On the representation of the search region in multi-objective optimization

Given a finite set $N$ of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point of $N$, i.e. the part of the objective space which may contain further nondominated points. In this paper, we consider a representation of the search region by a set of tight local upper bounds (in the minimization case) that can be derived from the points of $N$. Local upper bounds play an important role in methods for generating or approximating the nondominated set of an MOO problem, yet few works in the field of MOO address their efficient incremental determination. We relate this issue to the state of the art in computational geometry and provide several equivalent definitions of local upper bounds that are meaningful in MOO. We discuss the complexity of this representation in arbitrary dimension, which yields an improved upper bound on the number of solver calls in epsilon-constraint-like methods to generate the nondominated set of a discrete MOO problem. We analyze and enhance a first incremental approach which operates by eliminating redundancies among local upper bounds. We also study some properties of local upper bounds, especially concerning the issue of redundant local upper bounds, that give rise to a new incremental approach which avoids such redundancies. Finally, the complexities of the incremental approaches are compared from the theoretical and empirical points of view.Comment: 27 pages, to appear in European Journal of Operational Researc

Managing warehouse efficiency and worker discomfort through enhanced storage assignment decisions

Humans are at the heart of crucial processes in warehouses. Besides the common economic goal of minimising cycle times, we therefore add in this paper the human well-being goal of minimising workers' discomfort in the context of order picking. We propose amethodology for identifying the most suitable storage location solutions with respect to both goals. The first step in our methodology is to build data-driven empirical models for estimating cycle times and workers' discomfort. The second step of the methodology entails the use of these empirically grounded models to formulate a bi-objective assignment problem for assigning products to storage locations. The developed methodology is subsequently tested on two actual warehouses. The results of these practical tests show that clear trade-offs exist and that optimising only for discomfort can be costly in terms of cycle time. Based on the results, we provide practical guidelines for taking storage assignment decisions that simultaneously address discomfort and travel distance considerations

Managing warehouse efficiency and worker discomfort through enhanced storage assignment decisions

Humans are at the heart of crucial processes in warehouses. Besides the common economic goal of minimising cycle times, we therefore add in this paper the human well-being goal of minimising workers’ discomfort in the context of order picking. We propose a methodology for identifying the most suitable storage location solutions with respect to both goals. The first step in our methodology is to build data-driven empirical models for estimating cycle times and workers’ discomfort. The second step of the methodology entails the use of these empirically grounded models to formulate a bi-objective assignment problem for assigning products to storage locations. The developed methodology is subsequently tested on two actual warehouses. The results of these practical tests show that clear trade-offs exist and that optimising only for discomfort can be costly in terms of cycle time. Based on the results, we provide practical guidelines for taking storage assignment decisions that simultaneously address discomfort and travel distance considerations

On Solving Bi-objective Interval Valued Neutrosophic Assignment Problem

The assignment problem (AP) is a well-researched combinatorial optimization problem in which the overall assignment cost or time is minimized by assigning multiple items (tasks) to several entities (workers). Today's optimization challenges cannot be adequately addressed by a single-objective AP, hence the bi-objective AP (BOAP) is taken into consideration. This problem frequently occurs in practical applications with ambiguous parameters in real life. Henceforth, in this article the uncertain parameters are presented as interval valued neutrosophic numbers. In the present study, we formulate bi-objectives assignment problem (BOAP) having cost and time parameters as an interval valued neutrosophic numbers. We proposed interactive left-width method to solve the interval valued neutrosophic BOAP (IVNBOAP). In this method interval valued neutrosophic numbers is reduced to interval numbers using score function. Then, the bi-objective interval assignment problem (BOIAP) is reduced to a deterministic BOAP using the left-width attributes on each objective function. The reduced deterministic objective function is separated and constructed as a multi-objective AP. In the solution procedure, the global weighted sum method is adopted to convert the multi-objective AP into a single objective problem (SOP) and solved using Lingo 18.0 software. Finally, numerical examples are illustrated to clarify the steps involved in the proposed method and results are compared with the other existing methods

Solving a Dial-a-Ride Problem with a Hybrid Multi-objective Evolutionary Approach: Application to Demand Responsive Transport

International audienceDemand responsive transport allows customers to be carried to their destination as with a taxi service, provided that the customers are grouped in the same vehicles in order to reduce operational costs. This kind of service is related to the dial-a-ride problem. However, in order to improve the quality of service, demand responsive transport needs more flexibility. This paper tries to address this issue by proposing an original evolutionary approach. In order to propose a set of compromise solutions to the decision-maker, this approach optimizes three objectives concurrently. Moreover, in order to intensify the search process, this multi-objective evolutionary approach is hybridized with a local search. Results obtained on random and realistic problems are detailed to compare three state-of-the-art algorithms and discussed from an operational point of view

Warehouse design and management

Warehouse design and operations have undergone major changes over the past decades. In particular, with the onset of e-commerce, the complexity of warehouse operations has increased multi-fold with the storage of large SKU assortment in small quantities, volatile demand patterns and primarily single-line customer orders. They have grown in size due to consolidation, new and fast identification and communication technologies have found their way into the warehouse and process automation technologies have progressed improving speed and operational efficiencies. In line with these developments, this special issue pays attention to new technologies and methods and how they impact warehouse design and management

Two-phase strategies for the bi-objective minimum spanning tree problem

This paper presents a new two-phase algorithm for the bi-objective minimum spanning tree (BMST) prob-lem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematicalprogramming and algorithmic approaches, while the second phase is devoted to obtaining the remaining ef-ficient solutions (non-extreme supported and non-supported). This latter phase is based on a new recursiveprocedure capable of generating all the spanning trees of a connected graph through edge interchanges basedon increasing evaluation of non-zero reduced costs of associated weighted linear programs. Such a procedureexploits a common property of a wider class of problems to which the minimum spanning tree (MST) prob-lem belongs, that is the spanning tree structure of its basic feasible solutions. Computational experimentsare conducted on different families of graphs and with different types of cost. These results show that thisnew two-phase algorithm is correct, very easy to implement and it allows one to extract conclusions on thedifficulty of finding the entire set of Pareto solutions of the BMST problem depending on the graph topologyand the possible correlation of the edge cost

Bi-objective branch-and-cut algorithms based on LP-relaxation and bound sets

Most real-world optimization problems are multi-objective by nature, with conflicting and incomparable objectives. Solving a multi-objective optimization problem requires a method which can generate all rational compromises between the objectives. This paper proposes two distinct bound set based branch-and-cut algorithms for general bi-objective combinatorial optimization problems, based on implicit and explicit lower bound sets, respectively. The algorithm based on explicit lower bound sets computes, for each branching node, a lower bound set and compares it to an upper bound set. The other fathoms branching nodes by generating a single point on the lower bound set for each local nadir point. We outline several approaches for fathoming branching nodes and we propose an updating scheme for the lower bound sets that prevents us from solving the bi-objective LP-relaxation of each branching node. To strengthen the lower bound sets, we propose a bi-objective cutting plane algorithm that adjusts the weights of the objective functions such that different parts of the feasible set are strengthened by cutting planes. In addition, we suggest an extension of the branching strategy "Pareto branching". We prove the effectiveness of the algorithms through extensive computational results

Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item, multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory.In Paper I, we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II, we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III, we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV, using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap