literature to reduce this handicap, acting by reduction of peel and shear peak stresses at the damage initiation sites in structures or alterations of the failure mechanism emerging from local modifications. In this work, the effect of hole drilling at the overlap on the strength of single-lap joints was analyzed experimentally with two main purposes: (1) to check whether or not the anchorage effect of the adhesive within the holes is more preponderant than the stress concentrations near the holes, arising from the sharp edges, and modification of the joints straining behaviour (strength improvement or reduction, respectively) and (2) picturing a real scenario on which the components to be bonded are modified by some external factor (e.g. retrofitting of decaying/old-fashioned fastened unions). Tests were made with two adhesives (a brittle and a ductile one) varying the adherend thickness and the number, layout and diameter of the holes. Experimental testing showed that the joints strength never increases from the un-modified condition, showing a varying degree of weakening, depending on the selected adhesive and hole drilling configuration.

A genetic algorithm for the job shop scheduling with a new local search using Monte Carlo method

This paper presents a methodology for applying scheduling algorithms using Monte Carlo simulation. The methodology is based on a decision support system (DSS). The proposed methodology combines a genetic algorithm with a new local search using Monte Carlo Method. The methodology is applied to the job shop scheduling problem (JSSP). The JSSP is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. The methodology is tested on a set of standard instances taken from the literature and compared with others. The computation results validate the effectiveness of the proposed methodology. The DSS developed can be utilized in a common industrial or construction environment.

A two-level genetic algorithm for the multi-mode resource-constrained project scheduling problem

This paper presents a genetic algorithm for the multimode resource-constrained project scheduling problem (MRCPSP), in which multiple execution modes are available for each of the activities of the project. The objective function is the minimization of the construction project completion time. To solve the problem, is applied a two-level genetic algorithm, which makes use of two separate levels and extend the parameterized schedule generation scheme by introducing an improvement procedure. It is evaluated the quality of the schedule and present detailed comparative computational results for the MRCPSP, which reveal that this approach is a competitive algorithm.

Implementation of fractional-order electromagnetic potential through a genetic algorithm

Several phenomena present in electrical systems motivated the development of comprehensive models based on the theory of fractional calculus (FC). Bearing these ideas in mind, in this work are applied the FC concepts to define, and to evaluate, the electrical potential of fractional order, based in a genetic algorithm optimization scheme. The feasibility and the convergence of the proposed method are evaluated.

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.

Single-lap joints of similar and dissimilar adherends bonded with an acrylic adhesive

In this study, the tensile strength of single-lap joints (SLJs) between similar and dissimilar adherends bonded with an acrylic adhesive was evaluated experimentally and numerically. The adherend materials included polyethylene (PE), polypropylene (PP), carbon-epoxy (CFRP), and glass-polyester (GFRP) composites. The following adherend combinations were tested: PE/PE, PE/PP, PE/CFRP, PE/GFRP, PP/PP, CFRP/CFRP, and GFRP/GFRP. One of the objectives of this work was to assess the influence of the adherends stiffness on the strength of the joints since it significantly affects the peel stresses magnitude in the adhesive layer. The experimental results were also used to validate a new mixed-mode cohesive damage model developed to simulate the adhesive layer. Thus, the experimental results were compared with numerical simulations performed in ABAQUS®, including a developed mixed-mode (I+II) cohesive damage model, based on the indirect use of fracture mechanics and implemented within interface finite elements. The cohesive laws present a trapezoidal shape with an increasing stress plateau, to reproduce the behaviour of the ductile adhesive used. A good agreement was found between the experimental and numerical results.

Dynamical modelling of a genetic algorithm

This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.

Effect of temperature on the shear strength of aluminium single lap bonded joints for high temperature applications

An experimental and numerical investigation into the shear strength behaviour of adhesive single lap joints (SLJs) was carried out in order to understand the effect of temperature on the joint strength. The adherend material used for the experimental tests was an aluminium alloy in the form of thin sheets, and the adhesive used was a high-strength high temperature epoxy. Tensile tests as a function of temperature were performed and numerical predictions based on the use of a bilinear cohesive damage model were obtained. It is shown that at temperatures below Tg, the lap shear strength of SLJs increased, while at temperatures above Tg, a drastic drop in the lap shear strength was observed. Comparison between the experimental and numerical maximum loads representing the strength of the joints shows a reasonably good agreement.

The use of the boundary element method in the analysis of single lap joints

The most common techniques for stress analysis/strength prediction of adhesive joints involve analytical or numerical methods such as the Finite Element Method (FEM). However, the Boundary Element Method (BEM) is an alternative numerical technique that has been successfully applied for the solution of a wide variety of engineering problems. This work evaluates the applicability of the boundary elem ent code BEASY as a design tool to analyze adhesive joints. The linearity of peak shear and peel stresses with the applied displacement is studied and compared between BEASY and the analytical model of Frostig et al., considering a bonded single-lap joint under tensile loading. The BEM results are also compared with FEM in terms of stress distributions. To evaluate the mesh convergence of BEASY, the influence of the mesh refinement on peak shear and peel stress distributions is assessed. Joint stress predictions are carried out numerically in BEASY and ABAQUS®, and analytically by the models of Volkersen, Goland, and Reissner and Frostig et al. The failure loads for each model are compared with experimental results. The preparation, processing, and mesh creation times are compared for all models. BEASY results presented a good agreement with the conventional methods.

A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.