Order acceptance and scheduling problems in two-machine flow shops: new mixed integer programming formulations

We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must be made simultaneously: which orders to be accepted for processing and how to schedule them. To speed up the solution procedure, we present several techniques such as preprocessing and valid inequalities. An extensive computational study, using different instances, demonstrates the efficacy of the new formulations in comparison to some previous ones found in the relevant literature

A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming

We present a new heuristic algorithm to approximately generate the nondominated frontier of bi-objective pure integer linear programs. The proposed algorithm employs a customized version of several existing algorithms in the literature of both single-objective and bi-objective optimization. Our proposed method has two desirable characteristics: (1) there is no parameter to be tuned by users other than the time limit; (2) it can naturally exploit parallelism. An extensive computational study shows the efficacy of the proposed method on some existing standard test instances in which the true frontier is known, and also some large randomly generated instances. We show that even a basic version of our algorithm can significantly outperform the Nondominated Sorting Genetic Algorithm II (Deb et al. 2002), and the sophisticated version of our algorithm is competitive with Multidirectional Local Search (Tricoire 2012). We also show the value of parallelization on the proposed approach

The magic of Nash social welfare in optimization: Do not sum, just multiply!

We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice. doi:10.1017/S1446181122000074

A new approach to select the best subset of predictors in linear regression modelling: bi-objective mixed integer linear programming

We study the problem of choosing the best subset of features in linear regression, given observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem. We explain the main weaknesses of existing approaches and, to overcome their drawbacks, we propose a bi-objective mixed integer linear programming approach. A computational study shows the efficacy of the proposed approach. doi:10.1017/S144618111800027

A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming

We present a new heuristic algorithm to approximately generate the nondominated frontier of bi-objective pure integer linear programs. The proposed algorithm employs a customized version of several existing algorithms in the literature of both single-objective and bi-objective optimization. Our proposed method has two desirable characteristics: (1) there is no parameter to be tuned by users other than the time limit; (2) it can naturally exploit parallelism. An extensive computational study shows the efficacy of the proposed method on some existing standard test instances in which the true frontier is known, and also some large randomly generated instances. We show that even a basic version of our algorithm can significantly outperform the Nondominated Sorting Genetic Algorithm II (Deb et al. 2002), and the sophisticated version of our algorithm is competitive with Multidirectional Local Search (Tricoire 2012). We also show the value of parallelization on the proposed approach

Design of a Hybrid Rebalancing Strategy to Improve Level of Service of Free-Floating Bike Sharing Systems

Project DescriptionIt is known that for bike sharing systems, the flow of customers can completely change the temporal and spatial distribution of the bikes and cause an imbalance of demand and supply in the system. Thus rebalancing/redistribution of bikes is critical to ensure the efficiency of bike sharing systems. Rebalancing of bikes can be done either by users with incentive program or by operator with a fleet of rebalancing vehicles. In an operatorbased rebalancing method, the operator collects and repositions bikes in order to balance certain number of bikes to predetermined locations. The rebalancing can be static or dynamic or a combination of the static and dynamic. Static rebalancing means that the bikes are rebalanced without the interference of users' activities. Such rebalancing is usually operated during the night when no customers borrow or return bikes. In contrast, dynamic rebalancing is operated periodically in the day when the borrowing and returning of bikes continuously occur. Recently, a new type of bike sharing systems, the dockless/free- floating bike sharing system, has emerged which does not need docking stations, and therefore, it cuts a large percentage of startup investment. With the built-in GPS device, the free-floating bike sharing system allows users to leave a bike almost anywhere which, beside the flexibility, makes the rebalancing of these systems more challenging than typical station-based ones. In light of the above, a hybrid rebalancing method is developed in this project by combining user-based incentive program and operator-based rebalancing to take the advantage of both in free floating bike sharing systems. This method has been featured by a multi-objective technique to optimize the system based on two objectives, cost and service level, which helps decision makers have a better knowledge about the trade-off between these two objectives caused by their decision. In addition, capability of used tools in this method guarantees its applicability on real world scale problems. This technique has been successfully applied on the data collected from ShareABull system at USF.U.S. Department of Transportation 69A355174711

Efficient algorithms for travelling salesman problems arising in warehouse order picking

We investigate two routing problems that arise when order pickers traverse an aisle in a warehouse. The routing problems can be viewed as Euclidean travelling salesman problems with points on two parallel lines. We show that if the order picker traverses only a section of the aisle and then returns, then an optimal solution can be found in linear time, and if the order picker traverses the entire aisle, then an optimal solution can be found in quadratic time. Moreover, we show how to approximate the routing cost in linear time by computing a minimum spanning tree for the points on the parallel lines. doi:10.1017/S144618111500014

A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs

We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of biobjective mixed integer linear programs. The proposed algorithm is developed based on the triangle splitting method [Boland N, Charkhgard H, Savelsbergh M (2015) A criterion space search algorithm for biobjective mixed integer programming: The triangle splitting method. INFORMS J. Comput. 27(4):597–618.], which can find a full representation of the nondominated frontier of any biobjective mixed integer linear program. The proposed algorithm is easy to implement and converges quickly to an optimal solution. An extensive computational study shows the efficacy of the algorithm. We numerically show that the proposed algorithm can be used to quickly generate a provably high-quality approximate solution because it maintains a lower and an upper bound on the optimal value of the linear function at any point in time