An effective genetic algorithm approach to multiobjective resource allocation problems (MORAPs)

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

We consider the Stackelberg problem composed of a single leader and several followers which are interacting but cooperative mutually. Then the followers choose an unique solution from the noninferior solution set of the multi-objective optimization problem by mutual agreement. On the other hand, under uncertainties regarding the followers' agreement, the leader makes an optimal decision against the case where the worst noninferior solution for leader's objective function might be chosen from the noninferior solution set of the followers. That is to say, let the leader adopt the min-max criterion.In this paper, we call such a decision “the min-max type Stackelberg strategy for the multiple objective problem”, and the problem solving such a decision is formulated. And then, in the case where the min-max type Stackelberg strategy is adopted in the multiple objective resource allocation problem, we propose an algorithm to obtain the strategy as the optimal resource allocation.

Many optimization problems encountered in practice are multi-objective by nature, i.e., different objectives are conflicting and equally important. Many times, it is not desirable to drop some of them or to optimize them in a composite single objective or hierarchical manner. Furthermore, cost parameters change over time which makes optimization problems harder. For instance, in the transport sector, travel costs are a function of travel time which changes depending on the time of the day a vehicle is travelling (e.g., due to road congestion). Road congestion results in tremendous delays which lead to a decrease in the service quality and the responsiveness of logistic service providers. In Chapter 2, we develop a generic approach to deal with Multi-Objective Scheduling Problems (MOSPs) with State-Dependent Cost Parameters. The aim is to determine the set of Pareto solutions that capture the trade offs between the different conflicting objectives. Due to the complexity of MOSPs, an efficient approximation based on dynamic programming is developed. The approximation has a provable worse case performance guarantee. Even though the generated approximate Pareto front consist of fewer solutions, it still represents a good coverage of the true Pareto front. Furthermore, considerable gains in computation times are achieved. In Chapter 3, the developed methodology is validated on the multi-objective timedependent knapsack problem. In the classical knapsack problem, the input consists of a knapsack with a finite capacity and a set of items, each with a certain weight and a cost. A feasible solution to the knapsack problem is a selection of items such that their total weight does not exceed the knapsack capacity. The goal is to maximize the single objective function consisting of the total pro t of the selected items. We extend the classical knapsack problem in two ways. First, we consider time-dependent profits (e.g., in a retail environment profit depends on whether it is Christmas or not).

Data quality on categorical attribute is a difficult problem that has not receivedas much attention as numerical counterpart. Our basic idea is to employ association rule for the purpose of data quality measurement. Strong rule generation is an important area of data mining.Association rule mining problems can be considered as a multiobjective problem rather than as a single objective one.The main area of concentration was the rules generated by association rule mining using gene tic algorithm. The advantage of using geneticalgorithm is to discover high level predictionrules is that they perform a global search and cope better with attribute interaction than the greedy rule induction algorithm often used in data mining. Genetic algorithm based approach utilizes the linkage betweenassociation rule and feature selection. In this paper, we put forward a Multi objective genetic algorithm approach for data quality on categorical attributes. The result shows that our approach is outperformed by the objecti ves like accuracy, completeness, comprehensibilityand interestingness.

Hybrid particle swarm optimization for multiobjective resource allocation *

Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters--holding costs, ordering costs, purchase costs, etc.--are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it's Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using Stochastic Non-linear Programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.

A significant number of search and optimisation techniques whose principles seek inspiration from nature and biology phenomena have been proposed in the last decades. These methods have been successfully applied to solve a wide range of engineering problems. This is also the case of greenhouse environment control, which has been incorporating this type of techniques into its design. This paper addresses evolutionary and bio-inspired methods in the context of greenhouse environment control. Algorithm principles for reference techniques are reviewed, namely: simulated annealing, genetic algorithm, differential evolution and particle swarm optimisation. The last three techniques are considered using single and multiple objective formulations. A review of these algorithms within greenhouse environment control applications is presented, considering single and multiple objective problems, as well as their current trends.

A genetic algorithm approach for solving the daily photograph selection problem of the SPOT5 satellite

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.

A Petri net with controller is used to model discrete events in flexible job shop scheduling, the objective of scheduling problems is to minimize make-span, the scheduling results is obtained based on genetic and Tabu Search (TS) algorithm. It is proved capable of providing optimized schedule to the job-shop where the machine tool and manpower resources are both constrained. After crossover and mutation operations, an optimal or suboptimal scheduling plan can be found. The result of the test shows that this method is feasible and efficient. Job shop scheduling is the primary content and critical technology of the production management of CIMS, in the past during 30 years, a lot of researchers and results focus on it, but most of them deal with single objective and resource scheduling problems which are fixed processing route and constrained by machine, and production period is its optimal objective. Nevertheless, the production styles are variable and processing route is determined under the special condition. Moreover, job shop scheduling problem is the most difficult combined constraints optimal problem and typical NP hard problem which can't be solved in polynomial time by an effective algorithm. Up to date, there are some traditional algorithms to solve JSP problem (1-2). About paper (3), Petri net is used to construct JSP model and L1 which combines branch and bound algorithm with dynamic program is used to search its optimal solution. And paper (4), the job sequence is assigned by genetic code firstly, and then filtered beam search which based on breadth-first algorithm is adopted to search. In recent years, the Petri net as a discrete event dynamic system modeling and analysis tool(5), has been successfully applied to the flexible manufacturing system modeling, analysis and control. Some researchers put forward to be based on Petri network scheduling method, but only on the production line itself can not reflect the modeling, as in the production line of external control scheduling strategy influence. A hybrid algorithm is proposed to solve dual-resource scheduling problem in flexible production environment, and Petri net model with a controller, which can effectively model control. It combines the advantage of global search ability of GA with the self-adaptive merit of Tabu Search (TS) and improves its convergence. It is proved capable of global and part searching ability and efficient.

This paper proposes a new multi-objective optimization algorithm inspired by the Newtonian Law of Gravity. The new algorithm is a multiple objective extension of the single objective optimization Gravitational Search Algorithm. Generally, we know various multi-objective algorithms with leader selection schemes. The Leader guides the population towards Pareto fronts. As a result, the algorithm becomes complex in nature. To reduce that part of the cost, we introduce a new algorithm which does not use the leader for guidance but relies on its own population to obtain the non-dominated set of solutions. The algorithm has been tested on several benchmark functions and has produced a good number of solutions. Our purpose of research is to showcase that the memory-less property of the single objective Gravitational Search Algorithm can be used to solve multiple objective problems.

Real-world sequential decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes only a single objective, or that multiple objectives can be adequately handled via a simple linear combination. Such approaches may oversimplify the underlying problem and hence produce suboptimal results. This paper serves as a guide to the application of multi-objective methods to difficult problems, and is aimed at researchers who are already familiar with single-objective reinforcement learning and planning methods who wish to adopt a multi-objective perspective on their research, as well as practitioners who encounter multi-objective decision problems in practice. It identifies the factors that may influence the nature of the desired solution, and illustrates by example how these influence the design of multi-objective decision-making systems for complex problems.

The Portfolio Optimization problem consists of the selection of a group of assets to a long-term fund in order to minimize the risk and maximize the return of the investment. This is a multi-objective (risk, return) resource allocation problem, where the aim is to correctly assign weights to the set of available assets, which determines the amount of capital to be invested in each asset. In this work, we introduce a Memetic Algorithm for port-folio optimization. Our system is based on a tree-structured genome representation which selects assets from the market and establish relationships between them, and a local hill climbing function which uses the information available from the tree-structure to calculate the weights of the selected assets. We use simulations based on historical data to test our system and compare it to previous approaches. In these experiments, our system shows that it is able to adapt to aggressive changes in the market, like the crash of 2008, with reduced trading cost.

This paper proposes an integrated approach for dynamic facility layout problem considering the material handling equipment (MHE). The objectives of this problem are minimization of the fixed costs of MHE, minimization of material handling cost (MHC) and minimization of machine rearrangement costs (MRC). To be more realistic, MHE fixed costs, MRC and MHC, which might be of different importance to decision maker, are considered separately in three objective functions. An integrated model is proposed which is able to simultaneously select the MHE along with the arranging and re-arranging facilities. The model belongs to the class of multi-objective nonlinear mathematical programming models. Considering the NP-hard nature of the model and inspiring the existing water flow like algorithm, a novel Pareto-based meta-heuristic algorithm called multi-objective water flow like algorithm (MOWFA)is developed to solve the problem. We comprehensively discuss the parameter tuning of the algorithms utilizing Taguchi method. Finally, the performance of the proposed MOWFA is evaluated against two well-known meta-heuristic algorithms called non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA). Computational results indicate the greater efficiency of the algorithm compared to the two addressed algorithms for solving the given multi-objective problem.