A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

Scalarizing Functions in Bayesian Multiobjective Optimization

Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving (computationally) expensive multi- and many-objective optimization problems in Bayesian multiobjective optimization is scarce. Scalarizing functions can play a crucial role on the quality and number of evaluations required when doing the optimization. In this article, we study and review 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models (as surrogates, metamodels or emulators) on them. We use expected improvement as infill criterion (or acquisition function) to update the models. In particular, we compare different scalarizing functions and analyze their performance on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights when using and selecting a scalarizing function when using a Bayesian multiobjective optimization method

Generalized decomposition and cross entropy methods for many-objective optimization

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs

Improved dynamical particle swarm optimization method for structural dynamics

A methodology to the multiobjective structural design of buildings based on an improved particle swarm optimization algorithm is presented, which has proved to be very efficient and robust in nonlinear problems and when the optimization objectives are in conflict. In particular, the behaviour of the particle swarm optimization (PSO) classical algorithm is improved by dynamically adding autoadaptive mechanisms that enhance the exploration/exploitation trade-off and diversity of the proposed algorithm, avoiding getting trapped in local minima. A novel integrated optimization system was developed, called DI-PSO, to solve this problem which is able to control and even improve the structural behaviour under seismic excitations. In order to demonstrate the effectiveness of the proposed approach, the methodology is tested against some benchmark problems. Then a 3-story-building model is optimized under different objective cases, concluding that the improved multiobjective optimization methodology using DI-PSO is more efficient as compared with those designs obtained using single optimization.Peer ReviewedPostprint (published version

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Programming Problems with Fuzzy Parameters

This paper presents an interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters in the objective functions and the constraints are characterized by the fuzzy numbers. On the basis of the alpha-level sets of the fuzzy numbers, the concept of alpha-multiobjective nonlinear programming and alpha-Pareto optimality is introduced. Through the interaction with the decision maker (DM), the fuzzy goals of the DM for each of the objective functions in alpha-multiobjective nonlinear programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the satisficing solution which is also alpha-Pareto optimal, if the DM specifies the degree alpha of the alpha-level sets and the reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding alpha-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree alpha. Then by considering the current values of the membership functions and as well as the trade-off rates, the DM responds by updating his reference membership values and/or the degree alpha. In this way the satisficing solution for the DM can be derived efficiently from among an alpha-Pareto optimal solution set. Based on the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs

Production planning of biopharmaceutical manufacture.

Multiproduct manufacturing facilities running on a campaign basis are increasingly becoming the norm for biopharmaceuticals, owing to high risks of clinical failure, regulatory pressures and the increasing number of therapeutics in clinical evaluation. The need for such flexible plants and cost-effective manufacture pose significant challenges for planning and scheduling, which are compounded by long production lead times, intermediate product stability issues and the high cost - low volume nature of biopharmaceutical manufacture. Scheduling and planning decisions are often made in the presence of variable product titres, campaign durations, contamination rates and product demands. Hence this thesis applies mathematical programming techniques to the planning of biopharmaceutical manufacture in order to identify more optimal production plans under different manufacturing scenarios. A deterministic mixed integer linear programming (MILP) medium term planning model which explicitly accounts for upstream and downstream processing is presented. A multiscenario MILP model for the medium term planning of biopharmaceutical manufacture under uncertainty is presented and solved using an iterative solution procedure. An alternative stochastic formulation for the medium term planning of biomanufacture under uncertainty based on the principles of chance constrained programming is also presented. To help manage the risks of long term capacity planning in the biopharmaceutical industry, a goal programming extension is presented which accounts for multiple objectives including cost, risk and customer service level satisfaction. The model is applied to long term capacity analysis of a mix of contractors and owned biopharmaceutical manufacturing facilities. In the final sections of this thesis an example of a commercial application of this work is presented, followed by a discussion on related validation issues in the biopharmaceutical industry. The work in this thesis highlighted the benefits of applying mathematical programming techniques for production planning of biopharmaceutical manufacturing facilities, so as to enhance the biopharmaceutical industry's strategic and operational decision-making towards achieving more cost-effective manufacture

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance

Self-adaptive fitness formulation for constrained optimization

A self-adaptive fitness formulation is presented for solving constrained optimization problems. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions. The performance of the method has been examined by its application to a set of eleven test cases from the specialized literature. The results have been compared with previously published results from the literature. It is shown that the method is able to find the optimum solutions. The proposed method requires no parameter tuning and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution