Abstract: In many practical situations the decision-maker has to pay special attention to decision space to determine the constructability of a potential solution, in addition to its optimality in objective space. Practically desirable solutions are those around preferred values in decision space and within a distance from optimality. This work investigates two methods to find simultaneously optimal and practically desirable solutions. The methods expand the objective space by adding fitness functions that favor preferred values for some variables. In addition, the methods incorporate a ranking mechanism that takes into account Pareto dominance in objective space and desirability in decision space. One method searches with one population in the expanded space, whereas the other one uses two populations to search concurrently in the original and expanded space. Our experimental results on benchmark and real world problems show that the proposed method can effectively find optimal and practically desirable solutions. PubDate: Wed, 08 Nov 2017 00:00:00 +000

Abstract: This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable with binary restriction, is considered as real number between 0 and 1, with the penalty of , in which is a large number. Values not near to the boundary extremes of 0 and 1 make the component of large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future. PubDate: Tue, 17 Oct 2017 00:00:00 +000

Abstract: This paper presents a biobjective problem for a solid waste collection system in a set of islands in southern Chile. The first objective minimizes transportation cost and the second one reduces the environmental impact caused by the accumulation of solid waste at the collection points. To solve this problem, biobjective mixed integer linear programming is used. In the model, an itinerary scheme is considered for the visit to the islands. The model decides which collection points are visited per island, the collection pattern, and quantity of solid waste to be collected at each site. The quantity of solid waste is obtained dividing the solid waste generated in the island by the number of collection points selected in that same island and the frequency of visits. For this problem, we considered that the environmental impact function varies through the days during which solid waste is accumulated at each collection point. We present an instance based on real data for a set of islands in Chiloe and Palena regions in southern Chile, in which the deposit node is Dalcahue. We used the epsilon-constraint method and the weighted sum method to obtain the Pareto front, using commercial optimization software. PubDate: Thu, 10 Aug 2017 07:22:36 +000

Abstract: Consider the problem faced by a purchaser of solid waste management services, who needs to identify waste collection points, the assignment of waste generation points to waste collection points, and the type and number of receptacles utilized at each collection point. Receptacles whose collection schedule is specified in advance are charged a fixed fee according to the number of times the receptacle is serviced (emptied) per week. For other receptacles, the purchaser pays a fee comprised of a fixed service charge, plus a variable cost that is assessed on a per-ton-removed basis. We develop a mathematical programming model to minimize the costs that the purchaser pays to the waste management provider, subject to a level of service that is sufficient to collect all of the purchaser’s required waste. Examining historical data from the University of Missouri, we observed significant variability in the amount of waste serviced for nonscheduled receptacles. Because this variability has a significant impact on cost, we modified our model using robust optimization techniques to address the observed uncertainty. Our model’s highly robust solution, while slightly more expensive than the nonrobust solution in the most-optimistic scenario, significantly outperforms the nonrobust solution for all other potential scenarios. PubDate: Sun, 29 Jan 2017 00:00:00 +000

Abstract: In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem, the project is subject to renewable resources, each renewable resource is available for limited time periods during the project life cycle, and keeping the resource for each extra period results in some tardiness penalty cost. We introduce a branch and bound algorithm to solve the problem exactly and use several bounding, fathoming, and dominance rules in our algorithm to shorten the enumeration process. We point out parameters affecting the RCPSP-TWRTPC degree of difficulty, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using the customized algorithm and also CPLEX solver. We analyze the algorithm behavior with respect to the changes in instances degree of difficulty and compare its performance for different cases with the CPLEX solver. The results reveal algorithm efficiency. PubDate: Tue, 10 Jan 2017 00:00:00 +000